UNIVERSITY OF CALIFORNIA SANTA CRUZ

Transcription

1 UNIVERSITY OF CALIFORNIA SANTA CRUZ GIS GPS INTEGRATION: CHALLENGES OF UNCERTAIN REALITY A thesis submitted in partial satisfaction of the requirements for the degree of MASTER OF SCIENCE in COMPUTER SCIENCE by Amin P. Charaniya June 2002 The thesis of Amin P. Charaniya is approved: Professor Suresh Kumar Lodha, Chair Professor Patrick Mantey Professor Roberto Manduchi Professor William Ribarsky Professor Pramod Varshney Frank Talamantes Vice Provost and Dean of Graduate Studies

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3 Contents List of Figures List of Tables List of Abbreviations Abstract Dedication Acknowledgements vi viii ix xi xiii xiv 1 Introduction 1 2 Background GIS Geo-Spatial Registration Accuracy of Points Aerial Imagery/ Digital Ortho-photos Digital Line Graphs (DLGs) AutoCAD Drawings Street Maps Schematic Diagrams Digital Elevation Models (DEMs) Light Detection and Ranging (LiDAR) data Software and Utilities Global Positioning System Historical Background Satellite Constellation GPS Receiver Position Determination using Ranging Signals Navigation Algorithms iii

4 2.2.6 GPS Signals Sources of Uncertainty Differential GPS (DGPS) GPS Integrity GPS Manufacturers Previous Work Virtual Geographic Information System (VGIS) Introduction and Overview of the System Data Organization and the GSD Data Format User Interface and Navigation Level of Detail Management Architecture GIS-VIS Program Alexandria Digital Library (ADL) Uncertainty Visualization GIS GPS Infrastructure GIS Infrastructure Digital Ortho-photos AutoCAD Drawings Street Maps Schematic Diagrams Digital Elevation Models (DEMs) LiDAR Data GPS Equipment and Data Collection Setup GPS Receivers Calibration Differential GPS and Radios GPS Readings Ashtech Software Type of environment Data Logging Convention and Log File Format Modes, Environments and Movement Observations, Analysis and Modeling Static Data Constant Velocity Walk Random Walk Modeling Visualization Visualization of Uncertain Particle Movement Visualization on a GIS Background iv

5 7 VGIS extension at GIS-VIZ Lab Initial Setup Building VGIS datasets Insertion of Santa Cruz data into VGIS Visualization of GPS tracked objects in VGIS D Object support in VGIS Visualizing GPS position information as uncertain objects Current Research in VGIS Conclusion and Further Research 122 Appendix A GPS receiver log file format 123 Appendix B Building VGIS datasets 127 Appendix C AutoCAD Drawings Layers 131 Bibliography 134 v

6 List of Figures 2.1 WGS-84 Ellipsoidal Model of Earth, 1984 (a= m, b= m) Latitude, Longitude and Height Universal Transverse Mercator Zones [9] UTM Coordinate System Old State Plane Coordinate System Zones [19] Current State Plane Coordinate System Zones NGS Control Point at the East Field House, UC, Santa Cruz A Photogrammetry Control Point on the UCSC Campus DEM sampling profiles for a USGS quad within a UTM grid DEM sampling profiled for a USGS quad within an ellipsoidal datum A sample LiDAR system and an aircraft collecting LiDAR data[29] A typical path taken by the LiDAR aircraft[29] GPS Satellite Constellation and Planar Projection[7] Principle of triangulation Effect of independent errors on position estimates Range measurement timing relationships Dilution of Precision Circular Error Probable (CEP) and Horizontal 95% accuracy measures Differential GPS successive views with increasing detail while zooming into the Georgia Tech Campus within VGIS quads associated with the Santa Cruz County DOQs of different resolutions for the same area (College 8, UCSC) Digital ortho-photo and AutoCAD Drawing for the same area (School of Engineering, UCSC). Digital ortho-photo is derived from 3.75 x 3.75 minute DOQQ and has a resolution of 1:1800 (1/2 ft) Low Detail AutoCAD Drawing of Baskin Engineering (UCSC Campus) Street Map of the Santa Cruz County Schematic Diagram of UCSC vi

7 4.7 Sample DEM for the Santa Cruz City rendered as an image LiDAR and DEM data compared side by side LiDAR point and gridded data for College 8, UCSC Base antennas (on the roof of Baskin School of Engineering) Rover GPS Equipment Image of a student moving around collecting GPS data Satellite visibility (green) and DOP (red) charts for UCSC Campus (Lat: 37deg 0min 0sec, 122deg 05min 0sec) An aerial view of the UCSC Campus Distribution of GPS readings at a stationary position (approximately 100 readings each), S: Standalone, D: DGPS, U: Urban, F: Foliage Distribution of means: (from left to right) horizontal error, vertical error, SNR, and DOP; (from bottom to top) standalone urban (SU), standalone foliage (SF), DGPS urban (DU), and DGPS foliage (DF) Distribution of velocities in urban conditions: (from top to bottom) slow walk, regular walk, and fast walk; the arrows underneath denote the true (assumed) velocity Fitting linear (dark line) and exponential curves (faint line) for horizontal errors vs. SNR in standalone mode for urban and foliage environment using static data Circular annulus representing the position of the uncertain object after a short time interval Visualizing horizontal position and velocity uncertainty Visualization of Uncertain Objects in VGIS C.1 Codes for AutoCAD Layers C.2 Codes for AutoCADLayers continued vii

8 List of Tables 2.1 Error estimates for Standalone and Differential GPS Mean and standard deviations for static Data; H-Error (horizontal error) and V-Error (vertical error) are in meters, SNR is in db-hz, DOP is measured as a ratio Mean and standard deviations for speed error (S-error) in meters per second, direction error in degrees, SNR, and DOP values using three different types of walk:slow walk (SW) at 1.26 m/s, regular walk (RW) at 1.61 m/s, and fast walk (FW) at 1.89 m/s using standalone/differential mode in the urban environment 107 viii

9 List of Abbreviations ADL ADR BLM CEP COG DEM DGPS DLG DoD DOQ DOQQ DRG ECEF EPA ESRI FAA FCC GDOP GIS GIS VIS GPS GSD HDOP IMU INS LCC LiDAR LORAN NAD NAPP NAVD Alexandria Digital Library Accumulated Delta Range Bureau of Land Management Circular Error Probable Course Over Ground Digital Elevation Model Differential Global Positioning System Digital Line Graph Department of Defense Digital Orthophoto Quad Digital Orthophoto Quarter Quad Digital Raster Graphics Earth Fixed Earth Centered Environmental Protection Agency Environment Systems Research Institute Federal Aviation Administration Federal Communications Commission Geometric Dilution of Precision Geographic Information Systems GIS Visualization Global Positioning System Geographic Surface Data Horizontal Dilution of Precision Inertial Measurement Unit Inertial Navigation System Lambert Conformal Conic Light Detection and Ranging Long Range Radio Navigation North American Datum National Aerial Photography Program North American Vertical Datum ix

10 NCGIA NGS NHAP NMAS NNSS NRL NSRS PDOP PLSS PRN RAIM RF RMSE RTCM RTK SEP SNR SPCS TDOP UCSC USGS UTM VDOP VGIS VRML WAAS WGS National Center for Geographic Information and Analysis National Geodetic Survey National High Altitude Aerial Photography Program National Map Accuracy Standards Navy Navigation Satellite System Naval Research Laboratory National Spatial Reference System Position Dilution of Precision Public Land Survey System Pseudo-Random Noise Receiver Autonomous Integrity Monitoring Radio Frequency Root Mean Squared Error Radio Technical Commission for Maritime Services Real Time Kinematic Spherical Error Probable Signal to Noise Ratio State Plane Coordinate System Time Dilution of Precision University of California, Santa Cruz United States Geological Survey Universal Transverse Mercator Vertical Dilution of Precision Virtual Geographic Information System Virtual Reality Markup Language Wide Area Augmented System World Geodetic System x

11 Abstract GIS GPS Integration: Challenges of Uncertain Reality by Amin P. Charaniya Location-Based Services have the potential for enhancing our daily lives and improving our work practices. For instance, it would greatly improve the response of fire-fighters or paramedics if they could see a three-dimensional visualization of the fire or the accident scene in real-time. It would be very helpful if one could find the nearest bookstore or coffee shop in an unknown city. Such services can now be provided as a result of the integration of Geographic Information Systems (GIS), Global Positioning System (GPS) and Communication Services. This work has two main objectives. The first objective is to create a GIS-GPS infrastructure at the GIS Visualization lab, UCSC. This 3D GIS environment includes Digital Elevation Models, Digitally Ortho-rectified Aerial Imagery, Street Maps, AutoCAD Drawings, LiDAR height fields, Schematic Maps and other data for the University of California, Santa Cruz Campus, the City of Santa Cruz and Santa Cruz County. The GPS infrastructure consists of setting up Differential GPS (DGPS) that can provide real-time differential corrections to receivers within the UCSC Campus and the City. This system is capable of tracking objects within a radius of five miles centered around the Jack Baskin School of Engineering. Some of the effort has been focussed towards integrating the system with the Virtual Geographic Information System (VGIS) [8] created by the Graphics, Visualization and Usability Center at Georgia Institute of Technology. The second objective is to study the behavior of position and velocity

12 uncertainty associated with GPS-tracked objects in different modes of operation and under different environmental conditions. We have modeled this uncertainty based on our observations and present our results and visualizations.

13 To my parents, Dilshad and Pyarali Charaniya. xiii

14 Acknowledgements First and foremost I would like to thank Professor Suresh Lodha without whose continuous support it would have been extremely difficult for me to carry out this mammoth task. I would also like to thank my colleagues Nikolai Faaland and Srikumar Ramalingam and Grant Wong for working with me all throughout the project, especially Nikolai who pointed out many grammatical errors in this document. I thank Robert Vitale of Baskin Engineering Labs Support who worked tirelessly with me setting up the GPS base-station and always helped us with many administrative problems. I thank Brian Fulfrost of the UCSC GIS lab, Oscar Camarena of UCSC Physical and Construction and Steve Belcher of Santa Cruz Police Department for providing us with great amount of Campus and City data. I would also like to thank the students Ed Kreps, Jonathan Cheatam and Robert Chen who worked on this project previously with me. I thank Nick Hansard and Josh Homan of the technical support at the school of engineering. I thank Professor Bill Ribarsky, Zachary Wartell, Chris Shaw, Nick Faust, Tony Wasilewski, Olubenga Omoteso of Georgia Institute of Technology, Professor Avideh Zakhor, Christian Fruh, Hassan Foorosh of UC Berkeley, Professor Pramod Varshney, Kishan Mehrotra, C K Mohan of Syracuse University, Ulrich Neumann of University of Southern California and Carolyn Jones of University of California, Santa Barbara. Many thanks to Art Sauer, Don Speedy and Richard Phelan for their continuous support with Ashtech receivers, Todd Stennet and Bryant Bertrand of Airborne1 corporation for collecting the LiDAR data for us, Stephen Peterson of Professional Licensing, George Smiley of Dewitt and Associates, Patrick Feuser for his communications port library. I thank Judith and Tom Dillon who allowed us to set up a differential base station in their backyard for collecting xiv

15 LiDAR data. I thank Professor Patrick Mantey and Professor Roberto Manduchi for reading my thesis and providing me with valuable feedback. I also that Professor William Ribarsky at the Georgia Institute of Technology and Professor Pramod Varshney at Syracuse University of reading my thesis. This work is partly supported by Multidiscplinary Research Initiative (MURI) and NSF Grants. xv

16 Chapter 1 Introduction The twentieth century gave rise to a great many different technologies, including the computer, wireless and cellular communication services, satellite navigation systems and the Internet. What used to be cutting edge technologies have become commonplace items and part of our daily lives. The power of a technological innovation is significantly enhanced when it is integrated with other technologies. Making different technologies work individually in a laboratory environment is one thing, but putting all pieces together and making it work in a real scenario is another. One such integration seen recently is Location-Based Services. Location-Based Services have the potential for enhancing our daily lives and improving our work practices. These services are a result of the integration of Geographic Information Systems (GIS), the Global Positioning System (GPS) and Communication Services. A Geographic Information System is a collection of geographically referenced information along with software that provides the capability of organizing, manipulating and visualizing that information. GIS has caused a revolution in the way we look at geographic and 1

17 environmental data. Datasets are organized as layers to create a digital representation of an area. Each layer provides some information (sometimes contradictory) about the reality. A layer can be a surface model of the terrain, an aerial image, a street map, or a distribution of population for a given area. Depending upon the application, different layers are combined to provide a composite view. Collecting data and putting them together is just a means to an end, not an end in itself. Therefore, one can see that the focus is now changing towards utilizing this data more intelligently. A large and comprehensive geographic dataset contains a huge wealth of different relationships, both within and between different layers. This is where visualization plays a major role. It is the purpose of visualization to present the data in such a way that relationships and structures contained therein are made apparent. The Global Positioning System (GPS) is a space-based radio navigation system operated by the United States Federal Government. The technology has been in existence for more than 20 years, and has been used by the US Military and Air Force, but was not of much use at first for civilian users as the accuracy available for civilian applications, until recently was very poor. The removal of accuracy restrictions on civil users and the innovation of real time carrier phase tracking has opened the doors for a large variety of GPS applications. Given a favorable environment and certain settings it has now become possible to determine three-dimensional position with sub-meter accuracy. There has been a great increase in the number of GPS receiver manufacturers as well as companies devising GPS applications. One can now buy recreational GPS devices at sporting goods and home electronics stores. Combined with the expansion and evolution of cellular technologies and field computers such as PDAs and Pocket PCs, GPS is increasingly becoming a core component of daily work practices using Location-Based Services. 2

18 As soon as we come out of the laboratory environment, we face the challenges of the real world. The first thing we must deal with is unpredictable uncertainty. This uncertainty is a part of every system that we use. It occurs in GIS while collecting and processing spatial data. GPS uncertainty can be due to receiver noise, clock offsets and other environmental factors. Uncertainty in communication services arises due to reflected signals, lost packets and other factors. A focus of this work to bring out this uncertainty in an organized and structured way instead of hiding it. This work has two main objectives. The first objective is to create a GIS-GPS infrastructure. Here at the Geographic Information Systems Visualization (GIS-VIZ) lab we have created a GIS using Digital Elevation Models, Digitally Ortho-rectified Aerial Imagery, Street Maps, AutoCAD Drawings, LiDAR height fields, Schematic Maps and other data for the University of California, Santa Cruz Campus, the Santa Cruz City and the Santa Cruz County. We have also set up a real-time Differential GPS that can provide highly accurate differential corrections to GPS users on the UCSC Campus and the Santa Cruz City. The second objective is to survey GPS technology, understand the principles and operation of GPS along with the uncertainty associated with GPS under various environments and in different modes of operation. We then model and visualize this uncertainty using different methods of visualization. We extend this work by visualizing this uncertainty on top the GIS platform that we have created. Different layers in the GIS give us a different picture of the reality. By registering GIS data layers with each other along with GPS and uncertainty information we have attempted to create a consistent representation of the reality. Efforts have also been focussed towards integrating the system with Virtual Geographic Information System 3

19 (VGIS) [8] created by the Graphics, Visualization and Usability Center at the Georgia Institute of Technology. We begin by providing some background information on GIS and GPS in Chapter 2. Chapter 3 describes some previous work in the area of GIS and uncertainty visualization. We describe the GIS and GPS infrastructure built at the GIS-VIZ lab in Chapter 4. Chapter 5 presents some observations and analysis of the GPS data collected and the results of modeling. We then present some visualization results in Chapter 6. Chapter 7 describes the efforts spent on extending VGIS. 4

20 Chapter 2 Background We start by presenting a brief overview of several GIS issues. These include geo-spatial registration, coordinate systems, map projections, data sources, and accuracy issues. We then present an overview of GPS principles and a discussion on sources of uncertainty that relate to the position, velocity, and time estimates provided by the GPS receivers. 2.1 GIS In this work, we visualize GPS objects, with associated uncertainty, on a background of 2D and 3D GIS data. We use appropriately processed aerial photographs (digital orthorectified imagery), AutoCAD drawings, street maps, schematic diagrams, digital elevation maps, and LiDAR height data. In later work, we will include 3D texture-mapped models of buildings and other information acquired through video cameras, stereo aerial images, and depth range laser scanners. We will now discuss each of these sources and types of GIS information in- 5

21 cluding accuracy and geo-spatial registration issues. However, in order to discuss geo-spatial registration issues, we first begin by discussing geodetic datums, coordinate systems, and map projections Geo-Spatial Registration Geo-spatial registration is a very important issue that must to be addressed before we discuss about any type of GIS data. In order to make use of different types of GIS data and GPS position information a common coordinate system is needed in which all the data can be expressed. We first discuss some map projections and geodetic datums often used by these coordinate systems. Geodetic Datums: Geodetic datums define the size and shape of the Earth. They also define the origin and orientation of the coordinate systems used to map the Earth. Through history hundreds of different datums have been used to frame position descriptions. Datums have evolved from those describing a spherical Earth to ellipsoidal models derived from years of satellite measurements. Spherical Earth models represent the shape of the Earth with a sphere of a specified radius. These models fail to model the actual shape of the Earth. The slight flattening of the Earth at the poles results in about a twenty kilometer difference at the poles between an average spherical radius and the measured polar radius of the Earth. This flattening can be better modeled using an ellipsoid. Reference ellipsoids are usually defined by semi-major (equatorial) radius and flattening (the relationship between equatorial and polar radii). In these ellipsoidal models, the lengths of the two horizontal radii are equal and they are referred to as 6

22 Figure 2.1: WGS-84 Ellipsoidal Model of Earth, 1984 (a= m, b= m) equatorial radii. Other reference ellipsoid parameters such as semi-minor axis (polar radius) and eccentricity can be computed from these terms. In this work, we employ only ellipsoidal models. There are two types of datums associated with these models: horizontal datum and vertical datum. A horizontal datum forms the basis for horizontal positions while the vertical datum refers to elevations. Although there have been many different types of ellipsoidal models that have been used over the years [13], Clarke s Ellipsoidal Model of 1866 was used as the standard ellipsoid to define the shape and size of the Earth until a few decades ago. The North American Datum of 1927 (NAD27), a reference horizontal datum is based on this model. The vertical datum associated with NAD27 is NAVD29 (North American Vertical Datum, 1929). Clarke s ellipsoid was then improved in 1984 to form the World Geodetic System of 1984 (WGS-84). Parameters for WGS-84 are shown in Figure 2.1. The horizontal datum based on this model is referred to as the North American Datum of 1983 (NAD83). The vertical datum associated with NAD83 is NAVD88 (North American Vertical Datum, 1988). Map Projections: Some coordinate systems such as the planar coordinate systems require that the surface of the Earth (or the reference ellipsoid) be projected onto another surface. Map 7

23 projections are attempts to portray the surface of the Earth (or a portion of the Earth) on a flat or a developable surface. A developable surface is a surface that can be opened up on a flat surface without geometric distortions. Examples of developable surfaces include cylinders and cones. Several important spatial relationships (or properties) between locations can be distorted when the globe is projected: distance, direction, angle, scale, and area. Some projections minimize distortions in some of these properties at the expense of increasing errors in others. Some projections are attempts to only moderately distort all of the spatial relationships. Here, we present an overview of some of the map projections, but focus on only those that are most relevant to our work. For further details, please refer to Iliffe [14]. Map projections can be classified into three general categories. 1. Cylindrical Projections: These projections result from projecting the Earth onto a cylinder. When the cylinder upon which the Earth is projected is at right angles to the poles, the cylinder and resulting projection are transverse. When the cylinder is at a non-orthogonal angle with respect to the poles, the cylinder and resulting projection is oblique. The Behrmann Cylindrical Equal-Area, Gall Stereographic Cylindrical, Peters, Miller Cylindrical, and Transverse Mercator projections are some examples of cylindrical projections. 2. Conic Projections: These projections result from projecting the Earth onto a cone. Albers Equal Area Conic, Lambert Conformal Conic (LCC), and Polyconic projections are some examples of conic projection. As seen later, in some parts of the Earth LCC preserves shapes and angles. It is also used to define some State Plane Coordinate Systems. 3. Azimuthal Projections: These projections result from projecting the Earth onto a plane. 8

24 Azimuthal Equidistant and Lambert Azimuthal Equal Area projections are examples of azimuthal projections. We do not use azimuthal projections in our work. Coordinate Systems: There are two types of geographic coordinate systems associated with the model of the Earth. These are spherical coordinate systems and planar coordinate systems. Spherical coordinate systems are associated with the ellipsoidal models of the Earth, while the planar coordinate systems are associated with the map projections of the ellipsoidal models of the Earth. Spherical Coordinates: Here we discuss the two most commonly used spherical coordinate systems. We refer the readers to Iliffe [14] for a more detailed discussion. Latitude, Longitude and Altitude: Among the most commonly used global coordinate systems is the latitude, longitude, and altitude system. The Prime Meridian and the Equator are the reference planes used to define latitude and longitude. The Prime Meridian is the line on the ellipsoidal model of the Earth joining the North Pole, the South Pole, and passing through Greenwich, United Kingdom. This coordinate system is illustrated in figure 2.2. The geodetic longitude of a point is the angle between a reference plane passing through the Prime Meridian and a plane passing through the point, both planes being perpendicular to the equatorial plane. The geodetic latitude of a point is the angle between the equatorial plane and the line normal to the reference ellipsoid at that point (the normal line does not necessarily pass through the center of the ellipsoid). The geodetic altitude at a point is the distance from the reference ellipsoid to the point in the direction normal to the ellipsoid. Since the Earth is not a perfect ellipsoid, the altitude of a point on the surface of the Earth can be negative, zero, or positive. 9

25 Figure 2.2: Latitude, Longitude and Height Earth Centered Earth Fixed (ECEF) Coordinates: Earth Centered Earth Fixed coordinates define three dimensional positions X, Y, and Z with origin at the center of the reference ellipsoid. The Z-axis points toward the North Pole. The X-axis is defined by the intersection of the plane defined by the Prime Meridian and the equatorial plane. It points towards the intersection of the Prime Meridian with the equatorial plane. The Y-axis completes a right handed orthogonal system. It is defined by the intersection of the equator with the plane perpendicular to the X-axis passing through the origin. Planar Coordinates: In our work, we will be utilizing two of the most commonly used planar coordinate systems Universal Transverse Mercator (UTM) and the State Plane Coordinate Systems (SPCS). These coordinate systems require map projections discussed earlier. Universal Transverse Mercator (UTM) Coordinates: The Transverse Mercator projection is essentially a cylindrical projection where a cylindrical surface is wrapped around the reference ellipsoidal model of the Earth. The old UTM coordinate system was based on NAD27 while the new system is based on NAD 83. Each point on the model is projected on to the cylindrical surface along lines originating from the center of the model. The cylindrical surface is 10

26 Figure 2.3: Universal Transverse Mercator Zones [9]. then opened to form a rectangular grid, and the UTM coordinates are associated with this grid. On this grid the world is divided into 60 zones horizontally and 20 zones vertically as shown in Figure 2.3. The grid extend from 180 degrees east to 180 degrees west in longitude and 84 degrees south to 84 degrees north. Each UTM zone is 6 degrees in longitude and 8 degrees in latitude (except for zones near the north and south poles). The entire contiguous United States is covered by 10 UTM zones (zones 10-19) while the state of California is covered by two zones (10 and 11). Figure 2.4 illustrates the naming conventions for the UTM coordinates. The horizontal coordinate associated with each point is referred to as the Easting. In defining UTM coordinates, a convention is used whereas the center of each zone is assigned an Easting of 500,000 meters which is referred to as the False Easting. The Easting of any point within the zone is then defined as the distance from the center of the zone plus the False Easting. Thus, the points to the right of the center have Easting values larger than 500,000 and the points to the 11

27 (a) Northern Hemisphere Zone (b) Southern Hemisphere Figure 2.4: UTM Coordinate System left of the zone have Easting values less than 500,000. This ensures that every point has positive Easting. The vertical coordinate associated with each point is referred to as the Northing. The Northing of each point in the Northern hemisphere is simply the distance of the point from the equator. The Northing of each point in the Southern hemisphere, however, is defined as, 10,000,000 meters minus the distance between the point and the equator. The value 10,000,000 is referred to as the False Northing. Again, this ensures that the Northing associated with any point on the Earth is positive. Due to this convention points on the equator have Northing of 0 when viewed as being in the Northern hemisphere and 10,000,000 when viewed as points in the Southern hemisphere [40]. State Plane Coordinate System (SPCS): SPCS was established by the US Coast and Geodetic Survey in the As shown in Figure 2.5 each state was initially divided into 1 to 7 zones depending on its size (Alaska has 10 zones). Later on, as shown in Figure 2.6, 12

28 Figure 2.5: Old State Plane Coordinate System Zones [19]. this partitioning was revised [17]. Under the current partitioning system, California is divided into 6 zones. Earlier there were 7 zones with Los Angeles County being a zone by itself. LA county is now merged into Zone 5. Santa Cruz falls into California Zone III (FIPSZONE 0403, ADSZONE 3326, UTM Zone 10). SPCS uses a Lambert Conformal or a Transverse Mercator projection depending upon the orientation of the state. The Transverse Mercator projection, as discussed earlier, is a cylindrical projection while the Lambert Conformal is a Conic Projection. The specific projection and the size of the zone was selected to fit the geometry of the state, and to minimize distortion errors. Low distortion makes the SPCS useful at the state and county levels. Zone boundaries are typically political boundaries such as county or city lines. Lambert Conformal Conic projection is used for states that are more east-west oriented while Transverse Mercator projection is used for states that are more north-south oriented. The only exception is the state of Alaska for which an Oblique Mercator Projection is used. The old state plane system was based on NAD27, while the new system is based on NAD83. 13

29 Figure 2.6: Current State Plane Coordinate System Zones A point is designated by Easting, Northing, state name, and zone. For example, Santa Cruz falls within the California SPCS Zone III. In order to specify the SPCS coordinates an origin is specified for each zone, typically located near the center of the zone. The central meridian is a vertical line of longitude that passes through the origin. The latitude of the origin is the horizontal line passing through it. In order for each point to have positive Easting and positive Northing, the origin is given a False Easting and a False Northing that varies from zone to zone. For SPCS Zone III (which uses Lambert Conformal Conic Projection), the origin is given a False Easting value of 2,000,000 feet and a False Northing of 500,000 feet. The horizontal distance (positive towards the east and negative towards the west) from the central meridian, plus the false easting value, is specified as the easting of a particular position. The vertical distance (positive towards the north and negative towards the south) is specified as the northing of the position. For further details refer to Stem and Dracup [30, 12]. 14

30 2.1.2 Accuracy of Points We now address the question of computing the geo-spatial coordinates of points on Earth. There are two primary sources of registered points on Earth in the United States. These sources are the National Geodetic Survey (NGS) and the National Aerial Photography Program. NGS Control Points: The National Geodetic Survey manages the National Spatial Reference System (NSRS) which is a standard framework for measuring and recording latitude, longitude, height, scale, gravity, and orientation of points on the Earth. Under this framework the NGS has established over 800,000 control points (also referred to as monuments or markers) within the US. These points have been established at different points of time and have varying horizontal and vertical accuracy. Approximately 3,700 points form the highest accuracy core of this control network [26]. Information on all these points can be obtained on the NGS web site [33]. These points are organized in rectangular blocks, referred to as USGS quads. A user can type in the name of a quad to find the control points within that region by selecting the USGS quad option. One can also view a map of surrounding region to find the names of surrounding quads. With each control point, a datasheet is associated that gives the geo-spatial coordinates of the points and the accuracy associated with the point. The input formats and format specifications of these control points are discussed in detail in Challstrom [6]. The history of each control point is also recorded including the last time when the point was retrieved or visited by the NGS. The user then must physically take a trip to the site in order to locate the control point. It is not always easy to find such points as they can for example be anywhere in a large open field and the markings on the ground are often very small. Figure 2.7 displays a picture of a NGS 15

31 control point inside the UCSC Campus. With the passage of time, some of these points have been lost due to construction and other issues. Furthermore, some of these points have become inaccessible or fall on private property. Based on the horizontal and vertical accuracies these control points have been classified into different orders and classes. The Federal Geodetic Control Committee has created standards and specifications for the geodetic control network of points [3] including accuracy standards[31]. For the purposes of horizontal accuracy, control points are categorized as A, B, First, Second and Third order points. Some of these are further classified into two classes Class I and Class II [33]. The distance accuracy of a third order, class II point is 1:5000, which is the ratio of the relative positional error of a pair of control points to the horizontal separation between the points. The distance accuracy of the A order points is within 5mm of 1:10,000,000 relative to other A-order points. The vertical accuracy of control points is described by categorizing the points into First, Second, and Third order points. Again some of them are further classified into two classes Class I and Class II. Vertical accuracy is described as the maximum elevation difference accuracy, which is the relative elevation error between a pair of control points that is scaled by the square root of the horizontal separation. The accuracy of a First Order vertical point is.5 mm / sqr km while the accuracy of a third order vertical control point is 2.0 mm / sqr km. Photo Ground Control Points: In addition to the NGS control points, there are additional control points on the ground that have been created by collaborative efforts of federal, state, and local government agencies often working with private surveying companies. A typical control 16

32 Figure 2.7: NGS Control Point at the East Field House, UC, Santa Cruz point is created by marking a large cross on the ground that is clearly visible on an aerial photograph. Figure 2.8 shows such a marker on the ground. Furthermore, well-defined points such as the intersection of two roads are surveyed using sophisticated surveying techniques including real-time kinematic techniques. Vertical tests are run separately to determine precise elevations. These ground control points are also classified into different orders and classes based on their accuracy as described before. Data on these control points can be obtained by contacting local city or county agencies or surveying companies Aerial Imagery/ Digital Ortho-photos We now discuss various GIS data sources. Aerial photographs have been used for several decades to capture images of the Earth. A digital ortho-photo is a digitally rectified aerial image that has the geometric qualities of a map. What this means is that unlike a standard aerial photograph, terrain relief displacement and distortions due to aircraft pitch, yaw, and altitude and camera tilt in images have been removed so that the ground features are displayed 17

33 Figure 2.8: A Photogrammetry Control Point on the UCSC Campus in their true ground position. This allows for the direct measurement of distance, areas, angles, and positions. Digital ortho-photos require several types of inputs to produce an ortho-rectified image from the original perspective image captured by the sensor. These inputs include (i) the unrectified raster image, (ii) calibration information about the sensor collector device (camera or other remote sensor parameters) to correct distortions due to camera parameters, (iii) a digital elevation model with the same area of coverage as the digital ortho-photo to remove distortions due to terrain relief, (iv) the image and ground coordinates of photo-identifiable ground control points to geo-spatially register the image, and (v) a user parameter file. These five inputs are used to register the image file and to remove the relief displacement from the image data. In order to ascertain that the image brightness values of the ortho-photo closely resembles the source image, very little image enhancement is performed when preparing the photograph for scanning. Some deviation of brightness values may also occur during the scanning and rectification 18

34 processes. The digital ortho-photos are then verified by visually inspecting and comparing them with the original unrectified images. For further information please refer to the USGS Standards for digital ortho-photos [34]. The end product of the above process is a digital ortho-rectified image that is referred to as Digital Ortho-photo Quadrangle (DOQ). These ortho-photos cover an area of 7.5 minute x 7.5 minute (7.5 minute of longitude and latitude in geographic extent) and have a resolution of 1 to 2 meters. 1 to 2 meter resolution refers to the distance on the ground represented by each pixel. The DOQs are often called DOQQs (Digital Ortho-photo Quarter Quadrangles) when they cover an area of 3.75 minute x 3.75 minute. The DOQQs generally have a resolution of 1 meter. A 3.75 x 3.75 minute DOQQ covers an area of approximately 7 kilometers x 7 kilometers near the equator. With 1 meter resolution per pixel, this translates to about 7000 x 7000 pixels. Assuming a typical print resolution of 300 pixels per inch, this translates to approximately 24 inch by 24 inch image. Assuming 300 pixels per inch, 1 meter resolution per pixel also translates to 1:12000 scale approximately, that is, 1 inch on the image corresponds to approximately inches on the ground. Typically a quadrangle (7.5-minute) digital orthophoto is produced either by mosaicing 3.75-minute digital ortho-photos or by generating the digital ortho-photo from lower resolution photography. Typically, there is an overlap of about 50 to 300 meters between adjacent DOQ images to facilitate tonal matching (adjusting the brightness and contrast) for mosaicing of adjacent images. Each DOQ can be coded in any image format (TIFF, JPEG) either compressed or uncompressed. A grayscale DOQ typically requires about 46 MB of storage space per 3.75 x 3.75 minute region. The primary source of raw aerial images is the National Aerial Photography Program 19

35 (NAPP). This is a multiple agency program coordinated by the USGS that provides panchromatic and color infrared coverage of the United States at 1:40000 scale. These images are quarter-quadrangles (3.75 minutes X 3.75 minute) and are captured at a height of 20,000 feet above mean terrain with a 6-inch (152.4 mm) focal-length camera. From , the National High Altitude Aerial Photography Program (NHAP), also a multiple agency program coordinated by the USGS, acquired panchromatic images at 1:80000 scale and photo images at 1:58000 scale. The United States Geological Survey (USGS) has produced DOQs for most parts of the United States. As per the seven-year acquisition plan of the NAPP aerial imagery for the entire United States will be available by the year DOQQs as well as DEMs and DLGs (to be discussed later) can be purchased directly from USGS from their web site [36]. The DOQs are geo-spatially registered using the ground control points provided as input. Each image file has some metadata associated with it, either in the form of an ASCII header file or an ASCII world file. These files specify the resolution of the image by indicating the size of each pixel in distance units (generally meters or feet). This file specifies the coordinates of the top left pixel in the image. The 1 meter resolution 3.75 minute DOQQs are specified typically in NAD83 UTM coordinates while the 1 to 2 meter resolution DOQs are specified typically in NAD27 or NAD83 UTMs. Depending upon the source of acquisition, these DOQs or DOQQs may also be specified in State Plane Coordinate System. Although the coordinates of the top left pixel are specified in the header or world file, mention of whether they are in NAD27 or NAD 83 datum is either specified by the providing agency separately or has to be inferred by viewing the dataset. 20

36 DOQQ Accuracy: The USGS established National Map Accuracy Standards (NMAS) in In testing a map, the USGS experts select 20 or more well-defined points, as discussed in Section 2.1.2, on the image. We first describe the horizontal accuracy standards. For DOQs with scales larger than 1:20000, not more than 10 percent of the points tested have an error of more than 1/30 inch, measured on the DOQ. For DOQs with scales of 1:20,000 or smaller, not more than 10 percent of the points tested have an error of more than 1/50 inch. The horizontal accuracy standards as applied to a DOQ at 1:24,000 scale require that at least 90 percent of the test points must fall within 1/50th of an inch on the map, that is 40 feet (24000 /50) of their true positions and within 1/30th inch, that is 33.3 feet (12000/30 inch) at 1:12000 scale. The vertical accuracy standards require that the elevation of 90 percent of all tested points must be correct within half of the contour interval. On a map with contour intervals of 10 feet, the map must correctly show 90 percent of all points within 5 feet (1.5 meters) of the actual elevation. The DOQs released by the USGS attempt to comply with these standards. Exceptions to this practice include areas covered by dense woodland or obscured by fog or clouds. For a detailed description of the accuracy standards refer USGS NMAS [37]. Conversion between Coordinate Systems: The DOQQs can be converted from one coordinate system to another using GIS programs such as ArcInfo. In our work, we have used ArcInfo to convert DOQQs from NAD83 SPCS Zone III coordinates to NAD83 UTM. We will discuss ArcInfo later in Section

37 2.1.4 Digital Line Graphs (DLGs) The Digital Line Graphs (DLGs) represent cartographic (map) information in a polyline vector form. These DLGs are created by the USGS using topographic and planimetric maps that are derived from either aerial photographs or from cartographic source materials using manual and automated digitizing methods. Each DLG file is composed of 3 elements - nodes, lines and areas, each with specific attributes. A node marks the start or end points of one or more lines. An area is defined as a continuous unbroken region on the map that is bounded by lines. Attributes are associated with every node, line and area elements. Attributes are used to specify some information associated with these elements. The attributes are represented as a 3-digit major and 4-digit minor code. These codes are based on the symbolic elements present on source maps. The DLGs are classified as large-scale, intermediate-scale and small scale maps. The large-scale DLGs are primarily derived from USGS 7.5-minute topographic maps at 1:24,000 and 1:25,000 scales. The Intermediate-scale DLGs are derived from USGS 1:100,000-scale, 30 by 60-minute maps while the Small-scale DLGs are based on 1:2,000,000-scale maps. The DLGs are created by the USGS from aerial photographs and stable-base maps. Stable-base maps are original hard copies of maps based on materials more durable and dimensionally stable than paper (e.g. polyester film). These maps are scanned and digitized using semi-automatic systems. They are then checked for valid attribute codes. Lines are checked to have nodes on intersections. Similarly areas are checked for edges at intersections. Finally quality control flags are embedded within the header of the DLG file. A DLG file depicts a variety of different kinds of data. The large-scale DLGs typically 22

38 include political and administrative boundaries, hydrographic data (flowing water, standing water, and wetlands), Hypsography (ground elevation data), Public Land Survey System (PLSS) describing rectangular boundaries that represent or reference property boundaries administered by the Bureau of Land Management (BLM), transportation data (roads, trails, rails, pipelines, transmission lines, and miscellaneous transportation features, other significant man-made structures, vegetative surface cover (e.g., woods, scrub, orchards, and vineyards), non-vegetative surface features, including information about the natural surface of the Earth (e.g., lava and sand), and survey control and markers. The intermediate-scale and small-scale typically consist of a subset of the data covered by large-scale DLGs. These include hydrography data, hypsography data, transportation data, political and PLSS boundaries. The large and intermediate scale DLGs are referenced using UTM coordinates while the small scale DLGs are projected using Albers Equal Area Conic Projection. The DLGs are distributed in DLG3 (DLG level-3) files in graphic, optional, standard and SDTS formats. The details regarding these formats can be found in DLG Specifications [39]. Also, for an overview of DOQQs, DEMs, and DLGs, another good source is [38]. DLG Accuracy: DLG files do not contain quantified accuracy statements. Instead, they follow different procedures including file fidelity and completeness, attribute accuracy, topological fidelity, edge matching, and quality control flags. For example, for manually scanned documents, an absolute accuracy of from.003 to.005 inches using an equipment with a resolution of.001 inch is required. For details, please refer to the DLG Specifications [39]. 23

39 2.1.5 AutoCAD Drawings One of the drawbacks of aerial imagery is that terrain details are often hidden under the thick foliage of the trees. Therefore, AutoCAD drawings are typically used for planning and construction purposes. These drawings are produced using several techniques. High detail drawings are often produced by surveying companies using ground survey techniques. Low detail drawings are generally produced by processing aerial images and then adding or editing further details using ground survey techniques. The end result is a drawing in AutoCAD format (with dwg or dxf file extensions). The DWG and DXF formats created by AutoDesk are the most popular format for storage and transfer of 2D and 3D drawings. These two formats can be freely converted between each other using AutoCAD. The DWG format is a binary format primarily used for storage of drawings while the DXF is an ASCII format used for transfer of drawings. Throughout the world it is estimated that billions of drawings exist in these formats. Significant amount of GIS data (street maps, topographic maps etc.) exists in the form of DWG and DXF files. Besides AutoCAD, these drawings can also be viewed in Arcview/ArcInfo that automatically converts the dwg and dxf files into shape files that we discuss later in Section AutoDesk has not published the dwg and dxf format. Therefore, as a result of substantial reverse engineering efforts at various institutions, the format has been well understood and there exists numerous viewers such as DWGviewer and utilities for DWG files. There is an alliance of CAD customers and vendors promoting free and open exchange of dwg format specifications and tools [1]. The DWG and DXF formats support 3D objects, lines, polylines, curves (splines), text and associative dimensioning. Data in a DWG file exists in layers. Layers of information 24

40 may include building footprints, tree footprints, lamp posts footprints, spot heights, contour lines, road curbs, unpaved roads, parking lots, underground infrastructural facilities such as communication lines and water-pipes. These files also contain textual and numeric information. The layered approach is based on the traditional approach of creating drawing layers on Mylar sheets and placing them on top of each other to view a composite drawing. The layers can be defined by the user and there are several pre-established layer standards available. Each layer contains some part of the drawing and can be made visible or invisible by the user. In a typical GIS map created as a drawing, the building footprints are organized as one layer, the topographic (height) information, organized as contours, are another layer, the streets are organized as a separate layer while the underground utilities are drawn on a separate layer. For further details refer to Burchard [4]. For our purposes, we will be extracting the information regarding buildings, trees, map posts, roads, and parking lots. Each layer of a drawing is registered using a common coordinate system. This coordinate system can be any arbitrary planar coordinate system or some standard coordinate system such as UTM or SPCS. The geo-spatial accuracy of the AutoCAD drawings can vary tremendously depending upon the accuracy of the ground control points used in the survey and the survey techniques themselves, but the relative accuracy of the drawings is expected to be quite good because these drawings are mostly used for construction purposes. Conversion between Coordinate Systems: ArcInfo/ArcView 3.1 or Cad2Shape can be used to convert AutoCAD drawings into shape files. ArcView can convert shape files from one coordinate system to another. We have used ArcView to convert shape files from NAD27 State 25

41 Plane to NAD83 State Plane. We will discuss ArcInfo and Cad2Shape later in Section Street Maps Street maps are the most traditional GIS data types. These maps typically consist of centerline information. The centerline information is useful for visualization of dynamic (motion) objects that are expected to move along the roads. Centerlines are generally computed by either digitizing paper based maps or using GPS techniques. Street maps are typically piecewise line segments with addresses associated with each line segment. There are standard file formats for street maps supported by the two most popular commercially available GIS software packages ArcView/ArcInfo and MapInfo. The file formats for the MapInfo have extension names mid and mif. The MIF file typically contains piecewise line segments while the MID file contains attributes such as street names and other such information associated with these line segments. The piecewise line segments associated with the street maps are typically specified in latitude and longitude. Therefore, in order to overlay this street map with other data sources, such as digital aerial imagery, conversion is often required. We have converted these MIF files into shape files using a utility called Mif2Shape within ArcView Schematic Diagrams Schematic maps are abstractions of cartographic maps. These maps are functional representations of real data. Schematic maps have traditionally received less attention by the GIS community. For the sake of simplicity, scale and linear details are removed, polylines 26

42 are replaced by simple lines and areas are generally replaced by symbols. The relative spatial positioning of the objects is generally preserved, although not very accurately. This implies that objects can be located on a schematic map by looking for adjacent objects in the same map. For instance, on the schematic map of the UCSC Campus it is easy to see that the Baskin School of Engineering and Communications buildings are towards the north of the Science Library and the user gets an overall idea of locations of landmarks with respect to each other. Schematic maps are very useful for several purposes including navigation for general visitors who get an excellent view of several resources without having to worry about too much geometric detail. A schematic map can be in one of many different file formats depending upon the source. It could be a rendering of an artist or an architect. A schematic map is generally not geo-spatially registered. This poses additional challenges that we address in later sections Digital Elevation Models (DEMs) All of the DOQs, AutoCAD drawings, Digital Line Graphs (DLGs) and street maps provide two-dimensional data. In order to visualize the elevation information emitted by the GPS we require elevation information. We have used two different sources for height data Digital Elevation Models (DEMs) and Light Detection and Ranging (LiDAR) data. In this section, we discuss DEMs. A Digital Elevation Model consists of a sampled array of elevations for ground positions at regularly spaced intervals. The elevations are expressed in meters or feet relative to North American Vertical Datum of 1929 (NAVD 29) for the United States and local mean sea level in Hawaii and Puerto Rico. The DEMs are created by several different procedures in- 27

43 cluding manual profiling from stereo aerial images. These images are generally acquired from the National Aerial Photography Program (NAPP) or National High Altitude Photography Program (NHAP). All the new DEMs are being created by interpolating from Digital Line Graphs (DLG) contours or using some electronic imaging sensors. The 30-minute DEMs are generally derived or re-sampled from 7.5-minute DEMs. Most of the 1-degree DEMs are created from photogrammatic sources. For further discussion refer USGS DEM Standards and Specifications [35]. The United States Geological Survey produces several types of DEM data that range from 7.5 minute, 15 minute, 30 minute and 1 degree quads. The 7.5 minute and 15 minute DEMs are classified as large scale DEMs, the 30 minute DEMs are classified as intermediate scale DEMs while the 1-degree DEMs are included under the small scale category. The scale ratio for DEMs is based upon the underlying maps or aerial images from which these DEMs are derived. For example, a 7.5 minute DEM with a scale of 1:24000 will register over a 7.5 minute DOQ of the same scale for the same region. The 7.5 minute DEMs generally have a scale of 1:24000 or 1:25000 with the horizontal grid spacing being either 10 meters (1/3rd of an arc-second) or 30 meters (1 arc-second). These DEMs are projected and referenced to the NAD 27 or NAD 83 UTM coordinate system. The 15 minute DEMs have a scale of 1:63360 with a horizontal grid spacing of 2 arc seconds of latitude (20 meters) by 3 arc seconds (30 meters) of longitude. These DEMs are referenced to the latitude/longitude of NAD27 or NAD83. The 30 minute DEMs have a grid spacing of 2 arc-seconds by 2 arc-seconds and are referenced to geographic coordinates. These DEMs are generally distributed as 4 15-minute DEMs. These DEMs are sometimes referred to as 2 28

44 arc-second DEMs. 1-degree DEMs have a scale of 1:250,000 with the horizontal grid spacing being 3 arc-seconds by 3 arc-seconds. Although there are many different DEM data formats, the most common one is an ASCII text file with.dem extension. This file has some header information including the general characteristics of DEM, the name of the USGS quad, the state, boundaries, units of measurement, minimum and maximum elevations, projection parameters, number of profiles, and statistics on the accuracy of data. The sample data itself is typically ordered from south to north in profiles that are ordered from west to east. The number of points in a profile will vary because of the angle between the quadrangle s geographic boundary and the UTM coordinate system. Figure 2.9 displays the geometry of the USGS quad within a UTM grid as well as the profiles. The inter-point distance between the samples is measured in meters. Figure 2.10 displays the geometry of the USGS quad within an ellipsoidal datum as well as the profiles. Note that in this case the inter-point distance between the sample points is measured in arcseconds. The DEMs can be viewed using several commonly available programs which we will discuss in Section DEM Accuracy issues: To verify the vertical accuracy of a DEM a minimum of 28 test points are chosen for a single DEM file. These 28 points are composed of 20 interior points and 8 edge points that are located along, at, or near the quadrangle boundary. The Root Mean Square Error (RMSE) is computed for these test points. This value of RMSE is encoded as part of the DEM file. According to the accuracy the DEMs are classified into 3 categories. Level 1 category 29

45 Figure 2.9: DEM sampling profiles for a USGS quad within a UTM grid Figure 2.10: DEM sampling profiled for a USGS quad within an ellipsoidal datum 30

46 has a RMSE of 7 meters with a maximum RMSE being 15 meters. The intent is to reserve level 1 category for 7.5 minute DEMs which are created by scaling NAPP/NHAP photography. Level 2 category DEMs have a maximum permitted RMSE value of one-half of the contour interval. Level 2 category DEMs are elevation data sets that have been derived by digitizing hypsographic (contours, spot elevations) and hydrographic data (lakes, shorelines, drainage) either photogrammetically or from existing maps. Level 3 DEMs are derived from DLG data by incorporating selected elements from both hypsography and hydrography. A RMSE value of one-third of the contour interval at maximum is permitted. For further details, refer to USGS DEM Standards [35, 38]. Conversion between Coordinate Systems: There are a number of utilities available to convert DEMs from one coordinate system to another. Among the most popular ones are the Geodetic Toolkit from NGS [32] and CorpsCon from the Geo-spatial Applications Branch of the US Army Topographic Engineering Center [5]. These utilities are freely available. In our work, we have used CorpsCon version This is a Windows-based program that allows conversion between NAD27 and NAD 83 using the NGS program Nadcon. In order to make this conversion, one first needs to convert the DEM data into ASCII point data. The output of the Corpscon is also an ASCII point data which then needs to be converted back into DEM form. Corpscon version 5.x also allows conversion between NAVD29 and NAVD 88 vertical datums using the NGS program Vertcon. In addition, this software supports conversion between UTM and SPCS coordinate systems based on NAD27 or NAD83. 31

47 (a) Aircraft collecting LiDAR data (b) LiDAR Equipment Figure 2.11: A sample LiDAR system and an aircraft collecting LiDAR data[29] Light Detection and Ranging (LiDAR) data LiDAR is a scanning and ranging laser system that is used to collect depth range data. Although LiDAR technology has been in existence for about 20 years, the development of supporting systems such as highly accurate GPS (Global Positioning System) and INS (Inertial Navigation System) has become available or affordable only in the last few years. Due to these recent developments, LiDAR data can be geo-spatially registered much more accurately which in turn helps to produce highly accurate and high-resolution topographic maps. The LiDAR system consists of a laser scanner (a transmitter and a receiver), a highly accurate GPS unit and an Inertial Navigation System (INS, also referred to as Inertial Measurement Unit, IMU). In this work, we will use LiDAR data collected from an aircraft. The laser scanner is mounted inside an aircraft and emits infrared laser beams at a high pulse rate. Figure 2.11 shows the aircraft carrying the LiDAR equipment and emitting these infrared beams. The 32

48 scanner records the difference in time between the emission of the laser pulses and the reception of the reflected signal. The round trip travel time of the laser pulses, from the aircraft to the ground and back, is measured and recorded. The position of the aircraft is recorded using the GPS receiver. In order to provide accurate position of the aircraft a differential GPS is set up with two or more GPS units on the ground at positions very accurately known. These units need to be within a limited range of the target area so as to provide differential corrections. There may be some amount of human error associated with setting up the differential units, up to a few centimeters. The orientation of the aircraft (heading, tilt, and roll) is measured using the INS at the time of the transmission of each pulse. Infrared light (wavelength about 1064 nm) is chosen because it provides excellent return signal from bare Earth as well as from vegetation. For measuring the depth of ground under water, green light (wavelength about 532 nm) is chosen as it can easily penetrate the water column. The laser pulses can be generated at the rate of 300 Hz to 15 khz. A typical LiDAR system is shown in Figure This unit generates laser pulses at the rate of 15 khz. A typical path taken by the aircraft is shown in Figure Note that in order to cover a certain region, the aircraft needs to return to the target region by flying way out in the direction of the flight before coming back. This is done in order to ensure that no more than a 15 degree change in the direction can occur if the accuracy of the INS unit tracking the orientation of the aircraft is to be maintained. Professional laser scanners can accept multiple returns reflected from the surface. In the LiDAR system we used, the scanner records the time of the first and the last return along with the associated intensity of the returns. Typically, if the laser beam hits a hard surface such as the road, then the first return will contain most of the reflected energy and help to determine 33

49 Figure 2.12: A typical path taken by the LiDAR aircraft[29] the three dimensional position of the spot on the road. If the beam hits vegetation, then the first return can have varying levels of energy. The last return is typically from a hard surface which is hit by the deflected beam. Once the GPS positions are determined, the scanner position and sensor orientation are used to compute the position of the laser spot on the ground. The horizontal resolution varies from 1 to 6 meters. The relative vertical accuracy is generally about 15 centimeters for clear hit surfaces such as roads. For vegetation points the accuracy is variable but it can be as good as 90 percent of the true height of the vegetation. The end result is a three dimensional point cloud with relative registration. This data is processed and bare earth points are extracted from the data using surface analysis. The data is generated at thousands of points per second and one hour of data collection can result in over 10 million points [11, 29, 27]. The data is expected to be highly accurate but extremely dense and, therefore, requires efficient techniques for visualization. For geo-registration of the three dimensional point cloud, a ground survey needs to be done at sample points in the target aream very similar to the accuracy verification process for the USGS DEMs. The resulting data is a geo-spatially registered point cloud. There are about 25 firms in the United States that collect LiDAR data and about 55 34

50 firms that process this data in order to create products and applications Software and Utilities In this section we describe several commercial and freely available software and utilities that are available for viewing or manipulating DOQQs, DEMs, DLGs, AutoCAD drawings, and Street Maps. ArcView/ArcInfo: ArcInfo/ArcView are products developed by Environment Systems Research Institute, Inc (ESRI 1 ). ArcInfo is the primary product of ESRI and one of the most powerful GIS software available. ArcInfo can be used to view as well as edit different types of GIS data in the form of ESRI shape files, DOQs, DRGs, DLGs, DEMs, AutoCAD drawings, MapInfo maps etc. ArcInfo can be used on Unix as well as Windows platforms. ArcInfo has the capability for editing GIS data including the transformation of DOQs from one coordinate system to another. This is supported for hundreds of different types of coordinate systems. ArcInfo supports a development environment in which users can write scripts using languages such as Visual Basic for Applications (VBA) to enhance the capability of ArcInfo and thousands of such scripts are freely available. ArcInfo also allows for querying and accessing GIS data stored in external databases such as SQL server and Oracle. ArcView is a Windows-based product developed by ESRI that has a subset of capabilities of ArcInfo. ArcView can be used to import different types of GIS data in raster as well as vector formats. Unlike ArcInfo, ArcView cannot be used to transform raster data (DOQ, DRG, DEM) from one coordinate system to another. The database access capabilities of ArcView are

51 also limited as compared to ArcInfo. To extend the capability of ArcView in the third dimension ESRI has developed ArcView 3D Analyst and Spatial Analyst. These extensions can be used with ArcView for viewing 3D spatial data such as DEMs. We have used ArcView for viewing DOQQ and DEM data. We now discuss the shape files used by ArcInfo/ArcView. Shape files can be created using ArcInfo/ArcView by either digitizing maps or by converting data in various other formats into shape file. In this work, we convert AutoCAD drawings in dwg and dxf formats (with layers) into shape files using CAD2Shape or ArcInfo. Shape files are flat files where all the layers are merged together. The shape file format is an open and simple file format released by ESRI and is easy to work with. When an AutoCAD drawing is converted to a shape file, two kinds of shape files can be produced. The first kind of shape file stores geometry and associated attribute information in a data set. The second kind of shape file stores text information as attributes and creates associated geometry such as points where these texts are to be tagged/displayed. A shape file contains no spot elevation information although it could store contours. From an implementation point of view, both types of shape files have three components: a main file with the extension shp ; an index file with the extension shx ; and a dbase table with the extension dbf. These are all binary file formats. The shape file consists of data records each describing a shape designator such as a line or a polygon. The main shp file contains the geometry information stored as a set of coordinates. Area elements are represented as closed loop polygons. Attributes such as textual information are stored in a separate table. There is a one-to-one correspondence between a shape and an attribute record in the dbase table. In the index file, each record contains the 36

52 offset of the corresponding main file record from the beginning of the main file. The dbase table contains feature attributes with one record per feature. The relationship between geometry, indices and attributes is based on record number. MapInfo: MapInfo professional is a GIS product developed by MapInfo Corporation 2. It provides modules for digitizing maps. It supports raster and vector maps in a variety of formats. Maps can be viewed in layers registered on a common coordinate system. MapInfo supports 18 different map projections and data can be converted from one projection to another. Maps can be created using points, polylines and polygons. Textual data associated with these elements can be stored in separate files, spreadsheets or databases. MapInfo supports SQL query access to the databases. It also supports 3D viewing capability using OpenGL. 3D data can be imported into a generic grid format and viewed using MapInfo. Maps/Images can then be texture mapped onto the 3D grid. The native file formats for MapInfo are.mid and.mif files. The MIF files typically contain coordinate information for the vector elements (Points, Polylines, Polygons) while the MID files generally contain the associated attribute information. Like ArcInfo/ArcView, MapInfo also supports script extensions in languages such as C++, Visual Basic, Power Builder, Delphi etc. AutoCAD: AutoCAD is the most popular CAD (Computer Aided Design) tool available. It is being used by architects, engineers, the GIS community, and millions of people from other disciplines. It is created by AutoDesk Inc. 3 AutoCAD by itself does not provide support for the GIS data or geo-spatial coordinate systems

53 AutoCAD Map and AutoCAD MapGuide are software packages created by Autodesk that are specific for GIS. AutoCAD Map provides the user with the ability to create and analyze GIS data along with the underlying functionality of AutoCAD. Some of the functions provided by AutoCAD Map include (i) import and export of GIS data in various other formats specific to other software such as ArcInfo/ArcView, (ii) Support for external database access such as MS Access, Oracle etc., (iii) support for raster file formats such as DOQs, DRGs, (iv) compatibility with various coordinate systems and converting data from one system to another, (v) spatial analysis tools for analysis of vector data, and (vi) creation and presentation of maps. For more details please refer to [4]. Miscellaneous Utilities: DLGV32 is a freely available Windows-based software utility developed by the USGS for viewing GIS data. The software is available from their web site 4. It was originally developed for viewing digital line graphs (DLG). The software allows preview and evaluation of USGS data such as DLGs, DOQs, DEMs etc. It contains no editing capabilities, and is not a substitute for commercial Geographic Information System (GIS) software like ArcInfo and MapInfo. We have used DLGV32 for viewing DEM and DLG data. MICRODEM is a windows-based free utility written by Professor Peter Guth of the Oceanography Department, US Naval Academy 5. It can be used to display DEMs, satellite imagery (LandSat), scanned maps, vector map data and other GIS data. Microdem uses OpenGL libraries to view 3D data such as DEM. AutoDesk has released a free viewer named VoloView Express for DWG and DXF 4 view.html

54 files. This can be downloaded from the AutoDesk website 6. VoloView Express allows easy viewing of the AutoCAD drawings by letting the user choose the combination of layers of interest to the user. CAD2Shape is an inexpensive utility to convert CAD files such as DWG and DXF files to Shape files developed by Gutherie CAD/GIS software Inc. 7. It can translate all Auto- CAD DXF and DWG versions up to and including AutoCAD It also allows for filtering of layers before conversion. 2.2 Global Positioning System We begin by presenting a brief historical background on the Global Positioning System (GPS) followed by a description of the general principles behind the system. We then focus on different sources of uncertainty associated with GPS Historical Background Since the beginning of human civilization, mankind has developed ingenious ways to navigate around the world. Use of angular measurements of the stars was a navigation technique developed by the ancient Polynesians. With the development of radios, another class of navigation system was born using radio beacons, omni-directional radios, and long-range radio navigation (LORAN). In 1960s, line-of-sight radio navigation signals became possible with the advent of artificial satellites. Instead of angular measurements to natural stars, greater accuracy

55 can be achieved with ranging measurements to artificial satellites, referred to as Navigation Stars (NAVSTARS). The Global Positioning System (GPS) is a space-based radio-navigation system managed and operated by the United States Government. By early 70s the US Air force and Navy had extensively studied the problem of improved navigation using space-based techniques. The first satellite-based navigation was called NNSS (Navy Navigation Satellite System) or TRAN- SIT. Location was determined by a local measurement of the Doppler shift of a tone broadcast at 400 MHz by polar orbiting satellites at altitudes of about 600 nautical miles. The TRAN- SIT system was inherently two-dimensional and limited the total number of satellites available worldwide to 5. Due to these limitations the system was not very useful for real-time navigation. By 1972, another satellite system was developed by the Naval Research Laboratory (NRL). This system was called Timation [41]. The system used highly precise clocks to provide precise time and navigation information at various points on the Earth. A third essential foundation for GPS was a US Air Force program called 621B. By 1972, this program demonstrated the ability to compute satellite ranges (distances) using a Pseudo-Random Noise (PRN) code that allowed the resulting signal to be detected even when the signal power was 1/100th of the noise. In addition, all satellites could broadcast on the same nominal frequency because properly selected PRN code sequences were nearly orthogonal to each other. The original concept of the 621B program proposed several different satellite constellations that could be deployed gradually (for instance, starting with Americas and extending it worldwide later). Initially the signals needed to be monitored continuously from the ground in order to keep them synchronized in time but later the concept of Timation clocks removed the necessity of reliance on continuous ground 40

56 contact. In 1973, the Department of Defense (DoD) decided to form Joint Programs that forced various DoD services to work together. One such program was meant to initiate the Global Positioning System. The first phase of the program included 4 satellites, the launch vehicles, three different types of receivers, a satellite control facility and an extensive test program. Since the minimum number of satellites required is 4, it became apparent that more satellites were needed. Thus, 2 more satellites were approved later for this purpose resulting in a total of 6 satellites in Phase I. The first prototype satellite was launched in February Although these satellites were designed for a life time of 3 years, several of them lasted for more than 10 years. The first series of operational satellites were launched in 1989 and the full operational capability was reached in spring 1995 when a total of 24 satellites were in place and extensive testing was completed. Since then several replacement satellites have been launched. For the early history, please refer Parkinson and Spilker [41] Satellite Constellation The GPS system is comprised of three components: the satellite constellation, ground control/monitoring network, and user receiver equipment. The ground control unit tracks and maintains the satellites in space. It also monitors the satellite health and integrity and updates the satellite clock corrections. The original satellite constellation consisted of 24 satellites distributed in 3 circular orbits. These orbital planes were inclined at an angle of 63 o with respect to the equatorial plane. Each satellite has a period of one-half of a sidereal day or 11 hours 58 minutes. This 41

57 (a) GPS Satellite Constellation (b) GPS Constellation Planar Projection Figure 2.13: GPS Satellite Constellation and Planar Projection[7] configuration provided a range of 6 to 11 satellites at any time, making the system robust and tolerant to occasional satellite outages. The original configuration was modified to accommodate 2 changes: the orbital inclinations has been reduced to 55 o and the number of orbits has been increased to 6 with 4 satellites in each orbit as illustrated in Figure 2.13a. Each satellite is equipped with solar panels for basic power and have an average lifetime of more than 5 years. Figure 2.13b presents the orbits in a planar projection at 0000 hr July 1, The orbital plane locations with respect to the Earth are defined by the longitude of the ascending node while the location of satellite within the orbital plane is defined by the mean anomaly. The longitude of the ascending node is the point of intersection of each orbital plane with the equatorial plane. The Greenwich meridian is the reference point where the longitude of the ascending node has 42

58 the value zero. Mean anomaly is the angular position of each satellite within the orbit with the equator being the reference or point with a zero mean anomaly. The relative phasing between most satellites in adjoining orbits is approximately 40 degrees. Satellite Availability: Although there are 31 satellites are in the orbit currently, only a few of these are available to the user at any time. The satellite is available to the user if it is in the line of sight. Therefore, the number of satellites available to a user also depends upon the antenna mask angle of the GPS receiver. Mask angle is the elevation angle above the horizon at which satellites are considered visible by the receiver. Generally, a mask angle of 10 degrees or more will ensure visibility unless obstructed by tall objects in the vicinity of the receiver. For a specific location and time, the number of visible satellites, as well as the geometry of these satellites, can be obtained from the US Coast Guard Navigation Center and as an output from some GPS receivers GPS Receiver The equipment that the user needs to carry is referred to as a GPS receiver. The purpose of the receiver is to decode the signals broadcast by the satellites and provide Position, Velocity and Time (PVT) estimates. The receiver can vary in size from that of a wrist watch to a unit that has a foot print of about 20 square feet. The receiver equipment consists of an antenna, a receiving unit,a processor, an input/output device and a power supply. GPS antennas can be single frequency or dual frequency antennas. The physical design of the antenna can vary from helical coils to a thin microstrip. 43

59 There are a number of factors that need to be considered for antenna selection such as antenna gain pattern, available mounting area, aerodynamic performance, multipath performance, and stability of the electrical phase center of the antenna. GPS receivers can either track only C/A codes or both C/A and P(Y) codes as discussed in Section Most receivers have multiple channels, where each channel tracks transmission from a single satellite. There can be a maximum of 12 such channels. The receiving unit forwards the signals to the processor. The processor performs position, velocity, and time estimation from the signals received from the receiving unit. The processor is responsible for issuing commands to the receiving and input/output units. The I/O device acts as an interface between the receiver equipment and other user equipment. In most cases the I/O devices is a simple display unit that displays the instantaneous position while in configurations where the GPS is used along with other sensors, the interface could be a RS-232, RS-422 or ARINC 429. The power supply could be either be external or integrated into the receiver. It may even be a combination of both. Typically, alkaline or lithium batteries are used for integrated power supplies while external supplies are generally AC adapters Position Determination using Ranging Signals The fundamental navigation technique for GPS is one-way ranging from the GPS satellites that are also broadcasting their own estimated positions. Ranges are measured from at least four satellites simultaneously in view. The incoming signal is correlated with a user- 44

60 (a) 2-dimensions (b) 3-dimensions (c) Plane of satellites Figure 2.14: Principle of triangulation generated replica signal, and the received phase is measured against the user s relatively crude crystal clock. With four satellites and appropriate geometry, four unknowns can be determined: latitude, longitude, altitude, and a correction to the user s clock. We now describe this position determination in a little more detail. GPS works on the principle of triangulation. We must find the distance of a given object (receiver) from some known objects (transmitters). We can compute this distance by measuring the time taken by a signal traveling from the transmitter to the receiver. We can then calculate the distance as the product of the signal travel time and the speed of signal. In two dimensions, if we know that the receiver is at a distance R1 from transmitter T1, and that the distance of the receiver from transmitter T2 is R2 then the receiver is either point A or point B as illustrated in Figure 2.14a. By estimating the distance from the third transmitter T3 we will know the exact position which is the intersection of the three circles. Figure 2.14b shows the 45

61 Figure 2.15: Effect of independent errors on position estimates same idea extended to three dimensions. In three dimensions a distance R1 between the satellite and the receiver defines a sphere of radius R1 with its center being at the satellite position. Two such spheres intersect in a circle. A third distance narrows down the possibility to 2 positions that are mirror images of each other with respect to the plane of the satellites. For a user on the surface of the Earth, the lower position is the true position. However, as stated before, since there is some error in user s clock, one needs at least 4 satellites to accurately compute the position. The distance from a satellite is measured simply by multiplying the time taken by a Radio Frequency (RF) signal to reach the receiver from the satellite and the speed of the RF signal. The satellites send signals along with the timestamp (Time of Transmission). When the receiver gets this signal it takes the current time as the receiving timestamp (Time of Arrival). It can then compute the difference that is the signal travel time. Thus, it is required that the clock in the receiver be synchronized with the clocks in the satellites. An error of one nanosecond results in about 30-centimeter error in measuring the distance to that satellite (1 ns * speed of light). 46

62 The transmitters in the satellites are equipped with very accurate Cesium atomic clocks. These clocks have an error of one nanosecond every 3 hours. These clocks are constantly monitored by control stations on the Earth and are synchronized to the GPS System time. It is impossible to equip the receivers with the cesium atomic clocks as they weigh about twenty kilograms and are extremely expensive. Besides, these clocks require extensive care and temperature control. If the receivers were equipped with an inexpensive clock with an unknown error rate and if it has an error of 1 millisecond, which is quite common, then the error in computation of distance is 300,000 meters! Fortunately, since all the transmitter clocks are synchronized with each other, the receiver clock error is a constant offset, introducing just one more unknown variable, and can be computed by taking the distance from a fourth satellite. Thus, we need distance measurements from 4 satellites in order to computer the receiver position Navigation Algorithms A navigation algorithm embedded in a GPS receiver combines raw measurements from the signal processor with GPS satellite orbit data to estimate the observer state. A typical state includes three components of position, clock offset, and clock drift. In an application involving movement, three components of velocity are added. The algorithm requires two sets of models a measurement model and a dynamics or process model. There are three types of common measurement models. These are Pseudorange, Doppler, and Accumulated Delta Range (ADR). The Pseudorange measurement is based on the time interval between the signal transmit time and local receive time that we discussed in Section Doppler model first computes the shift caused by satellite and user motion and 47

63 then converts this pseudorange rate observation to position estimate. The observation geometry of this technique is substantially weaker than the pseudorange model and is not much used in GPS, except to set a priori position estimate. The ADR model keeps track of changes in the observed range and has also been referred to as integrated Doppler and carrier beat phase model. For standalone GPS, ADR cannot be used for absolute estimation of position. It can be used for differential GPS to be discussed later in Section In standalone GPS, ADR can only be used for smoothing noise. However, ADR measurement models are pivotal to kinematic and differential operations and surveying. Measurement models described above can be used to provide an estimate of user position. However, these estimates are extremely dependent upon the instantaneous satellite geometry. In order to improve this estimate, process models are typically incorporated in computing the user position and velocity estimates. Process modeling refers to the modeling of user clock bias and drift (2 parameters) as well as the user position (3 parameters) and velocity (3 parameters). If the user is known to be stationary, then only clock model and stationary user model is required. A velocity model is needed for slow moving objects such as cars and boats. For high velocity aircrafts, it is necessary to measure and account for the changes in velocity using integrated GPS/INS systems such as those employed during LiDAR data collection. Measurement models are coupled with process models to estimate user s position and velocity using extended Kalman Filter formulations [7, 2, 41]. 48

64 2.2.6 GPS Signals GPS ranging signals are broadcast by the satellites at 2 different carrier frequencies: a primary signal at MHz L f 0 and a secondary signal at MHz L f 0. The frequency f 0 is referred to as a reference frequency and is equal to MHz. These two signals are generated synchronously so as to compute the ionospheric delay that affects the signals. Inexpensive GPS receivers typically use only L 1 frequency. The 2 carriers are modulated by 2 different PRN (Pseudo-Random Noise) codes. These codes are streams of random bits that are repeated. Each transmitting satellite is assigned a unique code that is uncorrelated with the others. These codes also define the type of services available to the GPS user, and are briefly discussed below. C/A code (Clear or Coarse Acquisition Code): This is a short PRN code transmitted at the rate of MHz. This code is broadcast unencrypted and it defines the Standard Positioning Service (SPS) available to any civil user. P Code (Precise or Protected Code): This is a very long code that is broadcast at the rate of MHz, ten times the rate of C/A code. This signal provides the Precise Positioning Service (PPS) which is not available to any unauthorized user as it is generally encrypted. It is also referred to as P/Y code when it is encrypted. Because of the higher modulation bandwidth this signal is more precise and can help improve the accuracy of the position estimate. Satellite signal strength: The GPS receiver outputs the signal strength received from each of the satellites as Signal to Noise Ratio (SNR) [41] values expressed in db-hz. The signal power levels are generally expressed in terms of decibels with respect to 1W (dbw) while the Noise 49

65 Figure 2.16: Range measurement timing relationships power is expressed in dbw-hz. The minimum power that must be received by the receiver for a 3dB gain antenna are: (C/A code, L1 carrier) dbw (P(Y) code, L1 carrier) dbw (C/A or P(Y) code, L2 carrier) dbw Sources of Uncertainty There are several sources of uncertainty in GPS position determination [7, 41]. For example, the ranges R1, R2 and R3 shown in Figure 2.14a have errors e1, e2 and e3 associated with them. As a result, the position estimated is actually not a single point in space but a gray area as shown in Figure The accuracy of the position determined by GPS is ultimately expressed as the product of a satellite geometry factor and a pseudorange factor. Roughly speaking, the error in GPS can be estimated by the following formula: Position Error = Geometry Error * Range Error. 50

66 Range Errors: The distance measured by the receiver is referred to as the pseudo-range as opposed to the true distance (referred to as the geometric range). Range errors refer to errors in these distance measurements due to a variety of sources including satellite and receiver clock offsets, inaccurate information about the exact location of satellites, atmospheric delays, multipath and foliage errors, hardware errors, selective availability, and noise. Figure 2.16 shows the timing relationship between true geometric range and the measured pseudo-range. As shown in the figure the pseudo-range can be expressed as: ρ c T u e D u T s D s where, ρ = pseudo-range measured by the receiver c = velocity of light T s = the true time of transmission of the signal by the satellite D s = the satellite clock offset T u = the true time when the receiver should have received the signal D u = receiver clock offset e = external errors due to atmospheric delays, multipath effects etc. The above equation can be re-written as: ρ c T u T s c e D u D s ρ R ce where, 51

67 R = True geometric range = c T u T s E = Cumulative error = e D u D s The cumulative error can be represented as: e I T M R S where, I = Ionospheric delay T = Tropospheric delay M = Multipath, shadowing and foliage error R = Receiver noise and hardware errors S = Error due to Selective Ability (no longer present) Each of the errors is briefly discussed below. For a more detailed description please refer Kaplan and Parkinson et al. [7, 41]. Satellite ephemeris error: Ephemeris errors occur due to incorrect estimation of satellite location. The orbits of satellites are monitored continuously from several monitoring stations around the Earth and their predicted orbital information is transmitted to the satellites, which they in turn transmit to the receivers. The history of GPS has shown, thus far, that the accuracy of the orbital prediction is in the order of a few meters. As reported in [7], the effective ranging error caused by incorrect satellite ephemeris prediction is about 4.2 meters for a 24 hour period. Receiver clock offset (D u ): The receiver clock error applies uniformly to all satellites and hence we can eliminate it by taking the distance from one more satellite. 52

68 Selective ability (S): One of the major sources of satellite clock and ephemeris errors is an intentional degradation known as Selective Ability (SA). It is implemented by manipulation of the broadcast data by reporting the orbit of the satellites inaccurately. Military receivers are equipped with special hardware and codes that can mitigate the effect of SA. SA can be turned ON or OFF through ground commands by the GPS system administrators. With SA on the typical ranging error is about 20 meters but can go up to as much as 100 meters. As of May 1, 2000 SA has been turned off [25]. Satellite clock offset (D s ): Even very accurate clocks accumulate an error of 1 billionth of a second every three hours. To resolve the satellite clock drifts, they are continuously monitored by ground stations. Even with the best efforts of the control centers in monitoring the behavior of each satellite clock, their errors cannot be precisely determined and the resulting ranging errors can still be about 3 meters. The ground stations or Master Control Stations (MCS) compute the clock correction parameters and send them to the satellites that then rebroadcast these parameters in their navigation messages. The receiver implements the correction parameters as 2 D s a 0 a 1 t t r a 2 t t r a 3 where, D s = Satellite clock offset (sec) a 0 = clock bias (sec) a 1 = clock drift (sec/sec) a 2 = frequency drift (sec sec 2 ) t r = clock reference time (sec) 53

69 t = current time (sec) a 3 = correction due to relativistic effects (discussed later in the section) Ionospheric errors (I): Atmospheric errors typically can be classified into ionospheric and tropospheric errors. We first discuss the ionospheric errors. The speed of light varies due to atmospheric conditions. The upper layer of the atmosphere, called the ionosphere, contains free electrons that decrease the speed of the signal. The amount of delay incurred by a signal is directly proportional to the number of free electrons encountered and inversely proportional to the square of the carrier frequency. Since the number of free electrons in the ionosphere decreases during the night the magnitude of the effect of the ionosphere is much more during the day than during the night. The magnitude also has a cyclical period of 11 years that reaches a maximum and a minimum. For the current cycle, the ionosphere reached its peak magnitude in 1998 and will reach its minimum in The GPS signal is broadcast at two frequencies (L1 and L2) so that this delay can be computed and removed from the pseudorange measurements. This is the most accurate means for determining the ionospheric delay. Single frequency receivers are incapable of tracking the L2 frequency and therefore, they use a six-parameter model of the ionospheric conditions in order to eliminate the delay that can remove 50-70% of the error. The effects of the ionosphere, if not mitigated, can introduce measurement errors greater than 10 meters. For further details please refer Kaplan [7]. Tropospheric errors (T): The lower level of the atmosphere, which contains water vapors, is called the troposphere. Variations in temperature, pressure and humidity can decrease the speed of RF signals in this layer [41]. This delay is easier to model and can be eliminated using simple 54

70 models so that the effective accuracy due to tropospheric errors can be limited to about 1 meter or less. Relativistic effects: The relative motion of the satellites with respect to the user and the gravitational potential difference between the satellites and the user create a drift in the satellite clock which in turn causes an error in the pseudo-range measurement. This is referred to as the relativistic effect. There is a fixed frequency offset in the satellite s clock rate when observed from the Earth. This effect is removed by providing a constant to the satellite clock before launching. Thus the frequency of the satellite clocks is set to MHz which will be observed by the user as MHz. The orbits of the satellites are slightly eccentric causing an additional periodic offset in their clocks. There is an additional delay caused by the rotation of the Earth at the time of launching of the satellite. This delay is referred to as Sagnac delay. Users moving on the surface of the Earth and users at a height above the Earth s surface have to account for additional clock offsets. Multipath, shadowing and foliage errors (M): In measuring the distance to each satellite, we assume that the satellite signal travels directly from the satellite to the antenna of the receiver. But in addition to the direct signal, there are reflected signals, from the ground and the objects near the antenna, that also reach the antenna through indirect paths and interfere with the direct signal. The compound signal creates an uncertainty about the true signal arrival time. Reflected signals are generally delayed and are weaker than the direct signal. Signals can be reflected off the ground, tree trunks, or foliage. Signals reflected off the ground produce a very strong direct signal and some scattered signals. Signals reflected off the foliage and trees generally have a 55

71 randomly attenuated direct signal and some scattered components. It has been shown that signal attenuation by a tree with full foliage is about 35% more than that of a deciduous tree without foliage. Thus, the bulk of the reflection is caused by the tree trunks, limbs and branches than the leaves. GPS signal structure and receiver designs have several features that help to reduce the effects of multipath. Also, the GPS antenna is designed to attenuate or reject reflected signals so they have very little effect on the observations. Thus, multipath errors can be reduced substantially in most circumstances. With proper satellite siting and antenna selection, the net impact of multipath errors to a moving user should be less that 1 meter under most circumstances [41, 7]. Receiver hardware errors (R): Range errors are also caused by the thermal noise, oscillator instability, and the effects of dynamic stress in the receiver hardware. Receiver firmware can also contribute to some of the range error. Typically all these errors combined can cause about 20 centimeters of the range error. Dilution of Precision (DOP): We now discuss geometry related errors, referred to as Geometric Dilution of Precision (GDOP). This error occurs due to the geometric configuration of the satellites with respect to the user. To illustrate the concept the part of Figure 2.15 is redrawn in Figure The area of intersection of the two spheres (which represents uncertainty) increases with poor satellite geometry with respect to the user. The DOP also depends upon the elevation angle of the satellite. This is the angle made by the satellite with local horizontal. The GDOP is further classified so as to represent the accuracy of the components of position and time. These are termed as Position Dilution Of Precision (PDOP), Horizontal 56

72 (a) Low DOP (b) High DOP Figure 2.17: Dilution of Precision Dilution Of Precision (HDOP), Vertical Dilution Of Precision (VDOP) and Time Dilution Of Precision (TDOP). The actual position errors are computed as: RMS Position error = σ 2 x σ 2 y σ 2 z = PDOP * Range error RMS Horizontal position error = σ 2 x σ 2 y = HDOP * Range error RMS Vertical position error = σ z = VDOP * Range error RMS Time error = σ t = TDOP * Range error where, σ x = RMS error in X direction σ y = RMS error in Y direction σ z = RMS error in Z direction σ t = RMS time error Thus, GDOP PDOP 2 TDOP 2 57

73 and PDOP HDOP 2 VDOP 2 Generally, more satellites used results in smaller DOP values, and hence smaller position errors. GPS receivers use special algorithms in order to select the satellites that result in minimum DOP. VDOP values are generally larger than HDOP values giving us more confidence in horizontal position estimates than vertical position estimates. This is because all the satellites from which we obtain signals are above the receiver. If the RF signals could penetrate the Earth then we could obtain negative elevation angles (satellites below the horizontal) resulting in better VDOP values. Aircrafts that can listen to GPS transmitters on the ground (referred to as pseudolites) as well as the satellites above can have much better DOP values [41]. Accuracy measures: There are a number of conventions used for reporting the accuracy of GPS readings. Some of them provide an idea about just the horizontal accuracy of the receiver while some provide vertical accuracy while others represent both. If the readings from a stationary GPS receiver are logged we observe that the reading is not constant but it varies with time. Thus, if we plot these point on a graph we obtain a scatter plot with x and y axis being the longitude and latitude respectively. Based on this scatter plot we can define accuracy conventions that are discussed below. Root Mean Square error (RMS): The RMS is defined as the square root of the average of the errors squared. RMS can be used to represent horizontal as well as vertical accuracy. rms E 2 i Twice Distance RMS (2DRMS): 2DRMS is defined as twice the RMS of horizontal 58

74 Figure 2.18: Circular Error Probable (CEP) and Horizontal 95% accuracy measures errors. 2DRMS is used to represent horizontal accuracy. Circular Error Probable (CEP): CEP is defined as a radius of a circle that has its center at the true user position and contains 50% of the points in the horizontal scatter plot. Figure 2.18 illustrates this concept. CEP is used to express the horizontal accuracy of the receiver. Horizontal 95% accuracy (R95): R95 is very similar to CEP except that the circle contains 95% of the points in the horizontal scatter plot. R95 can represent horizontal accuracy. Spherical Error Probable (SEP): SEP is defined as a radius of a sphere that has its center at the true user position and contains 50% of the points in the three-dimensional scatter plot. SEP is used to represent three-dimensional accuracy of the specified receiver Differential GPS (DGPS) GPS was originally designed only to be used in standalone mode, which means that the receiver uses 4 or more satellites to determine its position. As we have seen in the previous section, in this mode various errors can crop into the readings. With Selective Ability (Section 59

75 Figure 2.19: Differential GPS 2.2.7) on these errors can degrade the position estimation by as much as 100m (horizontally) and 150m (vertically) [7]. As shown in Table 2.1 even without SA the error can be as much as 16 meters in the standalone mode. GPS can be operated in two different modes: the standalone mode and the differential mode. 1. Standalone mode: As discussed before in the standalone mode the GPS receiver uses the satellites as the only source of reference for positional information. In this mode various errors can crop into the readings such as the atmospheric errors, satellite orbit errors and receiver clock errors. 2. Differential mode: The use of GPS in differential mode can drastically improve the accuracy by eliminating the common (correlated) errors from two or more GPS receivers that are viewing the same satellites. The receivers we have employed are capable of being used either in the standalone or the differential mode. One of the receivers, as will be described later, is capable of accepting both code-phase and carrier-phase differential 60

76 corrections while the other can only accept carrier-phase differential corrections. The use of GPS in differential mode can drastically improve the accuracy by eliminating the common (correlated) errors from two or more GPS receivers that are viewing the same satellites. In the differential mode one of the receivers is set as a reference base station whose antenna position is very accurately known. The other receivers are called rover units. If the rover units are not very far from the base station then they see almost the same satellites as the base. The base station computes its distances from each of the satellites just as as any normal receiver but since it knows its position very accurately it can compute the errors in the distance measurement from each of the satellites. It then transmits these errors, called differential corrections to the rover units. The rovers apply these corrections to their measurements in real time thus eliminating all the errors they have in common with the base. This improvement is possible because most GPS errors vary slowly and are very strongly correlated within short distances. Typical range for local area differential GPS is about 150 km. Within this range the differential corrections greatly improve the accuracy for all rovers listening to the base. The concept is illustrated in Figure Differential GPS can be implemented in a number of different ways [42]. Local Area Differential GPS (LADGPS): Most DGPS systems use a single reference station that computes scalar corrections for each of the satellite ranges and then transmits them to the local rovers. Local here means that the correction can be delivered within 10 seconds and the rover is within about 100 km. This can improve the accuracy to about 1 meter for the rovers. Wide Area Differential GPS (WADGPS): In WADGPS, networks of reference stations 61

77 can be used to form a vector correction for each satellite formed by multiple reference stations. The vector consists of satellite clock error for each of the satellite, three components of satellite positioning error and parameters of an ionospheric delay model. Wide Area DGPS corrections can be applied to rovers that are as much as 3000 km away, as the vector corrections are valid over much larger geographical areas. Carrier-Phase Differential GPS (CDGPS): The DGPS systems discussed above compute corrections based on code-phase measurements. With code-phase measurements the rovers measure the difference in the phase of the generated and received PRN code signals. Users with very high accuracy requirements employ a technique known as carrier-phase differential GPS. Using this technique the rovers compare the phase of the carrier signal with the carrier phase of the reference station, thus achieving range measurement precisions that are a fraction of the carrier signal wavelength which is typically about a centimeter. The carrier-phase differential techniques are extensively applied in survey applications. If the rover antennas are fixed then the survey is called static, whereas if the antennas a moving, the survey is termed as kinematic. It is possible to achieve millimeter accuracy with static surveys, while with kinematic surveys the accuracy can be within a few centimeters. RTCM Messages and RTK positioning: Several data formats have been established for transmission of DGPS corrections among which the standard established by the Special Committee 104 of the Radio Technical Commission for Maritime Services (RTCM) is most widely used [42]. The standard defines 64 different messages that can be broadcast by the base station. These messages include Pseudo-range corrections, satellite health, estimated accuracy, age of 62

78 the data being used by the reference station and many other types of messages. Messages 1, 2, 9 are code-phase differential corrections while messages 18, 19, 20 and 21 are for real-time broadcast of differential carrier-phase corrections and they are also referred to as Real-Time Kinematic (RTK) messages. The RTK messages were added to the RTCM message list in the later part of A receiver capable of listening to these messages can provide centimeter level accuracy in real-time even while moving. For RTK operations RTCM messages (18, 20 or 19, 21) must be sent every 0.52 seconds, rather than 10 seconds as mentioned before for codephase differential corrections. To support this the data link needs to be at least 2400 bits/second and preferably 9600 bps or even bps. The bandwidths required to support such data rate is found in the VHF (Very High Frequency) and UHF (Ultra High Frequency) part of the radio spectrum. In North America, frequencies in the VHF band from 150 to 174 MHz and in the UHF band from 450 to 470 MHz are generally licensed for RTK radio links. Since RTK data links operate at VHF/UHF frequencies their use is limited to a maximum of d kilometers that can be approximately computed as: d 3 57 k h b h r where h b and h r are heights in meters of base and rover antennas above their common horizon. k is a factor that varies with weather conditions between 1.2 and 1.6 with the typical value being If the base antenna is 30 meters above the ground and if the rover is about 2 meters above the ground then the maximum propagation distance is about 28 kilometers. This is a theoretical value and is difficult to achieve in practice. For a more detailed description on RTK refer Langley [20]. 63

79 Error Source Standalone mode Differential (RTCM) Differential (RTK) Satellite Ephemeris error 4.2 m (corrected) Satellite clock error 3.0 m (corrected) Ionospheric delay 2.3 m Tropospheric delay 2.0 m Receiver noise error 1.5 m Multipath error 1.2 m Other miscellaneous errors 0.5 m Effective range error 6.5 m Typical GDOP 2.5 Cumulative RMS position error m About 1 m cm Table 2.1: Error estimates for Standalone and Differential GPS GPS uncertainty estimates: Table 2.1 summarizes the error estimates for standalone and differential GPS GPS Integrity Apart from the errors discussed above, there may be situations when GPS produces gross errors that go far beyond the ranges discussed above. In these situations, its best for the receiver not to trust such readings or warn the user about it. This is referred to as the Integrity of GPS. These gross errors occur very rarely and are referred to as GPS Integrity Anomalies. GPS Integrity Anomalies can occur due to a number of reasons. The satellite clocks sometimes experience a random run-off or a large jump that can result in a large amount of offset. Sometimes during the period of eclipse some of the satellites fall under the shadow of the Earth and can no longer avail solar power. During that time the satellites have to rely on their internal power sources. As the satellites age, they can no longer sustain regular operation without external power. During that time there can be large ranging errors to those satellites. At times, the Master Control Stations (MCS) can incorrectly predict the Ephemeris of some 64

80 satellites causing large error. On rare occasions, the MCS clocks also experience random jumps. Since GPS Integrity Anomalies are very critical for Aviation, the Federal Aviation Administration (FAA) has formed a special federal advisory committee to develop techniques for detecting and correcting integrity anomalies. The two methods used are Receiver Autonomous Integrity Monitoring (RAIM) and Wide Area Augmented System (WAAS). RAIM is a technique used by GPS receivers that use additional satellites to determine if any of the satellite used in computing the position has a gross error. RAIM algorithm requires a minimum of 5 satellites to detect an anomalous situation and a minimum of 6 satellites to detect and isolate the anomalous satellite. WAAS is a network of ground stations and satellites that monitor the integrity of the satellite messages and detect anomalous situations. In case of an anomaly the WAAS network broadcasts correction messages to special satellites referred to as the INAMARSAT-3 satellites which then broadcast the corrected messages to the user GPS Manufacturers Every year the GPS World Magazine publishes a comprehensive survey of available receivers. The survey includes more than 500 receivers by nearly 60 manufacturers. The receivers include highly accurate survey-grade receivers as well as inexpensive consumer grade receivers. The description in this section is based on the latest issue of GPS World [44]. Survey-Grade Receivers: Survey-grade receivers are generally highly accurate and can be operated in standalone as well as differential modes. These are typically dual-frequency and 65

81 are also capable of receiving corrections from WAAS and other such services. These receivers can output position information in a wide variety of coordinate systems. The Ashtech Z-sensor and Ashtech Z-Xtreme receivers are highly popular in this category. They are manufactured by Thales Navigation/Ashtech Precision Products. As per the specifications these receivers provide horizontal position accuracy of 3m in standalone mode and 1cm in differential RTK mode. The maximum position update rates are 10 Hz. The 4000MSK DGPS Reference Station by Trimble Navigation Ltd. is also very popular among surveyors. According to the specifications the horizontal position accuracy is about 5m in the standalone mode and less than 50cm in differential mode with a maximum position update rate of 0.5 Hz. The GPS Total Station 5700 is also a more recent product in the same category introduced by Trimble. Consumer-Grade Receivers: Consumer grade receivers typically have low accuracy. They can generally be operated only in the standalone mode, although a few of the recent ones can also be operated in differential mode. These receivers are typically accompanied by maps and navigation software. Maps can be stored internal memory in the receivers. Among the consumer receivers, Garmin and Magellan receivers are the most popular. The GPS V by Garmin international and Meridian Gold by Magellan Corporation are the most popular ones. 66

82 Chapter 3 Previous Work In this section we discuss previous work in the areas of GIS and uncertainty visualization. 3.1 Virtual Geographic Information System (VGIS) Introduction and Overview of the System VGIS is a real-time 3D Geographic Information System developed by the Graphics, Visualization, and Usability Center at the Georgia Institute of Technology [8]. The system visualizes large volumes of geographic data consisting of: terrain elevations, digital ortho-photos (photo-texture, as referred in VGIS), GIS raster layers (such as weather data, demographic data), 3D objects such as buildings, vehicles, trees and other objects. VGIS can be used instead of a traditional GIS which is essentially 2D. The applications of VGIS include urban planning, flood planning, evaluation of roadways, waterways etc. Planning personnel can get instant 3D views of their site from various angles. VGIS is developed using Simple Virtual Environment (SVE) 67

83 Toolkit. The SVE toolkit is a device independent library used to build virtual environments using the OpenGL library created by Silicon Graphics. VGIS is primarily run on Silicon Graphics Workstations and is ported on to various platforms including Windows NT. One of the driving factors behind VGIS is the ability to respond in real-time. Real-time is defined by the system designers of VGIS as a mean speed of 15 frames/second while navigating with an interaction delay of 1/10 to 1/15 of a second. VGIS consists of two components - the data pre-processing component and the run-time visualization component. The data processing component is used to convert/resample the GIS data from a variety of formats into a format that is native to VGIS. Data is stored at various resolutions for real-time visualization. The run-time visualization component is multithreaded so as to support real time interactive rates Data Organization and the GSD Data Format. VGIS uses a native data format called GSD (Geographic Surface Data) format for storing the elevation and imagery data. This is a data format designed by the Data Visualization group at the Georgia Institute of Technology. It is a proprietary data format and the documentation on this data format is available on the web for authorized users at the VGIS web page. The GSD format supports storage of multi-resolution data sets with 8 levels of hierarchy. This storage mechanism is designed to support interactive real-time display (15 frames per second) of the data by bringing out coarse or fine levels of detail as needed by the user. We describe this storage mechanism in greater detail below. Since the elevation data is generally available in the form of USGS DEMs and the imagery data is available in the form of USGS DOQQs, there is a need to convert this data into GSD format, which requires multi-resolution extraction 68

84 Figure 3.1: 4 successive views with increasing detail while zooming into the Georgia Tech Campus within VGIS 69

85 of information. To this purpose there is a set of utilities provided by the developers of VGIS. GSD data is organized such that the entire surface of the Earth is divided into 32 quadnodes. Each quadnode spans 45 degrees in latitude and 45 degrees in longitude. Each of these quadnodes is further divided into 256 subsections. GSD storage mechanism uses a simple hexadecimal scheme to store the elevation and imagery information. The directories 00/ - 1f/ store data for 32 top-level quadnodes. To begin with, these directories can simply contain the coarse resolution data that may suffice to give the whole view of Earth from very large distances. Further high-resolution data can be added into these directories for a particular region. A quadcode is a 16-digit hexadecimal number that delineates the exact location within VGIS of some given spot. The multiple resolution elevation and imagery data is organized in separate directory structures. For instance, VGISROOT/data/terrain/geometry/elevation/XX/ gsd contains elevation information for a particular region while VGISROOT/data/terrain/imagery/ phototexture/xx/ gsd contains imagery data for the same region. Note that XX is a directory from 00-1F User Interface and Navigation VGIS can be used either in a windows-based environment or with an immersive virtual reality interface. The immersive environment is created using a head-mounted display (HMD), a 3D mouse controller and head and mouse tracking devices. The user is allowed six degrees of freedom, three degrees of three-dimensional translation while three degrees of rotation. The head tracking device allows for displaying the appropriate view to the user according to the viewpoint while the mouse tracking device can be used in conjunction with the 70

86 head tracker to popup menus, selecting objects or selecting actions such as flying over a given terrain Level of Detail Management In order to maintain real-time rendering of the terrain, VGIS employs a terrain compression /simplification mechanism [28] that depends upon the level of detail required at a particular instant of time. The terrain is represented as a height field described by a rectilinear grid of points elevated above the x-y plane. Each grid point has a Z (elevation) associated with it. The terrain surface can be then rendered using a triangular mesh. The terrain simplification algorithm used in VGIS introduces certain constraints on the size and organization of the height field for efficient simplification/rendering. The algorithm consists of two-steps: a coarse- grained simplification followed by fine grained-simplification. The coarse-grained simplification determines the level of detail required which is essentially determined from the camera position and orientation. Fine-grained simplification involves elimination of individual grid points by way of combining adjacent triangles (if they meet certain simplification criteria). This provides the user with continuous level of detail which means that the surface geometry changes smoothly between successive frames Architecture Paging: The amount of elevation and texture data in VGIS is enormous and therefore, most of it is stored in secondary storage and fetched into the main and texture memories depending upon the user s viewpoint. The paging of terrain data is implemented as part of the VGIS back-end 71

87 and communicates with the VGIS display clients via shared memory mechanisms. Whenever there is a requirement for some terrain data, the clients allocate space on the shared memory for the data and send paging requests to the server. The requests are implemented using priority queues. Multi-threading: In order to achieve real-time performance the entire system is divided into a number of threads, each carrying a specific task. Earlier versions of VGIS used only two threads: a data paging thread and a terrain management/rendering thread. These tasks were further sub-divided in to seven major threads. Tracker thread acquires motion parameters from a 3D tracking device (such as a headtracked head-mounted display) and delivers it to the user interface/navigation thread. User Interface and Master thread is primarily responsible for handling user input (e.g. mouse clicks, menu selections) and calling appropriate threads. Navigation thread receives user input parameters from the User Interface thread and handles terrain navigation tasks. Render thread receives graphics calls encoded in display lists from one or more threads and executes these calls within one or more windows. Terrain Manager thread organizes the various layers of data (such as the terrain, buildings and other objects), manages terrain simplification depending upon the level of detail required and provides an interface for terrain queries. 72

88 Terrain Server thread reads the terrain index and properties and fetches the required data from the disk to the memory. Object Manager thread is responsible for reading the objects hierarchy and sending that data in display lists to the render thread. 3.2 GIS-VIS Program The GIS-VIS project is a joint effort of US Environmental Protection Agency s (EPA) Scientific Visualization Center and the Unix/VMS/GIS Technical Support Group, both of which are Lockheed Martin Services contractors working with the National Technology Services Division. The projects are executed by teams led by Thomas Fowler and Theresa-Marie Rhyne. Geographic Information Systems (GIS) are collections of computing techniques and databases that support the gathering, analysis and display of large volumes of spatially referenced data. Scientific Visualization (VIS) is associated with computer graphics tools that support the three dimensional display and animation of complex data sets. The GIS-VIS project of the Enterprise Technology Services Division (ETSD), EPA is an attempt to integrate GIS and VIS technologies to assist with environmental sciences decision making. The three main goals of the GIS-VIS project are: To expand the use of GIS data in visualization environments To provide new ways to present spatial data and Test emerging GIS - VIS software 73

89 The GIS-VIS team is involved in visualizing spatial data, which they integrate with other wellestablished standard products. Preliminary products: Some of the initial efforts were focussed on importing ARC/INFO data and products into AVS. They used beta versions of software to integrates data from Arc-Info into AVS 5.0. As discussed earlier Arc/Info is a commercial Geographic Information System software, from the Environmental Systems Research Institute, Inc. (ESRI). AVS 5.0 is a scientific visualization toolkit from Advanced Visual Systems, Inc. The beta software is a set of AVS modules that can directly read Arc-Info file formats and produce three-dimensional pictures of the spatial data. The areas included the Great Smoky Mountains National Park and other parts of eastern Tennessee and western North Carolina, the data being supplied by EPA. The analysis products as well as the visualizations were produced by the GIS - VIS Integration team. Virtual Reality Markup Language (VRML) 1.0, 2.0 and 97: The 3D models created have been converted to VRML form so that users can access them using any regular VRML capable browser. Texture data visualization: Electronically scanned images are applied as textures to threedimensional models of mountainous terrain. Several bitmapped images were converted into ARC data and then brought into AVS to be draped over elevation data. More advanced implementations and animations, from EPA data sets, are then presented. Terrain modeling: Two different user interfaces are used for selecting VRML terrain models. The first interface allows for selection of terrain data from a list of public domain 74

90 data sets. Once a data set is selected and display options specified, a VRML file is created. The second interface lets users determine a flight path over a terrain model data set. A VRML file is created once the flight path is selected. AVS-ARC documentation: The documentation for AVS-ARC products is freely available. Image and Movie repository: A number of images and movie data are available at their web site. 3.3 Alexandria Digital Library (ADL) ADL is a consortium of researchers, developers, and educators, spanning the academic, public, and private sectors, exploring a variety of problems related to a distributed digital library for geographically-referenced information. The ADL is inspired by the Map and Imagery Laboratory (MIL) in the Davidson Library at the University of California, Santa Barbara. ADL s catalogs and collections currently include A catalog of over 1.5 Million bibliographic records, 6M item gazetteer, Geo-spatial thesaurus of 15K items, Collections of 325k maps, 15K aerial photographs, 5K USGS digital ortho-photo quarter-quadrangles, 75

91 0.5K databases, 3K space photographs, 0.5K remote-sensing images, Geodex records representing published map sheets worldwide. The ADL provides access over the World Wide Web to a subset of the MIL s holdings, as well as other geographic datasets through a web interface. They have implemented a search engine to browse through their huge collection. The user can select the region of choice by clicking on a map and request for data for that region. ADL is in the process of loading significant collections of geo-spatially-referenced information. An important focus for ADL s collection is on information supporting basic science, including the Earth and Social Sciences. This information is being distributed over various sites, including San Diego Supercomputer Center and the UC Berkeley digital library. The Alexandria Digital Earth Prototype (ADEPT) is a comprehensive follow-on to the Alexandria Digital Library Project (ADL). ADEPT aims to use the digital Earth metaphor for organizing and presenting information at all levels of spatial and temporal resolution. 3.4 Uncertainty Visualization In this section we discuss previous work in uncertainty visualization. Uncertainty is associated with almost every engineering and science process. Most visualization research has separated uncertainty from the actual process. A likely reason for this may be that there are no 76

92 standard methods for presenting uncertainty along with the data. Uncertainty estimation and visualization is extremely crucial for decision making. When the user is provided with the real picture it gives him a sense of the quality of the data as well as the process. The user can then make a decision with a certain amount of confidence. Several definitions of uncertainty have been proposed in the past. Lodha et al. [23] have defined uncertainty as either statistical, error or range uncertainty. Statistical uncertainty can be represented either as mean and standard deviation or an actual distribution of the given data. Error uncertainty is defined as an absolute difference between a known truth and the estimate. Range uncertainty is an interval with minimum and maximum values within which the data must exist, but which cannot be quantified into either statistical or error definitions. Wittenbrink et al. [43] define uncertainty as a multi-faceted characterization of data that includes many concepts such as accuracy, confidence level, covariance, difference, distribution, inaccuracy, noise, precision, purity, randomness, reliability, residual, resolution, spread and validity. Uncertainty analysis and visualization is widely applied for spatial data. The National Center for Geographic Information and Analysis (NCGIA) initiative on Visualizing the Quality of Spatial Information classifies the sources of data uncertainty as source or acquisition errors, process or transformation errors and visualization errors. Source errors are introduced while capturing the data using sensors such as video cameras or other remote sensing devices. These errors can also be introduced when the data is acquired as output from mathematical models. The data is then processed using appropriate methods to transform into the required form. Typical examples of transformations are sampling, quantization and interpolation. These processes introduce errors in the resulting data. Finally visualization errors are introduced due 77

93 to limitations of the rendering hardware and algorithms. Wittenbrink et al. [43] visualized uncertainty in environmental data. This data is collected using radars and sonar buoys for measuring wind velocity and ocean currents. They visualize this data using different kinds of vector glyphs. Lodha et al. [23] have visualized uncertainty in fluid flow using uncertainty ribbons, envelopes, line segment glyphs, twirling batons and shearing barbell glyphs. Lodha et al. [24] have analyzed and estimated the geometric uncertainty introduced by surface interpolants. They visualize this uncertainty using swept probes, displacement mappings, cross hair glyphs and pseudo coloring. 78

94 Chapter 4 GIS GPS Infrastructure One of the most important aspects of this work is creation of a 3D GIS platform that can be used for visualization of uncertainty in the GIS-GPS data. We have made use of several layers of GIS datasets that are placed on top of each other. These include digital ortho-photos, digital elevation models, AutoCAD drawings, street maps, schematic diagrams, and LiDAR data. All the layers are projected and geo-referenced to the same underlying coordinate system in order to present a common consistent representation of reality. California State Plane Zone III coordinate system and Universal Transverse Mercator system have been used for most of the data. We begin by presenting the GIS-GPS infrastructure that we have created. This effort can broadly be classified into collection of GIS data from various sources and installation and operation of GPS equipment. 79

95 4.1 GIS Infrastructure Figure 4.1: 17 quads associated with the Santa Cruz County We begin by describing the USGS quads associated with the Santa Cruz County. There are 17 quads associated with the county. Figure 4.1 shows these quads with their names. Observe that the Santa Cruz quad actually spans two quads of which the left one is mostly ocean and also most of the southern part of both the quads is ocean Digital Ortho-photos Based on resolution and details the data sets used can be broadly classified as: Santa Cruz County data (Low resolution), Santa Cruz City data (Low to medium resolution), University of California, Santa Cruz Campus data (High resolution) The Digital Ortho-photos, as discussed earlier, are digitally rectified aerial images with geometric qualities of a map. We have used 1:12000 scale DOQs distributed by USGS for the Santa Cruz County which includes Santa Cruz City. 1:12000 scale translates to 1-meter pixel resolution with 300 pixels per inch. Figure 4.2b shows the College 8 area of the UCSC 80

96 (a) 1/2 ft. Resolution (b) 1 meter resolution Figure 4.2: DOQs of different resolutions for the same area (College 8, UCSC) 81

97 Campus using 1 meter resolution. These images were taken on October 30, These images are in a compressed JPEG format and are referenced with the NAD83 (North American Datum, 1983) California State Plane, Zone III coordinate system. Each DOQ covers 3.75 minute USGS quad and there is an overlap of about 700 meters between adjacent images. The total data size is about 350 MB for the entire county. There are 49 DOQQs covering the entire county. These images meet the 1:12000 scale NMAS accuracy standards as mentioned earlier. For the Campus we use 1:1800 scale DOQs provided by the UCSC Physical Planning and Construction department. 1:1800 scale translates to 0.5 ft. pixel resolution with 300 pixels per inch. Figure 4.2a shows the same College 8 area of the UCSC Campus using.5 ft resolution DOQ. These images were created as a result of an aerial survey conducted in the year These DOQs are encoded using TIFF image format and are also projected using the NAD83 California State Plane system, Zone III. Each image covers an area of 3000 X 3000 ft with an overlap of 0.5 ft. between adjacent images. There are 26 DOQs covering the whole Campus. These DOQs meet the 1:1800 scale NMAS accuracy standards (at least 90 of the test points lie within 5 feet of their true position) AutoCAD Drawings We have obtained some AutoCAD Drawings from the planning and construction department of UCSC. These drawings provide a highly detailed description of the terrain under the trees. We have used two types of drawings for the Campus. There are low-detail drawings for the entire Campus while there are high detail drawings for certain parts of Campus including the Baskin School of Engineering, Performing Arts center, Colleges 9 & 10, Baytree Bookstore, 82

98 (a) Digital Ortho-photo (b) AutoCAD Drawing Figure 4.3: Digital ortho-photo and AutoCAD Drawing for the same area (School of Engineering, UCSC). Digital ortho-photo is derived from 3.75 x 3.75 minute DOQQ and has a resolution of 1:1800 (1/2 ft). Chemistry Department and Cowell College. Figure 4.3b shows Baskin Engineering area with building and trailer footprints, tree footprints, paved and unpaved road boundaries, lamp posts, and parking lots displayed as line segments. We also have associated numeric and textual information such as spot elevations, tree diameters, building and trailer names, and tree types etc. This drawing dates back to April The high detail drawings are mostly in NAD27 California SPCS Zone III. We discovered that these AutoCAD drawings did not register very well with the DOQQs. The drawings seemed constantly off by about 100 meters from the DOQQs. The registration of these drawings was accomplished using some control points in the area. UCSC Campus has been divided into several sectors each spanning 1000 ft x 1000 ft. Some of the sector corners have been used as control points for many of these surveys. In addition, there are additional markers that have been used for registering the drawings. Figure 4.4 displays an 83

99 Figure 4.4: Low Detail AutoCAD Drawing of Baskin Engineering (UCSC Campus) AutoCAD drawing of the Baskin Engineering area with low details. This drawing dates back to April and July 1999 when the aerial photographs were acquired from which these drawings have been derived. These drawings are registered using NAD83 SPCS Zone III. These drawings contain several layers and the codes and the description of these layers are given in Appendix C. Although these low detail drawings include several layers, here we are displaying only building footprints, roads, vegetation boundaries, and building names. These low detail AutoCAD drawings were converted into shape files using Cad2Shape. This collection of shape files was then mosaiced together into one ASCIIshape file using a program created by us. We discuss this program in greater detail later Street Maps We have used centerline street maps for the Santa Cruz County provided by the Santa Cruz Police department in These maps are in MID/MIF format (MapInfo file). Figure 4.5 shows the street map of the Santa Cruz County. These maps are referenced using NAD83 spherical coordinates (latitude/longitude). We have converted these MIF files into shape files using a 84

100 Figure 4.5: Street Map of the Santa Cruz County utility called Mif2Shape within ArcView. These street maps when registered with DOQQs have non-uniform registration and are off by 8 to 9 meters. The low detail AutoCAD drawings of the UCSC Campus also contain the street maps as one of the layers. As stated before, these maps are in DWG format and have been provided to us by the Planning Department at UCSC. It is possible to extract street maps alone from these drawings and save them as shape files Schematic Diagrams We have acquired a schematic diagram of UCSC Campus. There are several versions available with varying levels of detail available in brochures, catalogs, calendars, souvenirs and web sites. Figure 4.6 shows a schematic diagram of UCSC Campus. This diagram contains information about building locations, names, street names, parking information, stop signs, 85

101 cross street, and several other facilities including 911 telephones. We have obtained this diagram as an AutoCAD drawing in the dwg format without any geo-spatial registration Digital Elevation Models (DEMs) We have acquired 16, 3.75 minute DEMs, one for each quad (data for one quad is missing) with 10 meter horizontal spacing that meets NMAS accuracy standards. These DEMs are 1:24000 scale. These DEMs are in NAD27 UTM coordinate system with vertical datum NAVD LiDAR Data We have acquired LiDAR data for the UCSC Campus and downtown Santa Cruz. This data was acquired in October 2001 by Airborne1 Inc. 1 In order to obtain accurate position for the aircraft we setup differential GPS stations at 2 NGS ground control points lying within 10 miles of the target area. One of the points was the CROWELL RM 3 monument ( deg N, deg W) on the UCSC Campus while the other monument was the TRAILL marker ( deg N, deg W) in Scotts Valley, CA. The data collection process took about 4 hours plus about 2 to 3 hours of setup time. We collected about 9 million points for the UCSC Campus and about 13 million points for downtown Santa Cruz. We have split the LiDAR data into 2 disjoint sets, one for the Campus and the other for the downtown. Each set is separated into 2 files: one for the vegetation points and the other for the bare earth. Each file is a point cloud represented as an

102 Figure 4.6: Schematic Diagram of UCSC 87

103 Figure 4.7: Sample DEM for the Santa Cruz City rendered as an image Figure 4.8: LiDAR and DEM data compared side by side 88

104 ASCII file with 5 columns namely Point type label, Easting, Northing, Height, and Intensity. The Point type label is used to identify the point as a bald Earth point or a vegetation point. The easting, northing and height point define the 3D coordinates of the point and the intensity value is the strength of the returned pulse. The data was provided to us with the horizontal coordinates based on Transverse Mercator projection with an unspecified origin. Since there was no ground survey done for the target area we were not provided with the absolute accuracy of the horizontal coordinates of the points. This data required geo-spatially registration. We performed this registration to NAD83 UTM coordinates by simple geometric transformations. We have converted the data into NAD83 SPCS coordinates using Corpscon utility [5]. The height values are based on NAVD 88 vertical datum. In order to render the LiDAR data more efficiently we have converted the point cloud to a grid by collecting the points into rectangular bins of a selected size. With the bin size 1 meter by 1 meter there are on an average about 2.6 points per bin. This gives us some idea of the horizontal data spacing of the resulting grid. The company that provided the data claims that the relative vertical accuracy of these points is about 15 centimeters. Figure 4.9 shows the LiDAR data as a point cloud and the same data gridded for the College 8 area on the UCSC Campus. This grid is 301 by 394 in meters and has points. 89

105 Figure 4.9: LiDAR point and gridded data for College 8, UCSC 4.2 GPS Equipment and Data Collection Setup In this section we begin by describing the GPS equipment that we have used and the experimental setup for data collection. We will also describe the type of terrain and environment available at the University of California, Santa Cruz Campus GPS Receivers We have used the Ashtech Z-12 sensor and G-12 sensor GPS receivers manufactured by Thales Navigation / Ashtech Precision Products Inc. As per the specifications, the G-12 unit is less accurate than the Z-12 unit. The G-12 sensor provides position accuracy up to 3 meters in standalone mode and 40 centimeters in differential mode. The velocity accuracy is 0.1 knots. The G-12 sensor is a single frequency receiver. It can only listen to L1 frequency messages. This implies that it depends on mathematical models in order to correct for the ionospheric delay. The G-12 sensor cannot listen to RTCM messages 18, 19, 20, 21. Therefore, it cannot be used for carrier phase differential corrections (RTK). This explains low accuracy of this unit. The maximum data update rate is 2 Hz. 90

106 The Ashtech Z-12 sensor is a high accuracy receiver. According to the specifications, it provides positional accuracy of 1 meter in the standalone mode and 1 centimeter in differential mode. The velocity accuracy is 0.1 knots. It is a dual frequency receiver which implies high accuracy in the standalone mode. This receiver can be operated in differential RTK mode which improves the positional accuracy tremendously. Both the receivers communicate with the PC via the serial I/O ports. The maximum data update rate for the Z-sensor is 10 Hz. A high data update rate is very useful when the receiver is operated in differential RTK mode Calibration The NGS (National Geodetic Survey) marker is the basis for calibration in our work. This marker is classified as a second order (horizontal accuracy) marker at 36 deg 59 min seconds N, and 122 deg 03 min seconds W. The vertical position is meters in NAVD88 datum. This marker has the following coordinates in California Zone III State Plane Coordinate System (SPCS III): 1,861, meters Easting, and 555, meters Northing. This marker (referred to as CROWELL RM3) is located near the East Field House on the UCSC Campus. With respect to this marker, we found that the average error in using the Ashtech Z-12 unit in standalone mode as 5.2 meters in horizontal position and 5.4 meters in vertical position. We calibrated the Baskin Engineering antenna using DGPS mode by placing the base station at the marker and placing rover at the Baskin Engineering antenna. We thus calibrated the Baskin antenna as 1,860, meters Easting, 556, meters Northing, and meters vertical. 91

107 Figure 4.10: Base antennas (on the roof of Baskin School of Engineering) It is not possible to calibrate the aerial imagery with respect to the NGS marker because it is not visible on the imagery. Therefore, the aerial imagery was calibrated using a cross-mark near the Theater Arts Building on Campus. This cross-mark was used originally by the surveyors in calibrating the aerial imagery. We calibrated this marker using DGPS mode by placing the base station at the Baskin antenna and the rover unit at the marker. The cross-marker was calibrated as 1,861, meters Easting, 555, meters Northing, and meters vertical. 92

108 Figure 4.11: Rover GPS Equipment Figure 4.12: Image of a student moving around collecting GPS data 93

109 4.2.3 Differential GPS and Radios We operate the GPS receivers as standalone as well as differential units. One of the Ashtech Z-sensors is set as a base reference station on the roof of the Baskin School of Engineering building (Figure 4.10). The other units (Figure 4.11) are used as rovers. For communication between the receivers we use Radio Frequency (RF) transmitters and receivers manufactured by Pacific Crest Corporation. These radios operate at the UHF band frequencies ( MHz). The specific band of frequency at is assigned to University of California Regents by the Federal Communications Commission (FCC) for DGPS operation. We set up DGPS in three different modes: Code phase differential mode (RTCM messages 1, 2, 9) Carrier Phase differential mode-rtk (RTCM messages 18, 19, 20, 21) Reverse Vector RTK The regular RTK mode of operation has been discussed in the previous sections. The reverse vector RTK is a special function provided by the Ashtech receivers in which the rover transmits its range readings to the base (instead of the base transmitting corrections to the rover as in regular RTK) and the base then computes the errors for the rover based on its known position. In this setup the rover cannot obtain its corrected position in real-time but the base can track the rover with a high degree of accuracy. In order for the rover to know its corrected position we need to establish a two-way communication channel between the base and the rover. 94

110 4.2.4 GPS Readings GPS units provide several outputs including information on position, velocity, satellite availability, DOP values, and signal strength. Position Antenna position is the most basic parameter of interest. We log several observations and then take an arithmetic mean of those observations in order to accurately locate the position. The three-dimensional position of the receiver can be expressed in X, Y and Z offsets in different coordinate systems. In geodetic coordinates X, Y, and Z are expressed using longitude, latitude and altitude of the receiver. The latitude and longitude are generally referred to as the horizontal coordinates and are measured in degrees, minutes and seconds while the altitude is referred to as vertical coordinate measured in distance units (meters/feet). The horizontal coordinates are sometimes also expressed in different systems such as Universal Transverse Mercator (UTM) system where X and Y are referred to as easting and northing respectively and are expressed in meters. This is sometimes useful for visualizing these coordinates over GIS data that has already been referenced to that system. Speed GPS receivers also provide user speed information. Some receivers determine the velocity by simply using the derivative of the position estimates. This method typically assumes a constant speed model. Some more intelligent receivers estimate user speed using the Doppler frequency of the received satellite signals which is caused by the relative motion of the satellite 95

111 with respect to the user [7, 41]. In case of a stationary user the speed estimates are highly erroneous. Direction or Course Over Ground (COG) Along with the position and speed the receivers also compute the direction (or heading) in the form of COG values. The COG value is the angle in degrees specifying the direction with respect to true north or magnetic north of the Earth. This direction is generally a derived value and indicates the direction of motion. This value is highly erroneous if the receiver is stationary. Available satellites One of our control parameters is the type of environment which includes semi-open and closed environments. At times, we may not be able to obtain the user position/velocity information because of insufficient number of satellites or poor signals. Therefore, the number of available satellites is an important parameter to take into account in these environments. Generally, more number of satellites decreases the DOP values thereby resulting in better accuracy. Dilution of Precision values To compute the position the GPS receiver selects satellites such that it minimizes the Geometric Dilution of Precision (DOP). The receiver also outputs these DOP values along with the position and velocity estimates. Satellite availability and DOPs: The accuracy of GPS position depends upon the 96

112 (a) Satellite visibility (b) Availability and DOP Figure 4.13: Satellite visibility (green) and DOP (red) charts for UCSC Campus (Lat: 37deg 0min 0sec, 122deg 05min 0sec) 97

113 number of visible satellites and the Dilution of Precision that depends upon the geometry of the satellites. The number of visible satellites and the DOP values at any given position varies with time but can be computed since the orbit of the satellites is very accurately known. The satellite visibility and DOP charts are shown in Figure These charts are for UCSC Campus (Lat: 37deg 0min 0sec, 122deg 05min 0sec). The satellite availability is determined using the GPS Almanac data which contains the position of all the satellites at a given instant of time. This almanac data can be obtained from the satellites through the GPS receiver. Since the satellite orbits are highly predictable, using the almanac data we can determine the availability and hence the DOP values for any other time. The visibility chart in the shows the availability period and time for each satellite. The availability chart shows the total number of satellites available at a given instant of time and the corresponding PDOP values for that location. Satellite Signal-to-Noise Ratio As discussed earlier the GPS receiver outputs the signal strength received from each of the satellites as Signal to Noise Ratio (SNR) [41] values expressed in db-hz. It is generally observed that the receiver accuracy improves with increased signal strength and therefore, we will use SNR as one of the parameters for modeling the uncertainty Ashtech Software In order to make receiver communication easier Ashtech also provides software called Ashtech Evaluate to perform the basic communication with the receiver. Ashtech Evaluate provides an easy-to-use interface to the user. The software provides basic functions of initializ- 98

114 ing, querying the receiver and logging the responses in an ASCII text file. It can also perform certain basic analysis on the data received such as computation of arithmetic mean and standard deviations in the values. It also performs preliminary visualization by displaying scatter plots with error bounds that can be set by the user. In order to perform visualization in real-time in a GIS environment, we have developed a program that communicates with the receiver and registers the GPS position and velocity estimates on the GIS background in real-time Type of environment The University of California, Santa Cruz Campus consists of different types of terrain and environments. A large portion of academic part of the Campus consists of areas of thick foliage with tall redwood trees. There are also large open field areas with perfectly clear access to the sky. Certain areas are hilly with ravines and valleys while others are relatively flat. This provides us with many options for choosing the type of environment we want to study. The Campus is divided into 26 zones by the Campus Planning department, each about 3000 ft. wide and 2000 ft. long. Figure 4.14 shows an aerial view of the UCSC Campus. Since GPS uses RF (Radio Frequency) signals that require line of sight, the type of environment then becomes a major factor affecting the accuracy of the readings. There are two parameters directly affected by this the satellite visibility and multipath effects. Ideal environment: We define an ideal environment as being completely open with clear access to the sky. In such an environment there are no obstructions such as trees, buildings or other objects above 10 degree antenna mask angle. Therefore, we expect to be able to see 99

115 Figure 4.14: An aerial view of the UCSC Campus more satellites with negligible multipath effects, resulting in minimum error. Urban environment: In an urban environment we do not have a very clear access to the sky. There are objects such as buildings, trees and and other objects obstructing the satellite signals. This results in certain satellite signals getting either blocked or reflected. In such an environment we expect to be able to get position data that is relatively more erroneous. Foliage environment: In a thick foliage environment where we have almost no access to the sky we expect not to be able to see enough satellites for estimating the position. The satellites we see may have a very poor, badly reflected signal. 100

116 4.2.7 Data Logging Convention and Log File Format We log the data emitted by the GPS receiver using the Ashtech Evaluate software. The naming convention is as follows: zone number/date time mode position# sensortype.log (format) ddc/dddddd dddd c dd c.log (example) 07c/ s 01 z.log The log file created consists of a sequence of readings. Each reading spans multiple lines recording responses to queries issued. Some of the important queries are discussed below briefly. For a more detailed explanation, please refer Appendix A. Instantaneous position query ($PASHQ, POS): The response to this query includes the instantaneous position in latitude, longitude and altitude along with the dilution of precision values Satellite status query ($PASHQ, SAT): In response to this query the receiver outputs the various parameters associated with each satellite such as the satellite signal strength and whether the satellite has been used for position fix. Position query in UTM coordinates ($PASHQ, UTM): The response for this query includes the easting, northing and zone number in UTM coordinates Modes, Environments and Movement All data reported in this work was taken during the afternoon on clear and sunny days. These times yield the most desirable (smallest) DOP values. Data was collected in two modes: standalone and differential, and in two types of environments: urban and foliage. We 101

117 identified the area around College 8 on UCSC Campus as an urban environment with some obstructions to satellite visibility by low height buildings, trees, vehicles etc. We chose the area behind the Baskin School of Engineering on the UCSC Campus as a foliage environment. This area is covered with dense foliage such that the ground under the foliage is not visible in the aerial imagery. Therefore, we have used high detail ground survey AutoCAD drawings for visualization of this area superimposed over the aerial imagery. We used three different types of movement to collect data. In the first movement type, referred to as static, data was collected in a stationary position (typically about 100 readings at the rate of 1 reading per second for less than 2 minutes). In the second type of movement, data was collected while walking in a straight line with as close to constant speed as possible. This is referred to as constant velocity walk model. In the third type of movement, the user walks comfortably on a random path, referred to as random walk. 102

118 Chapter 5 Observations, Analysis and Modeling In this section we present some observations and preliminary analysis of GPS data collected using methods described in Section These results have also been discussed in detail by Lodha et al. [21]. 5.1 Static Data In College 8 area of UCSC Campus, readings were obtained for 44 points in standalone mode and 15 points in DGPS mode with negligible loss of readings. In Baskin Engineering area, readings were obtained for 40 points in standalone mode and 8 points in DGPS mode. Out of these 40 points in standalone mode, no reading was obtained at 10 points due to heavy foliage and less than 5% readings at 1 point. The remaining 29 points returned more than 85% readings. In DGPS mode, 1 point returned less than 5% readings and the remaining 7 points 103

119 (a) Horizontal Posi- (b) Horizontal Posi- (c) Vertical Position (d) Vertical Position tion (S U) tion (S F) (S U) (S F) (e) Horizontal Posi- (f) Horizontal Posi- (g) Vertical Position (h) Vertical Position tion (D U) tion (D F) (D U) (D F) Figure 5.1: Distribution of GPS readings at a stationary position (approximately 100 readings each), S: Standalone, D: DGPS, U: Urban, F: Foliage returned more than 85% readings. Our observation was that the foliage region can be divided into two zones, one returning very few readings and the other returning most of the readings. Figure 5.1 presents typical distributions of horizontal and vertical readings at one fixed point in urban or foliage environment using standalone or DGPS mode. Figure 5.2 presents the distribution of horizontal errors, vertical errors, SNR values, and DOP values in urban and foliage environment using standalone or differential mode. Table 5.1 presents the mean and standard deviations of these data attributes. For the 104

120 Figure 5.2: Distribution of means: (from left to right) horizontal error, vertical error, SNR, and DOP; (from bottom to top) standalone urban (SU), standalone foliage (SF), DGPS urban (DU), and DGPS foliage (DF) Standalone Differential H-Error V-Error SNR DOP H-Error V-Error SNR DOP U (6.67,2.38) (14.81,6.4) (50.23,1.09) (1.74,0.43) (0.77,0.51) (1.53,0.70) (49.17,0.51) (1.36,0.31) F (10.72,5.49) (14.64,12.78) (45.75,1.87) (5.38,3.20) (1.75,2.30) (3.31,1.89) (47.06,1.81) (8.89,3.09) Table 5.1: Mean and standard deviations for static Data; H-Error (horizontal error) and V-Error (vertical error) are in meters, SNR is in db-hz, DOP is measured as a ratio. computation of SNR and DOP values, each reading at a point uses a varying number of satellites and therefore a varying number of SNR values. We first compute the mean of the SNR and DOP values for each reading, taking into account only those satellites that were used to generate the GPS reading. A second averaging is done to obtain the mean SNR or DOP value at a point over all the readings. We now make some observations about the GPS readings. For both horizontal and vertical position, both error and standard deviation is much larger in foliage than in the urban environment, as expected. Errors using DGPS mode are much less than in the standalone mode, also as expected. Standalone data, however, exhibits a track pattern, while DGPS data seems more random. The track pattern is perhaps exhibited because a number of readings are obtained using a fixed set of satellites for a while and when that set of satellites changes, it causes a jump in the reading. In contrast, since DGPS readings deal with differences between the same set of 105

121 satellites used by the base and the rover, the errors are randomized. The number of satellites accessible in the urban environment were typically 7 to 8 of which about 5 to 6 are used to generate the GPS reading. In the foliage environment, there are regions where less than 4 satellites are available, generating no reading. Where readings are available, the typical number of accessible satellites was 5 to 6, while only 4 to 5 are used to generate readings. DOP (dilution of precision values) and SNR values associated with the readings are good indications of confidence in these readings. Figure 5.2 and Table 5.1 shows that the SNR values associated with foliage data are much smaller than the SNR values associated with the urban data. There does not seem to be any significant difference in SNR values between the standalone and differential mode for urban data. DOP values for DGPS are much larger than the DOP values for the standalone mode, even though the accuracy in differential mode is much higher. This occurs because in differential mode, the rovers are constrained to use the same satellites as the base stations. This reduction in the choice of the satellites causes an increase in DOP values. 5.2 Constant Velocity Walk We have found little literature on estimating the accuracy of velocity readings for GPS receivers. However, we needed some estimate of velocity and associated error for an object in order to predict the probable position of the object. To this purpose, we have attempted to model velocity errors using a constant velocity walk model. In this model, a user is constrained to walk on a straight line for about 2 minutes with a pace as uniform as possible. By measuring 106

122 Standalone Differential S-Error D-Error SNR DOP S-Error D-Error SNR DOP SW (0.18,0.13) (10.45,7.72) (50.55,1.27) (1.86,0.26) (0.08,0.13) (5.4,5.99) (49.0,1.37) (1.52,0.36) RW (0.26,0.21) (12.60,8.85) (50.96,0.88) (1.93,0.24) (0.13,0.16) (5.28,6.88) (49.72,1.21) (1.76,0.84) FW (0.40,0.31) (9.18,8.09) (50.19,1.22) (1.92,0.23) (0.31,0.26) (6.72,6.3) (49.75,0.91) (1.61,0.35) Table 5.2: Mean and standard deviations for speed error (S-error) in meters per second, direction error in degrees, SNR, and DOP values using three different types of walk:slow walk (SW) at 1.26 m/s, regular walk (RW) at 1.61 m/s, and fast walk (FW) at 1.89 m/s using standalone/differential mode in the urban environment the distance between the points, the start time and the end time, one can compute the constant velocity needed to cover the measured distance in the measured time. One can then compare the observed velocities with the assumed velocity. This experiment was repeated for three different values of speeds slow walk, regular walk, and fast walk in urban and foliage environment using standalone and differential mode. (a) Standalone mode (b) Differential mode Figure 5.3: Distribution of velocities in urban conditions: (from top to bottom) slow walk, regular walk, and fast walk; the arrows underneath denote the true (assumed) velocity In the foliage environment, most of the readings (more than 95%) were missing even though static data could be obtained at several points along this path. This occurs because it takes some time for the receiver to lock on to the satellites before a GPS reading can be generated. Therefore, during a constant velocity walk, there is not enough time at most of the 107

123 points to obtain a GPS reading in the foliage environment. The mean and standard deviation for errors in speed and direction, with associated SNR and DOP values, are shown in Table 5.2. Figure 5.3 visualizes the idealized (assumed) velocity with measured velocity. We observe that the error in speed tends to increase with the speed of the user in both standalone and differential mode. Directional errors seem to arise from the same distribution although hypothesis testing will need to be done to establish or refute this observation. In other words, directional errors do not seem to depend upon velocity. We also observe that errors in both speed and direction are much smaller in DGPS mode as compared to the standalone mode. Significantly, the standard deviations of both speed and directional errors are very large in comparison with the mean values. SNR values do not seem to be affected due to walking and are very close to values obtained during static data collection. There does seem to be an increase in DOP value for both standalone and differential mode. This is expected since there is less time at each position to lock the satellites while walking. 5.3 Random Walk Here we collected the data by walking through a random path in both urban and foliage environment in both standalone and differential mode. The walk lasted about 8 to 10 minutes. In the foliage environment, the readings obtained were too sparse to be of much use. 108

124 5.4 Modeling When a GPS reading is reported by a receiver, the point can be visualized on an aerial image by using a glyph, such as a small dot. This would be ideal if the readings were accurate and can be registered on the map with high accuracy. However, in practice, there is always an error associated with these readings. How do we model these errors? In this work, we have attempted to model errors associated with horizontal position, speed and direction for standalone mode that we later utilize in Chapter 6 to visualize the random walk. (a) (b) Figure 5.4: Fitting linear (dark line) and exponential curves (faint line) for horizontal errors vs. SNR in standalone mode for urban and foliage environment using static data. For horizontal errors, we use the least squares method to make a linear fit for horizontal error with SNR separately for urban and foliage environment. Figures 5.4a and 5.4b show the linear fit (dark straight lines) for the urban and foliage data respectively. The equations of the fits for the urban and foliage are respectively: E 0 6SNR 37 0, and E 0 8SNR Separation of these two data clusters seems justified because the data samples appear 109

125 to come from two different distributions. However, since accuracy is expected to deteriorate rapidly with the decrease in SNR below certain values, we also made a linear fit with log error vs. SNR. The equation of this line is lne 0 092SNR 6 5. This line is also shown in Figures 5.4a and 5.4b as a faint curve. For the purposes of visualizing uncertainty in Section 6, we have used the linear fits. We now describe how we have modeled the errors in speed and direction. For the standalone urban data, we have used the constant velocity walk model to estimate the uncertainty associated with speed. Since the standard deviations of both speed and direction errors are significant, one could use a sampling method to assign an error estimate for speed and direction at every point assuming Gaussian distribution for these errors. Means and standard deviations of these distributions, however, will depend upon the speed since errors seem to increase with increasing speed. In practice, using a one sigma deviation, uncertainty in speed can be estimated to be roughly one-third of the observed speed. Directional errors, for similar reason, can be taken to be roughly 20 degrees irrespective of the speed. Further research is required to estimate uncertainty in speed and direction more accurately. 110

126 Chapter 6 Visualization We now discuss visualization of the uncertainty associated with the GPS data. Using traditional deterministic methods without uncertainty, the standard technique to display the position would be to draw a dot for each reading obtained by the GPS. In our approach, we advocate computing uncertainty associated with each reading and visualizing the position of the particle along with its uncertainty. 6.1 Visualization of Uncertain Particle Movement In this section we present an algorithm for visualizing a particle with uncertain initial position and motion. We can represent the initial position, speed and direction of an object as probability density functions (PDF). We can then compute the probability of the object being present in a given region at any given instant of time using the position, speed and direction PDFs. We can propagate the object as a probabilty cloud that can be visualized as a galaxy 111

127 of spherical glyphs with the size of each glyph representing the probability of the object being at that position at that instance of time. We can also use transparency and pseudo-coloring schemes to visualize the cloud with more opaque regions indicating higher probability. We present the algorithm with the special case of gaussian probability distributions. Our algorithm assumes the availability of three probability density functions: Position PDF f 1 p that represents the initial position of the object Direction PDF f 2 d that represents the initial direction and Speed PDF f 3 s that represents the initial speed We compute the probability distribution of the position of the object after a short interval of time T. If T is small enough then we can safely assume that the speed and direction do not change much as compared to the uncertainty in their measurements. Thus the probability P of the object being in a region R can be computed as: P p R f 1 p f 2 d f 3 s ds dd d p The integral is replaced by summation for the discrete case. For the two-dimensional case, the world is defined as a rectangular grid and the initial position of the object is on a particular grid point. After a time interval T, all possible points that are reachable from this position are contained within a circular annulus as shown in Figure 6.1. The size of the arc of the annulus is proportional to the directional uncertainty while the thickness of the annulus is determined from the uncertainty in speed. If the initial position is exactly known then there is only one annulus arising due to uncertainty in speed and direction. However, if the initial 112

128 position is uncertain then there will be an annulus generated from every possible position the object could be. Our algorithm begins by computing the probability starting from every grid that has a non-zero probability of the object s initial position and determining the annulus of resulting points generated. The resulting probability values are snapped to the closest world grid points. This computation is performed for every initial grid point and the probabilities collected at every world grid points are aggregated to obtain the final probability of the object being at particular point. (a) (b) Figure 6.1: Circular annulus representing the position of the uncertain object after a short time interval We present the case where the probability distributions are Gaussian. For efficiency of computation we take advantage of the symmetry and separability of Gaussian PDFs. We also restrict the computation to three standard deviations. The complete algorithm along with the computational complexity is described in the paper by Lodha et al. [22]. 113

129 (a) Horizontal position error for random walk through an urban environment as diffused blobs (b) Horizontal position error in random walk in heavy foliage conditions (c) Speed and directional errors visualized as glyphs (d) Horizontal position error for random walk through an urban environment as diffused blobs Figure 6.2: Visualizing horizontal position and velocity uncertainty 114

130 6.2 Visualization on a GIS Background We have applied modeling described in Chapter 5.4 to estimate the uncertainty associated with each reading. Here, each reading is drawn not simply as a dot, but as a probability cloud gradually fading away as the probability of the particle being away from the observed position decreases. Figure 6.2a shows uncertainty in position of the particle in urban environment. We have sub-sampled the readings of the random walk by taking every fourth reading in order to display the uncertainty circles associated with each reading clearly. If we do not subsample, then a brush-stroke like tube is generated that displays the region of uncertainty. Figure 6.2b shows an attempt to display a similar image for the random walk around the foliage region. Since a static snapshot is shown for the whole walk, several readings have merged to form big blobs. We have viewed the evolution of the blobs as the walk proceeds in time. In contrast to the urban walk, where there is predictability of the path, uncertainty in random walk through the foliage region is so high that the path of the movement of the particle is not clear. In this case, additional assumptions or knowledge of the movement of the object need to be used to decrease the uncertainty. In our work, our goal is to visualize the spatio-temporal uncertainty associated with the particle s movement in time. We have used a number of techniques including deformed glyphs, texture mapping, pseudo-coloring, transparency, animation, overlays, and lighting for visualizing uncertainty [23, 24, 43]. In essence, we are trying to predict where the particle is in between the two readings. To this purpose, we estimate the uncertainty in speed and direction at every reading and advect the particle in time. Figure 6.2c shows the random walk along 115

131 with associated uncertainty in speed and direction. The directional spread in fans at each point indicate uncertainty in direction. The length of fans depict the uncertainty in speed. Due to these uncertainties, the particle gets smeared as time progresses. Figure 6.2d shows the spatiotemporal uncertainty in the position of the particle for the random walk data. Data was missing after the fourth reading for the next three units of time. Using the estimates of uncertainties for position, speed, and error, we obtained the smearing as a banana type shape. In our previous work [22], we have shown that depending upon the values of means and standard deviations, this and many other recognizable shapes such as bow-tie, fan, ball, etc. can arise that provide the user with a quick understanding of the nature of uncertainty associated with the particle s movement. 116

132 Chapter 7 VGIS extension at GIS-VIZ Lab 7.1 Initial Setup We have transferred VGIS at the GIS Visualization lab, UCSC. The system is functional on SGI (Octane2, Onyx2) as well as PCs. The system was difficult to compile as there were many path strings in the code that were specific to the data visualization lab at Georgia Tech. Also, the compilation options were set to suit the environment at Georgia Tech. For example, the linker options were set to use the old deprecated GL library instead of the newer one. We traced and corrected these problems. VGIS was originally packaged with 3 datasets. High resolution data for the Georgia Tech Campus along with low resolution data for Atlanta and the State of Georgia, Grand Canyon, and the US Military base in south-eastern California. 117

133 7.2 Building VGIS datasets With the help of some of VGIS developers (Tony Wasilewski, Olubenga Omoteso) we have acquired the utilities to build VGIS datasets. The process of building VGIS datasets is described in detail in Appendix B. 7.3 Insertion of Santa Cruz data into VGIS Using the method described in the previous section we have inserted 1-meter resolution DOQQs and 10-meter resolution DEMs for the Santa Cruz County, into VGIS. We have also inserted high- resolution (1/2 foot) Santa Cruz City imagery and the UCSC Campus imagery into VGIS. Currently, we are working towards inserting LiDAR height data into VGIS. 7.4 Visualization of GPS tracked objects in VGIS In this section we present the details of extending VGIS to support visualization of mobile objects that have uncertainty associated with their position and velocity D Object support in VGIS VGIS supports visualization of 3D geometric objects [10]. This support has been implemented as part of VGIS in the form of an Object API. Objects geometry and texture can be loaded from a file. The primary object format is the VGIS Object Format (VOF) which is native to VGIS. VGIS also supports external standards formats such as the OBJ format. Complex geometric models can be created using standard utilities such as Wavefront, Maya or 118

134 Figure 7.1: Visualization of Uncertain Objects in VGIS 3DStudioMax and can be exported into the OBJ format. These objects are then loaded into VGIS and placed in an appropriate scene graph. The use of scene graph allows for creating object hierarchies and groups that can be used to define various levels of detail for objects similar to the terrain. The object API supports traversal and modification of the object hierarchy. The position and orientation of individual objects in the hierarchy can be changed. Simple geometric transformations such as translation, rotation and scaling can be applied to these objects. 119