Availability and Reliability Advantages of GPS/Galileo Integration

Transcription

1 Availability and Reliability Advantages of GPS/Galileo Integration Kyle O Keefe Department of Geomatics Engineering The University of Calgary BIOGRAPHY Kyle O Keefe is a graduate student at the Department of Geomatics Engineering of the University of Calgary. He received a Bachelor of Science in Honours Physics from the University of British Columbia in 1997 and a second undergraduate degree in Geomatics Engineering from the University of Calgary in. ABSTRACT The performance of a Global Navigation Satellite System (GNSS) can be quantified by availability, accuracy and reliability. The deployment of Galileo by the European Union will provide double the number of navigation satellites currently available to users and offer improvements in accuracy and reliability. This paper briefly describes the design of the proposed Galileo system. Availability and accuracy are then defined and statistical reliability theory is reviewed. Worldwide availability, accuracy and reliability estimates for GPS, Galileo and the combined GPS/Galileo system are obtained by software simulation. The simulation results are presented using Horizontal Dilution of Precision (HDOP) as a measure of availability and accuracy and maximum Horizontal Position Error (HPE) due to one undetected blunder as a measure of reliability. The proposed 3 satellite, 3 orbital plane Galileo constellation shows a slight improvement over the existing GPS constellation when low elevation masks are employed. At higher mask angles GPS slightly outperforms Galileo. The use of the two systems together is shown to provide major improvements in accuracy and reliability. A local simulation comparing the availability of GPS and Galileo in an urban environment is also presented. The use of GPS and Galileo together is shown to provide the necessary satellite availability to obtain a navigation solution in extreme masking environments. INTRODUCTION The accuracy and reliability of Global Navigation Satellite System (GNSS) navigation solutions is of great importance to land, sea, and air users. Unfortunately, the existing GPS constellation in unable to provide the necessary accuracy and reliability demanded by some users. The European Union is currently developing a GNSS called Galileo. The system will provide worldwide coverage using multiple L-band frequencies. Four levels of service are planned, including a single frequency Open Access Service (OAS), two controlled access services (CAS1 and CAS), and a secure government access (GAS) (ISPA ). Provided that the EU approves the Galileo project, it is expected to be operational by. The proposed Galileo system is discussed in detail in Tytgat and Owen (), Lucas and Ludwig (1999) and Hein (). Having access to two independent GNSSs provides many availability and reliability advantages that have been discussed in many previous investigations. (Ryan et al. (199), Ryan and Lachapelle (1999), Ryan and Lachapelle ()). All of these papers have dealt with the use of either the Russian GLONASS system or the proposed Galileo system for augmentation of GPS. In this paper, GPS alone will be compared with both Galileo alone and a combined GPS/Galileo system. Galileo Constellation The Galileo System is still in the definition phase and a final constellation design has not yet been made public. Papers discussing the design of the constellation presented in the last two years have presented various proposed constellations consisting of combinations of Medium Earth Orbiting satellites (MEOs) and Geostationary satellites (GEOs). Lucas and Ludwig (1999) discuss a MEO + 3 GEO constellation (with Geostationary satellites visible to Europe and Africa only), Tytgat and Owen (1999) consider both MEOs + globally distributed GEOs and a 3 MEO constellation. In both cases they state that the orbital altitude will be around 3 km. Ryan and Lachapelle () present simulation results for a MEO plus 9 GEO constellation and a 3 MEO constellation, both with a MEO orbital altitude of km. Oehler et al. () consider only a 3 MEO constellation with orbital altitude of 3 km. Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page 1

2 In this paper, only the 3 MEO Galileo constellation is considered as it seems to be the most likely choice. It consists of 3 satellites equally spaced in three orbital planes with an inclination of 5 degrees. An orbital radius of km is used (orbital altitude of 3 km above the semi-major axis of the WGS reference ellipsoid). This constellation will be compared with the GPS constellation as it existed at the beginning of GPS week 19: 7 MEOs unequally spaced in orbital planes. Performance Measures for a GNSS Availability, accuracy, reliability and integrity are often used as measures to quantify the performance of a navigation system. Some of these have several different definitions. To avoid confusion, each is measure is defined below. In the context of GNSS, availability usually refers to the number of satellites or other ranging signals available to the user. From a generic radionavigation standpoint, availability refers to the percentage of the time a system is able to provide the user with navigation solutions. This is the definition used in the US Federal Radionavigation Plan (FRP). In this paper, availability will be used to refer to the number of satellites visible to the user. Accuracy is a measure of how close the navigation solution provided by the system is to the user s true location and velocity. Generally, the accuracy of a system can be decomposed in two quantities: User equivalent range error (UERE) and geometric dilution of precision (GDOP). UERE is obtained by mapping all of the system and user errors into a single error in one user measured range. GDOP is the satellite geometry dependent quantity that maps the UERE (an error in observation space) into a user accuracy (in position space). GDOP can also be decomposed in to constituents parts, namely position, horizontal position, vertical position, and time: PDOP, HDOP, VDOP, or TDOP respectively. DOP values are good measures of system availability as they represent the geometric strength of the solution. DOP values can also be used to represent system accuracy when it is assumed that all range measurements have the same UERE. In many navigation situations, the user is interested in using a GNSS to obtain a horizontal position. For example, marine users, or land users constrained to the surface topography. For this reason, HDOP will be used as a measure of availability and accuracy in this paper. In this paper, reliability will refer to the ability to detect blunders in the measurements and to estimate the effects of undetected blunders on the navigation solution. A brief overview of statistical reliability theory is given in the Statistical Reliability Overview section below. More detailed discussions of reliability theory can be found in Leick (1995) and Koch (1999). The final measure of GNSS performance, integrity, is defined as the ability of a system to provide timely warnings to users when the system should not be used for navigation (FRP, 1999). Other definitions of integrity combine the concepts of reliability and integrity under the title Integrity Monitoring. An example of this is presented in Zink et al. () and further definitions are given in Ober (1999). Integrity is only considered in this paper as a part of reliability theory. STATISTICAL RELIABILITY OVERVIEW Reliability can be subdivided into internal reliability and external reliability. Internal reliability refers to the ability of the system to detect a blunder through the statistical testing of the least squares residuals on an epoch-to-epoch basis. The largest such blunder is called the marginally detectable blunder (MDB). The external reliability of a system is quantified by size of the error in the navigation solution that is caused by a marginally detectable blunder. In order to detect a blunder in an observation using a least squares approach, statistical testing is conducted on the least squares residuals. In least squares estimation, it is assumed that the residuals are normally distributed. If a blunder is present in an observation, its residual will be biased, but will remain normally distributed. Note that residuals, and hence redundancy in the observations, are required. The least squares residuals are given by: rˆ 1 = C rˆ C l w = -Rw where C r is the covariance matrix of the residuals and C l is the covariance matrix of the observations. R is the redundancy matrix and the redundancy of an observation can be expressed by its redundancy number: R = 1 { C rˆc l } ii (1) ii () Which is the i th diagonal element of R. The covariance of the residuals is equal to the covariance of the observations minus the covariance of the parameters, C x, mapped into observation space by the design matrix A. As with availability and accuracy, there are multiple definitions of reliability. The FRP defines reliability as one minus the probability of system failure (FRP, 1999). C rˆ T = C l AC xˆ A (3) Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page

3 C r is always less than or equal than C l, meaning that R ii is always between and 1. A redundancy number of 1 would mean that the observation is completely redundant and thus easily monitored for blunders while a redundancy number of indicates that the navigation solution depends completely on the i th observation making the identification of a blunder impossible. To detect a blunder each residual can be statistically tested where the null hypothesis, H o, is that the residual is unbiased while the alternative hypothesis, H a, is that the residual is biased. The distributions of the two hypotheses are shown in Figure 1. When such a test is performed, two types of errors may occur. If a good observation is rejected, a type one error occurs. The probability of this is denoted by α. A type two error occurs when a blunder is accepted into the solution. The probability of committing a type two error is denoted with β. Choosing values of α and β determine a bias or non-centrality parameter of H a and is denoted by δ o. δ ο α/ β α/ H o H a Figure 1: Statistical testing of least squares residuals. The marginally detectable blunder for observation i, can then be obtained by multiplying δ o by the standard deviation of the residual and dividing by the redundancy number. i δ = o R C ii r ii () Since each residual has a different standard deviation and each observation has a different redundancy, each observation has a different MDB. Assuming only one blunder occurs in a given measurement epoch, the maximum effect of one undetected blunder can be determined by evaluating the effect of each marginally detectable blunder on the navigation solution. 1 T 1 T 1 X = ( A C A) A C (5) l Where is a column vector of zeros except for the i th row which contains the marginally detectable blunder of the i th observation. In the paper, reliability will be quantified by the maximum horizontal position error (HPE) due to a single l marginally detectable blunder. This is obtained by evaluating the horizontal component of X for each observation s marginally detectable blunder. SIMULATIONS The availability and accuracy (HDOP) and reliability (maximum HPE due to one marginally detectable blunder) of GPS, Galileo, and the combined system were compared using a software simulation. The simulations were conducted globally over 17 points corresponding to 5 degree spacing in latitude and 5 degree spacing in longitude with longitude spacing increasing at higher latitudes. The simulation points are shown in Figure. Isotropic masking angles of, 1,, 3, and degrees were employed. The GPS, Galileo and combined systems were each tested alone, and augmented with a height constraint, a clock constraint, and both a height and clock constraint. A height constraint is commonly employed in marine navigation and land navigation where a digital terrain model, or simple mean local elevation, is available to the user. A clock constraint can be applied by a more advanced user with a precise oscillator with modeled clock behavior. Variances of m and 1 m were used for the height and clock constraints respectively. Each simulation for each of 17 locations, 3 systems, 5 elevation masks, and constraint sets was conducted over hours in second increments. 9 o N o N 3 o N o 3 o S o S 9 o S 1 o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W Figure : 5 degree globally distributed simulation points. While HDOP is dependent on geometry alone, simulation of maximum HPE requires an observation variance or user equivalent range error and statistical reliability parameters. Two observation variances were used. m to simulate a single frequency standalone user and 1 m to simulation either a dual frequency or differential user. Reliability parameters of α =.1%, β=1% were used resulting in δ o =.57 meaning that the marginally Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page 3

4 detectable blunder for a completely redundant observation is.57 standard deviations from the mean, blunder free, value. The urban canyon simulation was conducted at one point, corresponding to the city of Calgary, using elevation masks corresponding to a user standing in the middle and at the side of a m wide street with 15 m high buildings on either side. Simulations were conducted with the street running North/South and East/West. SIMULATION RESULTS 9 o N o N 3 o N o 3 o S o S Gal HDOP 95% for Mask The simulations described in the previous section produced a very large number of results. Only a small subset are shown here. The section will begin with availability/accuracy results for the isotropic mask angle simulations, followed by reliability results for the differential/dual frequency case and reliability results for the standalone case. The section will conclude with availability results for the urban canyon simulations. Global Availability Results The easiest way to present the simulation results is a global contour map. Figure 3, Figure, and Figure 5 show contour maps of the 95 th percentile values of HDOP for a user with a degree elevation mask for GPS, Galileo, the combined system respectively. 9 o N GPS HDOP 95% for Mask 9 1 o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W Figure : 95 th percentile values of HDOP for a isotropic mask angle using Galileo with no constraints. 9 o N o N 3 o N o 3 o S o S GG HDOP 95% for Mask o N 9 1 o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W 3 o N o 3 o S o S 9 1 o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W Figure 3: 95 th percentile values of HDOP for a isotropic mask angle using GPS with no constraints Figure 5: 95 th percentile values of HDOP for a degree isotropic mask angle using combined GPS and Galileo with no constraints. In this case, no additional constraints were applied. To display all of the global results (3 systems, constraint cases, 5 mask angles) on contour maps would be very impractical. Instead, the results can be summarized by grouping all of the global points. Figure shows the 95 th percentile value of HDOP worldwide for all cases considered. This figure allows for easy comparison between the two independent systems and demonstrates the large improvement obtained by using the combined system. Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page

5 HDOP HDOP Percentile 95% 1 3 environments are evident while improvement at and 1 degree mask angles is marginal. An other interesting result is the slightly better performance of GPS compare to Galileo when a degree elevation mask is used. This may be due to the better geometry provided by six plane GPS constellation. With extreme masking angles, the possibility of observing only satellites in one orbital plane, and thus having very poor positioning geometry, is more likely with a three plane system. Differential/Dual Frequency Global Reliability Results 1 Figure : 95 th percentile values of HDOP (worldwide) for GPS, Galileo, and the combined systems with no constrants (N), height constraint (H), clock constraint (C), and both height and clock constraints (B). Results are plotted for isotropic elevations masks of, 1,, 3, and degrees. For a slightly different perspective, the results displayed in Figure can be reversed to show the percentage of the time that the HDOP is less than a given value. Figure 7 shows the percentage of simulation points (in time and space) where the HDOP is less than. 1 9 HDOP Value The reliability results can be displayed in an identical manner. Figure shows the 95 th percentile values of maximum HPE for one marginally detectable blunder using GPS alone. Figure 9 and Figure 1 show the same results for Galileo and the combined system respectively. Worldwide 95 th percentile values for all simulation cases are shown in Figure 11 and Figure 1 shows the percentage of simulation points where the HPE was less than 1 m. GPS HPE 95% for Mask 1 (Dual Frequency / Differential) 9 o N o N 3 o N o 3 o S Percentage of HDOPs < o S 9 1 o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W Figure : 95 th percentile values of HPE for a 1 degree isotropic mask angle using GPS alone with no constraints. Figure 7: Percentage of HDOP values (worldwide) less than for GPS, Galileo and the combined systems. Many positioning algorithms will report that a solution is not available when the HDOP exceeds a certain value, so Figure 7 demonstrates the system availability of GPS, Galileo, and the combined system. Again, the advantages of using a combined system in extreme masking Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page 5

6 Gal HPE 95% for Mask 1 (Dual Frequency / Differential) 9 o N 1 HPE Percentile 95% (Dual Frequency / Differential) 9 o N 7 3 o N o 3 o S HPE (m) o S o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W Figure 9: 95 th percentile values of HPE for a 1 degree isotropic mask angle using Galileo alone with no constraints. Figure 11: 95 th percentile values of HPE (worldwide) for GPS, Galileo, and the combined systems with no constraints (N), height constraint (H), clock constraint (C), and both height and clock constraints (B). GG 9 o N HPE 95% for Mask 1 (Dual Frequency / Differential) 1 9 HPE Value 1 (Dual Frequency / Differential) o N 3 o N o 3 o S o S 9 1 o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W Percentage of HPEs < Figure 1: 95 th percentile values of HPE for a 1 degree isotropic mask angle using combined GPS and Galileo with no constraints. Figure 1: Percentage of HPE values (worldwide) less than 1 for GPS, Galileo and the combined systems. From Figure 11 and Figure 1, the reliability advantage of using the combined system is evident. The combined systems provide enough availability for reliable positioning to be possible with mask angles as high as 3 degrees. Standalone Global Reliability Results For completeness, the following 5 figures present the reliability results for each of the three satellite systems in standalone mode. Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page

7 9 o N GPS HPE 95% for Mask 1 (Standalone) 9 o N GG HPE 95% for Mask 1 (Standalone) o N o N 3 o N 3 o N o o 3 o S 3 o S o S o S 9 1 o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W 9 1 o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W Figure 13: 95 th percentile values of HPE for a 1 degree isotropic mask angle using GPS alone with no constraints. 9 o N Gal HPE 95% for Mask 1 (Standalone) Figure 15: 95 th percentile values of HPE for a 1 degree isotropic mask angle using combined GPS and Galileo with no constraints. 1 HPE Percentile 95% (Standalone) 9 o N 3 o N 7 o 3 o S o S HPE (m) o S o W 135 o W 9 o W 5 o W o 5 o E 9 o E 135 o E 1 o W Figure 1: 95 th percentile values of HPE for a 1 degree isotropic mask angle using Galileo alone with no constraints. Figure 1: 95 th percentile values of HPE (worldwide) for GPS, Galileo, and the combined systems with no constrants (N), height constraint (H), clock constraint (C), and both height and clock constraints (B). Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page 7

8 1 HPE Value 1 (Standalone) Percentage of HPEs < # GPS SVs # Gal SVs Availability in a North/South Urban Canyon in Calgary 1 Figure 17: Percentage of HPE values (worldwide) less than 1 for GPS, Galileo and the combined systems. Figure 1 and Figure 17 show that it will be possible to use a combined GPS/Galileo Receiver to obtain reliable navigation solutions with low elevation angles in single frequency standalone mode. Urban Canyon Results The following four figures present GPS and Galileo availability during the first day of GPS week 19 to an urban user in Calgary with the two urban canyon elevation masks described earlier. Figure 1 shows the availability to a user standing in the middle of a m wide north/south running street with 15 m buildings on either side. Note that there are rarely four or more satellites in view when using either GPS or Galileo alone, but there are rarely less than when using the combined systems. Total SVs 1 1 : : : : : 1: 1: 1: 1: 1: : : : UT (h) Figure 1: N/S urban canyon availability time series (User in middle of canyon). The red and blue lines indicate the difference in availability between the two systems. Green indicates greater Galileo availability and red indicates greater GPS availability. Figure 19 shows similar results for a street running east/west while Figures and 1 show availability for a user standing at the base of the east wall of a North/South street and the North wall of an East/West street respectively. # GPS SVs 1 1 Availability in a East/West Urban Canyon in Calgary # Gal SVs Total SVs : : : : : 1: 1: 1: 1: 1: : : : UT (h) Figure 19: E/W urban canyon availability time series (user in middle of canyon). Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page

9 # GPS SVs # Gal SVs Total SVs Availability in a N/S Eastside Urban Canyon in Calgary 1 1 : : : : : 1: 1: 1: 1: 1: : : : UT (h) Figure : N/S urban canyon availability time series (user on east side of canyon). # GPS SVs # Gal SVs Total SVs Availability in a E/W Northside Urban Canyon in Calgary 1 1 : : : : : 1: 1: 1: 1: 1: : : : UT (h) Figure 1: E/W urban canyon availability time series (user on north side of canyon). The most noticeable result from the urban canyon simulations is that in this kind of extreme masking environment, navigation is almost impossible using only one system without constraints, additional sensors or dynamic modelling. However, with access to both GPS and Galileo, more than satellites are view most of the time making epoch-to-epoch positioning possible. For this simulation, only the masking effect of the urban canyon environment has been considered. There is also the problem of multipath. This problem is discussed in detail in Malicorne et al. (). CONCLUSION By comparing the simulated performance of GPS, Galileo and combined GPS and Galileo in terms of HDOP and HPE, the following conclusions can be made: In very extreme masking conditions (elevation angles greater than 3 degrees), the GPS plane constellation provides better performance. At lower elevation angles, the additional availability provided by the 3 satellite Galileo constellation provides a small improvement, both in availability and reliability compared to 7 satellite GPS. Using a combined GPS and Galileo system is advantageous in all of the situations presented in this paper. Most importantly, using two systems provides sufficient availability for navigation in extreme masking environments, where navigation with GPS is currently very difficult. ACKNOWLEDGEMENTS The Author would like to acknowledge his supervisor, Dr. Gérard Lachapelle for his assistance and suggestions. This project was funded by the Canadian Space Agency through the GALA project. REFERENCES FRP (1999) 1999 Federal Radionavigation Plan. United States Department of Defence and Department of Transportation. Hein, G. () Galileo: Design Options for the European GNSS-. Navtech Seminars Course 31 Notes, September 1,, Salt Lake City, Utah. ISPA () ISPA GNSS-Based Landing Systems: A European Strategy of Galileo support to precision approach and landing operations. ISPA%paper.pdf Accessed Oct. 3,. Koch, K. (1999) Parameter estimation and Hypothesis Testing in Linear Models ( nd edition). Springer- Verlag, New York, Leick, A. (1995) GPS Satellite Surveying ( nd edition). John Wiley & Sons Lestargquit, L & P. Brison. () Signal Choice for Galileo: Compared Performances of Two Candidate Signals. ION NTM Lucas, R. & D. Ludwig. (1999) Galileo: System Requirements and Architecture. ION-GPS Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page 9

10 Malicorne, M., M. Bousquet, C. Bourga, B. Lobert, & P. Ehrard. () Galileo Performance in urban environment. IAIN World Congress ION Annual Meeting, 3-5. Ober, P. (1999) Towards High Integrity Positioning. ION GPS Oehler, V., G. Hein, B. Eissfeller & B. Ott. () GNSS- /Galileo End-to-End Simulations for Aviation, Urban and Maritime Applications. IAIN World Congress ION Annual Meeting. 1-. Ryan, S., M. Petovello, & G. Lachapelle (199) Augmentation of GPS for Ship Navigation in Constricted Waterways. ION NTM Ryan, S & G. Lachapelle (1999) Augmentation of DGNSS with Dynamic Constraints for Marine Navigation. ION GPS Ryan, S. & G. Lachapelle () Impact of GPS/Galileo Integration on Marine Navigation. IAIN World Congress ION Annual Meeting Schweikert, R., T. Woerz & R. De Gaudenzi. (1999a) On New Signal Structures of GNSS-. ION NTM Schweikert, R., T. Woerz & R. De Gaudenzi. (1999b) Technical Assessment of Signal Structures for the Galileo Satellite Navigation System. ION GPS Tytgat, L. & J.I.R. Owen. () Galileo The Evolution of a GNSS. IAIN World Congress ION Annual Meeting Van Dierendonck, A. J., C. Hegarty, W. Scales, & S. Ericson () Signal Specification for the Future GPS Civil Signal at L5. IAIN World Congress ION Annual Meeting Zink, T., B. Eissfeller, E. Lohnert & R. Wolf () Analyses of Integrity Monitoring Techniques for a Global Navigation Satellite System (GNSS-). IAIN World Congress ION Annual Meeting Proceedings of ION GPS 1, Session C, Salt Lake City, UT, September 11-1, 1 Page 1