How can an Orbit Prediction Module speed up the TTFF and help to authenticate the position?

Transcription

1 How can an Orbit Prediction speed up the TTFF and help to authenticate the position? Mykhailo Lytvyn, Albert Kemetinger, Philipp Berglez TeleConsult Austria GmbH Graz, Austria Abstract Many GNSS applications require both, fast and trusted positioning. For example, in road toll collection this two requirements are extremely critical in order to provide fair road fee charges. One of the most effective measure to shorten the time to first fix is the usage of an assistance server to provide actual ephemeris and almanac information to the user. On the another hand, information from the assistance server can also be used as trusted reference data, which can help to detect spoofing attacks. The drawback is that a permanent connection to assistance server is required, in order to retrieve the latest ephemeris and almanac data. To overcome this problem the assistance server must be able to calculate and provide predicted orbits having a validity over a long period (e.g., up to 1-2 weeks). This paper describes a modular and cost-effective GNSS orbit prediction algorithm for reducing time to first fix as well as trusted positioning. The presented algorithm is implemented in the Positioning And Navigation Data Assistance Server, developed by TeleConsult Austria GmbH. I. INTRODUCTION The requirements for Global Navigation Satellite System (GNSS) receivers, especially for mass market receivers, are constantly increasing. Beside the demand for an increased positioning accuracy, there is also a strong need for reducing the time to first fix (TTFF) and for position authentication. The TTFF defines the time span of a receiver to output the first position fix, after the receiver has been switched on. Depending on the start conditions (i.e., available a-priori information) the TTFF is mainly influenced by the acquisition time and the reception of the essential parts of the navigation message (i.e., ephemeris). Thereby the time needed for the reception of the ephemeris data is the most time consuming task. One of the most effective way to shorten the time to first fix is to use assistance data from a data server via terrestrial networks (e.g., GSM, UMTS, LTA, etc.). This concept is commonly denoted as assisted GNSS (A-GNSS). The A-GNSS concept improves the TTFF in two ways. First, assistance data can be used to speed up the acquisition of GNSS signals by providing information about the potential visible satellites and the resulting acquisition search space. In addition ephemeris data are provided by the service, and thus, it is not longer necessary to wait for the reception of the navigation message, which reduces the TTFF significantly. Although, A-GNSS is commonly used to speed up the TTFF, some drawbacks still exist. In case of having no terrestrial network link (e.g., outside the coverage area, natural disaster), A-GNSS data are not available. One possible method of circumventing this issue is to provide predicted long-term high precision ephemeris data. These predicted high precision ephemeris data have to provide an accuracy higher than the almanac data for a long time (i.e., the satellite position error should be less than 1 km over a period of 1-2 weeks). The long-term validity data can be stored in non-volatile memory of the receiver, and thus, the assistance data are available even if there is no connection to an A-GNSS server. Beside reducing the TTFF, these long-term ephemeris data are used to authenticate the user position. The orbit prediction algorithm described in this paper has been developed in order to meet the user requirements. The quality of the predicted orbits over a period of at least one week should be better than almanac data quality (i.e., less than 1 km). The orbit prediction module should use as few as possible external data; the ideal case is to use only data provided by GNSS constellation (broadcast orbits, leap seconds number, Earth orientation parameters from CNAV message, etc.). The described orbit prediction algorithm is implemented in the Positioning And Navigation Data Assistance Server (PANDAS) developed by TeleConsult Austria GmbH (TCA). The proposed orbit prediction approach can be implemented on user side in mobile phones, PDAs, tablets, and so forth. This allows to use assistance data without having a connection to the A-GNSS server. Possible ways to adapt orbit prediction algorithm for mobile navigation devices are discussed. A. Algorithm description II. ORBIT PREDICTION The proposed GNSS orbit predicting algorithm is based on a well-known principle. Let s assume having a satellite position r and velocity v at epoch t 0 (initial conditions). Then the predicted satellite position at an epoch t can be computed by solving the following differential equation: ż t ˆ ż t rptq rpt 0 q ` vptq ` aptqdt dt, (1) t 0 t 0 where rptq represents the satellite position vector, vptq is the satellite velocity, and aptq denotes the satellites acceleration due to external forces. The initial satellite positions rpt 0 q can be taken from International GNSS Service (IGS) ultra-rapid orbits (predicted part) or from broadcast ephemeris. The velocities v can be

2 calculated using broadcast ephemeris. Note, that the satellite positions calculated from broadcast ephemeris are related to the antenna phase center. In order to use them as initial values for orbit prediction, they have to be related to the center of mass of the satellite. The accelerations a in equation (1) can be obtained by modeling the forces which are acting on the GNSS satellites, using Newton s Second law: aptq ÿ k F k ptq m, (2) where F k ptq represents the forces acting on the satellite and m denotes the mass of the satellite. B. Implementation The quality of the predicted orbits, calculated from (1), strongly depends on the accuracy of the initial conditions and the quality of the models in (2). Table I shows the characteristics of the main forces acting on GNSS satellites as well as some implementation details in TCA s orbit prediction software. The Earth gravitation field can be modeled using spherical harmonic expansion series for the gravitation potential U: Upr, φ, λq GM C r Nÿ ˆRC r n n n ÿ m 0 ` S nm sinpmλq Pnm psin φq, Cnm cospmλq where r, φ, and λ are the geographic coordinates of the satellite, G denotes the gravitational constant, M C and R C represent the mass and radius of the Earth, Cnm and S nm are the normalized harmonic coefficients, Pnm are the associated normalized Legendre functions, and N represents the order of model. The orbit predictor software uses the Earth gravity model 2008 (EGM2008) as recommended in [15]. The series is truncated at N = 12. This provides an accuracy better than 0.5 mm for high-orbiting GNSS satellites [15]. The point-mass attraction due to Sun and Moon are calculated as follows: a pm GM b ˆ rb r s r b r s r b r b (3), (4) where M b and r b are mass and geocentric position of the attracting body, and r s is the geocentric position of the satellite. The positions of Sun and Moon are obtained in the space-fixed reference frame using trigonometric series as discussed in [8]. The orbit predictor implements several solar radiation pressure force models: Cannonball model, ROCK ([9], [10]), modified ROCK with direct term, JPL GPSPM.04 with eclipse season extension ([5], [6]), extended CODE model ([19]). Note that all models are augmented with the conical shadow model (including penumbra) which takes into account satellite shadowing by Earth and Moon. An Y-bias appears due to satellite solar panels misalignment and results in additional acceleration along y-axis: a y bias C u y, (5) where C represents a satellite dependent constant term, u y is the unit vector in positive direction of the satellite s y-axis. Due to the fact that this additional acceleration changes slowly, it can be estimated for some epochs and therefore it can be used as an empirical parameter for 1-2 weeks. Beside natural forces, the motion of a spacecraft is also affected by self-generated forces. Man-made satellites communicate with Earth by the transmission of electromagnetic signals via antennas mounted on the outside of the spacecraft. The emission of these signals causes a recoil force on the spacecraft [1]. For the high-orbiting GNSS satellites, atmospheric drag is negligibly small. However, there is a small acceleration in direction tangential to the satellite s velocity. This acceleration is called along-track acceleration. In [11], thermal reradiation effects are mentioned as a possible reason for such acceleration. The value of along-track acceleration is in the magnitude of about m{s 2 and can vary depending on the applied solar radiation pressure model. It is convenient to consider along-track acceleration as a part of unmodeled empirical accelerations. All computations of accelerations are accomplished in the Earth-Centered Space-Fixed (ECSF) reference frame, but resulting values of predicted satellite positions should be provided to the A-GNSS user in the Earth-Centered Earth- Fixed (ECEF) reference frame. In order to transform between two systems one needs to account for mutual rotations between the two frames: r ECEF pt i q Wpt i qrpt i qnpt i qppt i q r ECSF pt i q, r ECSF pt i q P T pt i qn T pt i qr T pt i qw T pt i q r ECEF pt i q, where the matrices W, R, N, and P represent the polar motion, the Earth rotation, the nutation, and the precession. In case of the implemented orbit prediction software, the precession is modeled using the IAU1976 model, and the nutation is implemented using the full 106-term IAU1980 model including the geodetic nutation effect [13]. The polar motion matrix W is calculated using the polar coordinates x p, y p provided by International GNSS Service or International Earth Rotation Service as follows: Wptq R y p x p qr x p y p q, where R y and R x are the rotation matrices around y- and x-axis respectively. Since the polar motion is a complicated phenomena, empirical modeling and prediction of geodetic polar motion components remain enigmatic (cf. [3], [7]). The orbit prediction module can utilize predicted Earth orientation parameters (EOP) from IERS and IGS, calculating an Earth rotation matrix in (6) using an interpolated EOP. However, in normal mode TCA s orbit predictor uses the last available polar position and assumes that these values are constant over the whole prediction interval. If there is no information about (6)

3 TABLE I FORCES ACTING ON SATELLITE AND THEIR IMPACT ON PREDICTED ORBIT Force Acceleration, m{s 2 Orbit error after one day, m Implementation in TCA orbit predictor Two-Body Term of Earth s Gravity Field yes Oblateness of the Earth yes Lunar Gravitational Attraction yes Solar Gravitational Attraction yes Other Terms of Earths Gravity Field yes Radiation Pressure (direct) yes Y-Bias yes Solid Earth Tides yes, with simplified model [12] Antenna Recoil no Along Track (empirical force)?? no Atmospheric Drag no 200 Ref. - Predict X, m Ref. - Predict Y, m Ref. - Predict Z, m D prediction error, m 0 Fig. 1. Differences between reference and predicted orbits for GPS PRN16 (29 Oct Nov. 2011) polar motion available, the matrix W is set to unity matrix. Note that in this case the quality of the prediction is highly degraded. The polar coordinates are also available within the GPS CNAV navigation message (message type 32). The Earth rotation matrix R is a rotation matrix around the z-axis: Rptq R z p t GAST q, where t GAST is the Greenwich Apparent Sidereal Time. It is worth mentioning that the described orbit prediction algorithm is using data provided via the GNSS satellite constellation as a primary source. Additional required data which can not be obtained from the signal in space are: GNSS constellation information (satellite types, masses, etc.), and antenna phase center models. These data are commonly updated after the launch or activation of the satellites. Although the implemented orbit prediction algorithm requires a minimum amount of external data, different types of external a-priori information can be used for the implementation: IGS and NGS orbits (sp3 format), Earth orientation parameters from IGS (erp files) and IERS (C04 series, Bulletins A and B), Antenna phase center variation models for satellites (ANTEX file). The orbit prediction module implements ephemeris correction due to phase center offset and satellite specific nadir-dependent variations of phase center provided by IGS [16]. The history of the GNSS constellation status (correspondence between satellite PRNs and Block types) is obtained from theis file as well. C. Tests and preliminary results As mentioned above, the orbit prediction accuracy is required to be better than 1 km over a period of 1-2 weeks. The orbit prediction software was tested using IGS final ephemeris as a reference. The predicted orbits were calculated using a simple Runge-Kutta of 4th order integrator with a step width of 30 s and IGS orbits were interpolated at the same epochs using a Lagrange 11th order interpolation method. The initial satellite positions for the prediction were taken from IGS ephemeris, initial velocities were calculated from broadcast ephemeris, and the polar coordinates at initial epoch were taken from the IGS final solution. The modified ROCK solar radiation pressure model, including the direct term, was used to calculate the accelerations due to solar radiation pressure as well as thermal re-radiation from the satellite surfaces. The Y-bias parameters were taken from [18]. Fig. 1 shows the differences between the reference and the predicted satellite positions for GPS satellite PRN19 (type Block IIR) over the interval from October 29, 2010 to November 12, As shown, the prediction errors after two weeks of prediction are in the magnitude of about m, which totally meet accuracy requirement. Similar test were performed for different GPS satellites orbiting on different orbital planes, using different initial prediction epochs (midnight, midday etc.). All tests show similar results the orbit prediction error is in the magnitude of -350 m for a two weeks prediction interval. The deviations of the predicted positions from reference values show a main oscillating component with a period of 12 hours. This effect is caused by the remaining errors within the modeling of the satellite accelerations (along-track, Y-

4 EDAS - Client EDAS Decoder NTRIP-Caster Assistance Local Atmospheric (optional) Fig. 2. PANDAS Control Server Database PANDAS structure Man Machine Interface Orbit Differential Authentication PPP bias etc.). These errors can be highly reduced by estimating and introducing additional empirical accelerations which will absorb the unmodeled and missmodeled effects. However such improvements need to account not only for the initial satellite state, but also previous movement history. Calculation of empirical accelerations is a topic for future investigations. III. POSITIONING AND NAVIGATION DATA ASSISTANCE A. General description SERVER As mentioned above the orbit prediction algorithm is implemented as an additional module in the PANDAS server [14]. The PANDAS server is a modular correction and augmentation data server with a great variety of services and functionalities. PANDAS is capable to receive corrections and augmentation data from the EGNOS Data Access System (EDAS) and to provide real-time correction data to the user. The PANDAS structure is shown in Fig. 2. All necessary data for the correction data computation are stored in a sophisticated database and all the different software modules have access to it. Out of the received EDAS data together with the different correction models PANDAS computes either pseudorange and range rate corrections for each satellite or coordinate corrections in real-time. These corrections are then provided to the user. As another service, for featuring a faster TTFF and to improve positioning in environments with low GNSS signal strength (deep urban areas, indoors, etc.), assistance data are provided by the PANDAS server. Additionally, reference time, ephemeris based on EDAS data and self calculated long term ephemeris as specified in [4], as well as an approximate position via cell-id are provided and hence support a wide variety of land-based positioning, and navigation applications and services. In principle, the corrections and augmentations from PANDAS are sent via terrestrial communication link utilizing the Networked Transport of RTCM via Internet Protocol (NTRIP). NTRIP has the advantage that commercial off-the-shelf receivers can use the service without additional software since it is based on RTCM messages. A terrestrial communication link has been chosen in a first stage, since the target applications supported by PANDAS require high availability in urban areas and generally over land. Other communication links are possible as well. For an easy access to the different services of PANDAS, the following user interfaces can be used: RTCM, XML, or any other proprietary format. Another service application of PANDAS, which is worth to mention, is position authentication designed for applications requiring a high level of integrity and reliability (safety critical applications, liability critical applications). Special algorithms combined with data stored in the database (e.g., navigation bits, satellite status, integrity information) can be used for a safe positioning and to detect intentionally caused interferences. B. Performance tests Several tests were accomplished in order to validate the performance of the PANDAS orbit prediction module. During these performance tests, orbit predictions for two weeks were calculated using the same parameters as in section II-C. The calculation of all implemented acceleration models was activated. The tests were performed on the computer with the following characteristics: CPU Intel Core i5 (3.3 MHz), RAM 4 Gb, Ubuntu Linux (64-bit) operating system. Fig. 3 shows the execution time versus the number of processed satellites. The prediction of a full GPS constellation of 32 satellites for a two weeks interval (40320 epochs) takes about nine minutes (519 seconds). Normally, orbit predictions are calculated once per day and thus, the calculation time fits to PANDAS system requirements. Profiling results show that the orbit predictor spends about 43% of execution time for the computation of the nutation matrix. This fact will be investigated in the near future. C. Improving TTFF Reducing the TTFF with predicted orbits was tested with ASPHALT GPS/Galileo dual-frequency (L1/L5) receiver Calculation time, s Fig. 3. Number of SVs Orbit predictor performance

5 Fig. 4. ASPHALT receiver (Fig. 4). This receiver was developed by Fraunhofer Integrated Circuits Institute (hardware and signal processing) and TCA (position, velocity, time software) [21], [22]. During TTFF tests, the receiver was configured to operate in GPS L1-only mode. Without A-GNSS, it takes about 40 seconds for the receiver to compute a position fix. This procedure is referred to as cold start (no previous broadcast data, no almanac data). When the predicted orbit, generated by PANDAS, were sent to the receiver software and used during the start-up phase, the TTFF was shortened to 8 seconds. The result can be improved even more (up to 2-4 seconds), if the receiver additionally receives predicted satellite clock data and a rough user position. D. Spoofing detection with predicted orbits The predicted satellite orbits cannot only speed up the TTFF, but can be also used for spoofing detection. One possible way of spoofing a receiver s position can be achieved by changing the broadcast ephemeris data. Thus, it is necessary to validate the broadcast ephemeris data. This can be achieved by comparing them with the predicted orbits. If the differences between the predicted orbits and the broadcast ephemeris exceed a well-defined threshold, the user will be notified of a potential spoofing attack. The detection algorithm does not only constantly monitor the differences of the two orbits by means of coordinate differences, but also having a look at the velocities and accelerations. The test results show, that it is possible to detect such attacks with a high probability. Beside the comparing the broadcast orbits with the predicted ones, other countermeasures for position authentication are implemented in the PANDAS server. An overview about the used algorithms is provided in [2]. IV. CONCLUSION AND FUTURE IMPROVEMENTS Within the paper, a modular and cost-effective GNSS orbit prediction algorithm for reducing time to first fix as well as trusted positioning is presented. The presented algorithm is implemented in the Positioning And Navigation Data Assistance Server, developed by TeleConsult Austria GmbH. The orbit predictions are used to reduce the time to first fix by a factor of up to 5 times. Additionally, the predicted ephemeris data are used for spoofing detection by means of validating the broadcast ephemeris as well. Almost every required data for the introduced orbit prediction algorithm are provided via GNSS satellite signals in space. Only a few external data sources (i.e., polar coordinates on initial prediction epoch and the constellation status) have to be included. This allows to use proposed algorithm for autonomous high accuracy orbit prediction in navigation devices like mobile phones, PDAs, tablets, etc. ([17], [20]). Implementing orbit prediction on navigation devices provides the possibility to reduce TTFF and detect spoofing attempts in areas without connection to the A-GNSS server. In order to calculate orbit prediction on mobile devices the computation efforts have to be reduced especially during the satellite acceleration computations and the integration of equation (1). This can be done in two ways: Simplify models, for example use less terms within the Earth gravity series expansion (in [20] it is shown that using coefficients up to degree and order of five should be enough), reduce nutation model to several main terms etc.; Implement a more sophisticated integrator (e.g., in the terms of order). The most promising are multi-step Adams integrators with variable order. This will reduce the number of calculations in the orbit integrator while the integration accuracy can be kept constant. The orbit prediction module is currently in the test stage. In order to reach market readiness, it is necessary to develop satellite clock predictions as well. This enables the use of predicted information for signal acquisition and position solution. Further improvement steps within the orbit modeling are: Implementing satellite s yaw-attitude models for shadowing periods (especially for old GPS satellite types Block II and Block IIA), Introducing a more recent nutation-precession model described in [15] or correct nutation angles in longitude and obliquity with celestial pole offsets published by IERS. Estimating and introducing empirical accelerations for each satellite in equation (2). Calibrating solar radiation pressure models with precalculated scale factors for each satellite. REFERENCES [1] S. Adhya, Thermal Re-Radiation Modelling for the Precise Prediction and Determination of Spacecraft Orbits, Ph.D. dissertation, Department of Geomatic Engineering, Univ. 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