Significance of instrumental biases and dilution of precision in the context of GAGAN

Transcription

1 Indian Journal of Radio & Space Physics Vol. 36, October 2007, pp Significance of instrumental biases and dilution of precision in the context of GAGAN Quddusa Sultana 1, Dhiraj Sunehra, D Venkata Ratnam, P V D Somasekhar Rao 2 & A D Sarma Research and Training Unit for Navigational Electronics, Osmania University, Hyderabad , India ad_sarma@yahoo.com 1 Deccan College of Engineering and Technology, Hyderabad , India 2 UGC-ASC, Jawaharlal Nehru Technological University, Hyderabad , India Received 19 June 2007; accepted 4 September 2007 The positional accuracy of the GPS Aided GEO Augmented Navigation (GAGAN) system is basically dependent on ranging errors and the satellite constellation geometry. This paper focuses on enhancing the performance of the system through the estimation of instrumental biases and augmentation of GAGAN using pseudolites (pseudo-satellites). The lineof-sight ionospheric measurements derived from the Global Positioning System (GPS) observables are corrupted by the instrumental biases present in both the GPS satellites and the receivers. The instrumental bias and Total Electron Content (TEC) results (Hyderabad GAGAN station (78.47 E, N)) obtained using the Kalman filter technique are presented in this paper. It is found that the estimated biases are almost stable during the observation period and show close proximity with other reported values in the open literature. For some strategic applications further augmentation of GAGAN with pseudolites is necessary. Five configurations comprising GPS/geostationary satellites and pseudolites are considered for optimizing the Dilution of Precision (DOP). It is found that the pseudolite-system with properly located pseudolites can augment GAGAN and improves the positional accuracy of the user. Keywords: GPS aided GEO augmented navigation (GAGAN), Geometric dilution of precision (GDOP), Global positioning system (GPS), Instrumental biases, Pseudolites, Total electron content (TEC). PACS No.: g 1 Introduction The Global Positioning System (GPS) is a satellite based navigation system developed by the U.S. Department of Defense (DoD). It can be used for a wide variety of applications with a horizontal accuracy of 20 m and a vertical accuracy of 30 m (with 95% confidence level) 1. However, the accuracy of standalone GPS is not sufficient to meet CAT-I precision approach requirements for civil aviation. Therefore many countries including USA, Europe and Japan are developing regional Satellite Based Augmentation Systems (SBAS). The Indian Space Research Organization (ISRO) and Airports Authority of India (AAI) are jointly implementing an SBAS known as GPS Aided Geo Augmented Navigation (GAGAN) to provide seamless coverage over the Indian airspace 2. Basically, GAGAN will provide three services to users, viz. a ranging signal, which improves availability and reliability; differential GPS corrections (ionospheric and orbital corrections), which improve accuracy; and integrity monitoring which improves safety. The accuracy of the GAGAN user position estimate is mostly affected by the ranging errors. Ranging errors include satellite clock and ephemeris errors, errors due to ionospheric and tropospheric delay, and errors due to instrumental biases and multipath. For better position estimate these errors should be exhaustively analyzed and mitigated. The ionospheric delay, which is a function of the Total Electron Content (TEC) is the most predominant error affecting the accuracy of GAGAN. The dual frequency GPS receiver can be used to estimate the ionospheric delay or TEC, taking advantage of its dispersive nature. One of the main sources of error in the estimation of TEC is the effect of differential instrumental biases of the satellite and the receiver. These biases exist due to the fact that the signals at the two GPS frequencies (f 1 = MHz, f 2 = MHz) undergo different propagation delays inside the satellite and receiver hardware. Most of the ranging errors are investigated thoroughly by researchers around the world. However, errors due to instrumental biases are not paid adequate attention. Several prominent techniques for estimation of instrumental biases including Kalman filter, Self-Calibration Of pseudorange Error

2 406 INDIAN J RADIO & SPACE PHYS, OCTOBER 2007 (SCORE) algorithm, least squares fitting and neural networks are reported in the literature 3-6. Further, errors get magnified due to unfavourable satellite constellation geometry. This aspect also needs due consideration and should be dealt with utmost care especially for augmented configurations such as GAGAN. In this paper instrumental bias error, Geometric DOP (GDOP) in the context of various GPS/GEO/Pseudolites configurations is investigated. 2 Overview of GAGAN system The major segments of GAGAN are ground segment, space segment and user segment (Fig. 1). Ground segment consists of reference stations, Master Control Station (MCS), earth station and communication links. In the initial phase, eight Indian Reference Stations (INRES) at precisely surveyed locations are installed to receive data from GNSS satellites 7. If required additional INRES will be established in future. Communication links transfer data from the reference stations to Master Control Station known as Indian Mission Control Centre (INMCC). The INMCC performs integrity monitoring, ionospheric delay estimation, wide area corrections and orbit determination. The Indian Navigation Land Uplink Station (INLUS) receives messages from the INMCC and uplinks them to the GEO satellite for broadcast to the users. Space segment comprises of GPS/GLONASS satellites for the transmission of ranging signals and also GEO satellites for the broadcast of GAGAN signals. Navigation payload is expected to be carried by an Indian GEO satellite to be positioned in the Indian Ocean region between the orbital arc 48 to 100 E (Ref. 8). User segment consists of a receiver capable of receiving and decoding the GPS/GLONASS/GEO broadcast message. The GAGAN payload will be comprised of C-band Up-link, C-band Down-link and L-band Down-link (L1 and L5) (Ref. 7). The signal-in-space (SIS) provides data on GPS and GEO satellites along with ranging information. 3 Data processing In the GAGAN configuration, 20 TEC stations are located at various places in India. One such station is located at Hyderabad. The dual frequency receivers used at each of these stations are NovAtel receivers. For the estimation of instrumental biases and GDOP, dual frequency GPS data of Hyderabad GAGAN station is considered. The raw data obtained from GPS receiver is converted into the desired Receiver INdependent EXchange (RINEX) format using the Convert software. Two types of RINEX data files, viz. navigation and observation data are used in the processing. The required ephemeris and time parameters are extracted from the navigation data and the satellite position in earth-centered earth-fixed (ECEF) coordinates is computed. The dual frequency GPS code and carrier phase observables are extracted from the observation data. These are used to obtain the phase smoothed slant TEC measurements. Using the four satellites position and the corresponding pseudoranges, the ECEF coordinates of the receiver are computed using the Bancroft algorithm and converted to geodetic coordinates 9. Further, the satellite elevation and azimuth angle, slant factor and the sub-ionospheric point coordinates are computed for later use. 4 Methodology for estimation of instrumental biases and TEC using the Kalman filter technique The methodology adopted in this paper for estimation of the instrumental biases and TEC using the Kalman filter technique is briefly described in this section. The dual frequency GPS code and carrier phase measurements in meters can be expressed as (subscript i = 1, 2, refers to GPS frequencies, f 1 and f 2 ) (Ref. 10) follows: s Pi = ρ + c(dtu - d t ) + TD + Ii + SBPi - RBPi + ε( Pi ) (1) Fig. 1 Architecture of GAGAN System s L = ρ + c(dt - d t ) + TD - I + SB - RB i u i Li Li + λ N + ε( L ) i i i (2)

3 SULTANA et al.: PRECISION IN THE CONTEXT OF GAGAN 407 Here ρ is the true geometric range (m); c the speed of light (m/s); dt u, dt s the receiver and satellite clock offsets, respectively (s); TD the tropospheric delay (m); I i the ionospheric delay at frequency f i (m); SB Pi and RB Pi the satellite and receiver instrumental group delay biases at frequency f i, respectively (m); SB Li and RB Li the satellite and receiver instrumental phase delay biases at frequency f i, respectively (m); λ i the carrier wavelength at frequency f i (m); N i the carrier phase integer ambiguity (cycles); ε(.) includes measurement noise and multi-path error (m). The ionospheric delay at frequency f i is given by I i = k I (3) i where ki = fi /( f1 - f2 ), i = 1, 2 and I is the differential ionospheric delay (m). The differential ionospheric delay, I can be obtained from Eqs (1), (2) and (3) by differencing either the code or carrier phase observables, taking advantage of the dispersive nature of the ionosphere. The ionospheric delay or TEC thus obtained is still corrupted by the instrumental biases, measurement noise and multi-path. In this investigation, a two-step method is proposed to optimally combine both code and carrier phase data for improving the TEC estimation accuracy. In the first step, line-of-sight ionospheric delay derived from the code observables is smoothed out using the carrier phase derived ionosphere measurements to reduce the effect of measurement noise. In the second step, a single layer ionosphere model is used to estimate the vertical TEC and instrumental biases of the satellite and receiver using a five-state Kalman filter. The smoothed out line-of-sight differential delay is modeled as the sum of the actual line-of-sight TEC, a satellite bias, and a receiver bias 3. The biased ionospheric differential TEC 11 is represented as I ( t) = S( e)[ A1 ( t) + A2 ( t)dλ IP + A3 ( t)dφ IP ] + SB + RB (4) where A 1, A 2, and A 3 are the parameters for spatial linear approximation of TEC to be estimated, assuming a first-order Gauss-Markov stochastic process; S the slant factor, and e the elevation angle. The parameters SB = SB P1 SB P2 and RB = RB P1 RB P2 are referred to as the satellite and receiver differential instrumental group delay biases, respectively. The factor dλ IP is the difference between the longitude of the sub-ionospheric point and that of the receiver, and dφ IP the difference between the latitude of the sub-ionospheric point and that of the receiver. Equation (4) forms the measurement model of the Kalman filter. The parameters A 1, A 2, and A 3 are estimated for each time t along with the satellite and receiver differential instrumental biases. The system model as reported by Sardon 3 is considered here. The dual frequency GPS receiver (Ionospheric Calibration System) available at NERTU provides calibrated value of the receiver bias (0.18 ns). This receiver is used as a reference receiver, and the inter-frequency bias of Hyderabad GAGAN receiver and other GPS satellites in view are estimated relative to the reference receiver. 5 Estimation of TEC and instrumental biases A five-state Kalman filter is implemented for estimating the differential instrumental biases and vertical TEC. The smoothed out line-of-sight TEC, slant factor, sub-ionospheric point coordinates and the receiver coordinates form the input to the Kalman filter algorithm. The elements of error covariance matrix are chosen to be arbitrarily large for better convergence. The initial state vector is chosen for each satellite to maintain the standard deviation and range of the bias variables to the least minimum possible value. The observation noise and system noise covariance are assumed to be white gaussian. The smoothed out line-of-sight TEC for PRN 26 is compared with noisy code and ambiguous carrier phase TEC in Fig. 2. It can be observed that the smoothed out TEC estimates follow the carrier phase variations. The merits of both carrier and code ionosphere measurements are exploited in the smoothing process. The estimated vertical TEC, satellite (PRN 26) and receiver biases are shown in Fig. 3. The vertical TEC is found to vary between 30.9 and TECU during the observation period. The mean value of satellite Fig. 2 Code, carrier and phase smoothed TEC

4 408 INDIAN J RADIO & SPACE PHYS, OCTOBER 2007 FIG. 3 Vertical TEC and biases Table 1 Estimated biases for various GPS satellites S. No Satellite PRN # Bias value, ns S. No Satellite PRN # Bias value, ns instrumental bias (PRN 26) is found to be TECU ( ns) and the mean value of the receiver instrumental bias is found to be TECU ( ns). Here, 1 TECU corresponds to ns of differential delay. The measurements from other satellites are processed in a similar manner for a 12-hour data set. Table 1 lists the estimated differential instrumental biases for 16 satellites visible during the 12-hour observation period ( hrs UT). The absolute value of the instrumental biases for various satellites is found to range from 0.14 ns to 6.52 ns. The instrumental biases are found to be almost stable during the observation period. The equatorial anomaly phenomenon is not likely to exist from midnight to about 0900 hrs LT. The recorded data during hrs LT is considered for validation of the developed algorithm. 6 Augmentation of GAGAN using pseudolites for the improvement of DOP Pseudolites (PLs) can augment GAGAN whenever or wherever GPS and GEO satellites are not fully accessible. Optimally located pseudolites can significantly improve the geometric strength of positioning solutions, particularly for the height component Therefore the geometry consisting of pseudolites/gps/geo satellites should be carefully designed to take maximum advantage of the augmentation. The effect of satellite/pseudolite geometry on position accuracy is measured by estimating a dimensionless factor called as Dilution of Precision (DOP). The better the satellite/pseudolite geometry the lesser will be the DOP and the better the position accuracy of the user and vice versa. The following section describes a typical pseudolite system that can be used to augment GAGAN. 6.1 Pseudolite system and its implementation issues The proposed GAGAN pseudolite-system consists of multiple pseudolites connected to a central control unit (CCU). The CCU can be connected to the INMCC and can access and process the GAGAN messages. It replaces the data on GEO satellites with the corresponding pseudolite-data such as PRN number, position coordinates, differential corrections and integrity information. This modified information is broadcast through pseudolites on L1 frequency. The user equipped with GPS/GAGAN receiver receives the pseudolite signals in addition to GPS/GEO signals. Pseudolites can be synchronized with GPS/SBAS time reference 15. Though pseudolites are made to imitate GAGAN signals, few modifications in hardware and software are required at the receiver level to process pseudoranges due to pseudolites. As ionospheric corrections are not needed for pseudolite signals, relevant software modifications in the receiver are necessary 15. Since all the pseudolites are at surveyed locations on the ground, ephemeris corrections are not required. Also stable clocks can be used by pseudolites and can be highly synchronized with the system time to avoid clock errors. The Near-Far problem due to pseudolite, limits the coverage area. To overcome this problem various approaches such as, use of pulsed systems, transmission of signals with frequency offset can be used 14. Pseudolite signals are susceptible to multi-path disturbances. One of the important techniques to mitigate multi-path effects is shaping of the antenna radiation pattern Proposed configurations Various configurations with different PL/GPS/GEO satellite geometries are considered to see their effect on DOP and positional accuracy of the user. Receiver is assumed to be at Hyderabad (78.47 E, N) for all the configurations.

5 SULTANA et al.: PRECISION IN THE CONTEXT OF GAGAN Configuration 1 and 2 At Hyderabad 6-9 GPS satellites are visible at any particular point of time. In configuration 1 four GPS SVs (PRN2, PRN6, PRN26 and PRN29) are considered out of 8 satellites visible on 4 Mar at 0800 hrs UTC. These satellites provide the best GDOP at the epoch under consideration. In configuration 2, GAGAN system with one GEO and three GPS satellites is considered. The GEO satellite GSAT-4 is considered at 82-deg east longitude in the Indian Oceanic Region as planned for GAGAN 2. With GSAT-4, only those three GPS SVs (PRN2, PRN6 and PRN26) are selected, which give the best GDOP. Geodetic coordinate details of the three selected GPS SVs and GSAT-4 are given in Table 2. These coordinates of GPS SVs are estimated from the ephemeris parameters transmitted as part of the navigation message Configuration 3 In this configuration it is assumed that GAGAN is augmented by one pseudolite. This configuration is formed by replacing GPS SV2 of configuration 2 by a pseudolite PL1. It could also replace any other GPS SV, but the replacement of SV2 gives the best GDOP. Pseudolite PL1 is assumed to be placed on a tower of height 50 m (= 586 m geodetic) and is visible to the user within an area of 30 km radius as required at airports. The GEO satellite GSAT-4, GPS SVs 6 and 26 of configuration 2 are retained. Table 3 shows the geodetic coordinates of GPS/GEO/pseudolite of this configuration Configuration 4 and 5 In configuration 4 it is assumed that GAGAN is augmented by two pseudolites. This configuration is formed by replacing GPS SV26 of configuration 3 by another pseudolite PL2. Pseudolite PL2 is assumed to be placed on a tower of height 50 m (= 586 m geodetic) and is visible to the user within an area of 30 km radius. The GEO satellite GSAT-4, GPS SV6 and pseudolite PL1 of configuration 3 are retained. Table 4 shows the geodetic coordinates of GPS/GEO/pseudolites of configuration 4. Further, in this configuration, a change in PL2 position is assumed to observe its effect on GDOP. Let the new configuration formed be configuration 5. Table 5 shows the new coordinates of PL2. 7 Estimation of GDOP for the proposed configurations The GDOP values and the unit vector-tetrahedron volumes (due to four ranging sources and the user) for configuration 1, 2, 3, 4 and 5 are shown in Table 6. Table 2 Geodetic coordinates of GPS/GEO satellites (configuration 2) Ranging source Longitude Latitude Height, km E 0 0 N GPS SV W 44 3 S GPS SV W S GPS SV W 54 8 S Table 3 Geodetic coordinates of GPS/GEO/pseudolite (configuration 3) Ranging source Longitude Latitude Height, km GSAT E 0 0 N PL E N GPS SV W S GPS SV W 54 8 S Table 4 Geodetic coordinates of GPS/GEO/pseudolites (configuration 4) Ranging source Longitude Latitude Height, km GSAT E 0 0 N PL E N PL E N GPS SV W S Ranging source Table 5 New coordinates of PL2 Longitude Latitude Height, km PL E N Table 6 GDOP values and tetrahedron volumes for configuration 1, 2, 3, 4 and 5 Configuration No. GDOP Tetrahedron Volume, m From Table 6, it can be observed that configuration 1 is showing the maximum GDOP (except that of configuration 5) as it is of standalone GPS. Configuration 2 is of GAGAN, thus showing better GDOP than that of configuration 1. As configuration 3 is of augmented GAGAN using one pseudolite, its GDOP is better than that of configuration 2. Also the location of pseudolite PL1 is selected in such a way that the tetrahedron volume formed due to four ranging sources is increased reducing GDOP. Moreover the lesser the GDOP, the better will be the

6 410 INDIAN J RADIO & SPACE PHYS, OCTOBER 2007 positional accuracy. Thus the position accuracy due to configuration 3 will be more than that of configuration 2 due to its reduced GDOP value. As configuration 4 is further augmentation of configuration 3, where two pseudolites are used to augment GAGAN, improvement in GDOP is found. Also the location of PL2 is selected in such a way that the tetrahedron volume formed due to four ranging sources is increased. This leads to less GDOP and better accuracy. Results due to configuration 5 indicate unacceptable GDOP value for navigation. It is due to the improper selection of the PL2 position, which has lead to the least tetrahedron volume. In this case, GAGAN receiver will avoid PL2 for position estimate and from the remaining available ranging sources; best four will be selected to achieve least GDOP and highest accuracy. Thus it can be concluded that not only the number of pseudolites, but also their position are significant factors to be considered while implementing pseudolite-system for augmenting GAGAN. 8 Conclusions In this paper, estimation of satellite and receiver instrumental biases, TEC, and GDOP are considered for enhancing the accuracy of GAGAN system. In order to reduce the noise level in the code data, ionospheric measurements are smoothed out using the precise carrier phase data. To further improve the accuracy of TEC estimation, a five-state Kalman filter is used for estimating the differential instrumental biases. The biases thus estimated are found to be consistent over the observation period and agree with other reported values in the open literature. To account for large non-linearity in TEC due to equatorial anomaly phenomenon, an Extended Kalman filter can be used. A pseudolite system is proposed to augment the GAGAN system. Major implementation issues are briefly presented with their possible solutions. For stand-alone GPS, GAGAN and three-augmented GAGAN configurations, unit vectortetrahedron volume and GDOP are calculated. From the results, it is concluded that pseudolite-system with properly located pseudolites can improve the position accuracy of the user. Acknowledgements The work presented in this paper has been carried out under the Department of Science and Technology (DST), New Delhi sponsored Project No. SR/S4/AS- 230/03. The authors are also thankful to Shri Kalyan Bandyopadhyay and Dr. M R Sivaraman, Space Applications Centre, Indian Space Research Organisation (ISRO), Ahmedabad, India for providing the GPS data. 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