GPS NAVIGATION FOR INERTIAL MOTION AND FORMATION CONTROL, RENDEZVOUS AND PROXIMITY OPERATIONS A BRIEF REVIEW OF RECENT LITERATURE

Transcription

1 GPS NAVIGATION FOR INERTIAL MOTION AND FORMATION CONTROL, RENDEZVOUS AND PROXIMITY OPERATIONS A BRIEF REVIEW OF RECENT LITERATURE Hari B. Hablani, Professor, Department of Aerospace Engineering, Indian Institute of Technology, Bombay July 28, 2012

2 Acknowledgement 2 The material presented here is entirely from papers published by other authors. I greatly appreciate, indeed admire, their creativity and insights. I have stated the sources of the figures and tables individually, but in case of omission, I extend my apology. In this presentation, no claim of originality on my part is intended.

3 Highlights 3 Real-time navigation for formation control of remote sensing LEO satellites: Ionospheric delay for LEO satellites Mathematical modeling of signals, elimination of iono delay with GRAPHIC and estimation of associated biases Absolute navigation performance Relative navigation for formation control: Between-receiver, between-satellite carrier phase difference measurements Estimation of integer ambiguities with LAMBDA Estimation of vertical iono delay Hardware-in-the-loop simulation of formation control: Performance NASA Global Differential GPS and TDRSS Augmentation Service for Satellites (TASS) Precision real-time navigation with real-time GPS orbits provided by TASS Real missions: PRISMA, TerraSAR-X TanDEM-X Eccentricity/inclination vector seperation for LEO satellites in formation Absolute and relative nav accuracies Imminent navigation services in India: GAGAN and IRNSS Concluding remarks

4 Loiselet, M., Stricker, N., Menard, Y., and Luntama, J.-P., GRAS MetOp s GPS-Based Atmospheric Sounder, ESA Bulletin, 102, May

5 Montenbruck and Gill, Ionospheric correction for GPS Tracking of LEO Satellites, The Journal of Navigation, 2002, vol. 55, pp I 0 = vertical path delay, E = elevation angle of the satellite m(e) = mapping function to determine iono-delay at any elevation angle [Leung and Montenbruck, AIAA JGCD, vol. 28, No.2, 2005, pp ]

6 [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] 6

7 [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] 7

8 8 Local (Absolute, Inertial) Spacecraft Navigation with Single-Frequency Receiver using Reduced Orbit Determination and GRAPHIC ( Group and Phase Ionospheric Correction) [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] Because of ionospheric path delays, the single-frequency position solutions of GPS receivers could be in error by several tens of meters, and may have a radial error of several meters. Velocity solution offered by the receiver is accurate up to 1 cm/s. These absolute nav accuracies are inadequate for formation flying, which requires a smooth, continuous, and accurate onboard position and velocity knowledge Hence, a dedicated Kalman filter is required to determine the spacecraft s PVT. Trajectory Model: Compromise between computational efficiency and propagation accuracy leads to 30x30 JGM- 3 gravity field model. Compared to a 50x50 model, 1.5 m accuracy is achieved in position prediction in 30 minutes for a near polar orbit at a 450 km altitude. Drag, luni-solar gravity, radiation pressure are all ignored, but they are estimated as empirical acceleration a emp in radial, transverse, and normal direction [a R a T a N ] State updates and predictions only once every seconds Propagation (time-update) of the state vector is done with RK4 combined with Richardson extrapolation

9 GRAPHIC Measurements and State Vector Estimate [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] (cont d) 9 GPS receiver: Orion-S, 12 channels, L1 C/A code and carrier Ionospheric-Free GRAPHIC Measurement [Yunck, JPL, 1995]: Code and carrier phase (CP) measurements of single-frequency receiver are averaged: ρ = (ρ C/A + ρ L1 )/2 = ρ + c(δt δt GPS ) + b which is an iono-free measurement with half the code noise but with an unknown bias b (1/2 * wavelength * integer ambiguity of the CP measurement). Neglecting the iono delay, an approximate value of b to initialize state vector estimate is b (ρl1 ρc/a)/2 Because Orion-S has 12 channels, up to 12 GPS satellites will be tracked and there will be as many unknown biases b, forming a 12x1 vector B State vector x consists of 22 parameters x = (y, a emp, cδt, B) where 6x1 vector y consists of spacecraft position and velocity. The initial condition of x is: y = GPS provided solution, a emp = 0, zero clock offset, and B as specified above.

10 Error Covariance Matrix, State Transition Matrix, Process Noise Matrix [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] (cont d) 10 The initial value of the state estimate error covariance matrix P: diagonal with standard deviation of 10 m (position, clock, and biases), 0.1 m/s (velocity), 5e-7 m/s 2 (acceleration) Because measurement intervals are seconds, an interpolating polynomial is required for a continuous representation of the trajectory for relative navigation; a quintic Hermite polynomial is used for this purpose. State transition matrix: For the state vector x = (y, a emp, cδt, B) Φyy = y(ti )/ y(ti 1) accounting for the J 2 effect Φya = y(ti )/ aemp(ti 1) Process noise matrix Q for filter update interval seconds: position: (10-3 m) 2, velocity: (10-6 m/s) 2, acceleration: (2.5*10-6 m/s 2 ) 2 ; clock: (3 m) 2

11 Estimated Measurements [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] (cont d) 11 The measurement update is performed in a sequence of scalar update; this avoids large matrix operations Because the measurements are ρ = (ρ C/A + ρ L1 )/2 = ρ + c(δt δt GPS ) + b for all the satellites in view, estimated measurements g(x) are formed using the latest position of the LEO satellite, GPS satellites broadcast ephemeris parameters, receiver and GPS clock offsets, and GRAPHIC bias. Broadcast ephemeris errors contribute signal-in-space range error of about m. Linearization of measurements for extended Kalman filter lead to the partial derivative vector shown on the next chart relative to the state vector. The Measurement standard deviation is equal to ½ * σ (code noise). The rest of the Kalman filtering is straightforward

12 Hardware-in-the-loop simulation results [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] 12 A formation of four spacecraft at 450 km altitude. See earlier Table 3 GPS signals were generated with a 48-channel Spirent STR4760 signal simulator

13 [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] (cont d) 13

14 Leung, S., and Montenbruck, O., High Precision Real-Time Navigation for Spacecraft Formation Flying, ION GPS/GNSS 2003, Sept. 2003, Portland, OR; reprinted with permission 14 Reprinted with permission of Montenbruck

15 Leung, S., and Montenbruck, O., High Precision Real-Time Navigation for Spacecraft Formation Flying, ION GPS/GNSS 2003, Sept. 2003, Portland, OR; reprinted with permission 15

16 Leung, S., and Montenbruck, O., High Precision Real-Time Navigation for Spacecraft Formation Flying, ION GPS/GNSS 2003, Sept. 2003, Portland, OR; reprinted with permission 16

17 Leung, S., and Montenbruck, O., High Precision Real-Time Navigation for Spacecraft Formation Flying, ION GPS/GNSS 2003, Sept. 2003, Portland, OR; absolute Navigation: Results Summary 17 For absolute navigation, the system achieved an accuracy of 2.98 m in position, and 0.34 cm/s in velocity. Compare this with GPS receiver nav solution which has a typical error of 15 m and 5 cm/s This 5 times higher accuracy is attributed to GRAPHIC which eliminates iono delay. GRAPHIC introduces biases, but filter is able to estimate them. This absolute nav accuracy is comparable to the broadcast ephemeris errors of GPS satellites. The filter takes about an orbital period to converge to steady-state in position, and ½ orbital period for velocity, when the measurement is at 20 s interval. This long convergence period is due to the GPS ephemeris errors and GRAPHIC biases.

18 Montenbruck, et al., A Real-time kinematic GPS sensor for spacecraft relative navigation, Aerospace Science and Technology, vol. 6, 2002, pp

19 Relative Navigation: Trajectory Model [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] (cont d) 19 Kalman filter estimates relative position and velocity of a remote spacecraft from differential GPS carrier phase measurements. The absolute state vector of the local spacecraft at the measurement is assumed to be known and can be calculated with interpolation polynomials The absolute nav accuracy of ~ 3 m would cause a maximum error of ~1.5 mm to rel-nav accurcy for a 10 km baseline. Trajectory Model: CW equations inadequate, so develop a numerical trajectory model Given the inertial PV of spacecraft A and relative PV of spacecraft B at t i, propagate inertial PV of both using RK4 with Richardson extrapolation to t i+1, and then determine the relative PV of spacecraft B at t i+1. JGM-3 gravity model with spherical harmonics up to degree and order 10 is adequate for this propagation. No empirical accelerations need to be considered for relative PV, but if the two spacecraft are different, differential atmospheric drag should be considered.

20 Relative Navigation: Between-receiver, between-satellite carrier phase measurement differences [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] 20

21 Relative Navigation: Measurement Model [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] 21 Between-receiver, between-satellite difference defined by Eq. (14) below is called double-difference (DD). The difference between receivers eliminates the GPS satellites ephemeris errors. Difference across GPS satellites eliminates the user clock error. If the baseline is long, such as 10 km, the iono delays at the two receivers may not be the same, so differencing it will leave some residual iono delay. DD carrier phase (CP) is related to DD range, DD integer ambiguity, and DD ionospheric delay as shown in Eq. (15). The DD carrier phase measurement will have some measurement noise. The DD CP ambiguity is fixed after initial convergence of the Kalman filter.

22 Relative Nav Kalman Filter State Vector [Leung, S., and Montenbruck, O., Real-time navigation, AIAA JGCD, vol. 28, no. 2, pp ] 22 This state vector, denoted x, shown below, consists of a maximum 18 parameters: Δy: 6x1 relative position and velocity vector I 0 vertical path iono delay N: 11x1 double-difference carrier phase ambiguities for the 12-channel GPS receiver I 0 and N are constant and are not propagated. Initial values for relative position and velocity are obtained from differential pseudoranges and carrier phase based differential range rates using the kinematic navigation algorithm Coarse ambiguities are obtained from the difference of code and carrier observations; then apply Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) method) Kalman Filter State Vector:

23 Relative Nav Kalman Filter Operation: Process Noise Matrix Q, Initial Error Covariance Matrix, and Fixing Integer Ambiguities [Leung, S., and Montenbruck, O., op cit] 23 Q is a diagonal matrix, with standard deviations of the state vector parameters as: 0.1 mm for relative position; 0.01 μm/s for relative position; these are for the two spacecraft experiencing the same drag acceleration I 0 and N are constant, so the diagonal entries of Q for these are zero. State estimate error covariance matrix P(t=0): Standard deviation for relative position and integer ambiguities: 2 m Velocity: 0.1 m/s Vertical ionospheric path delay: 3 m Carrier phase ambiguities are fixed if the float ambiguity estimate lies within 2% of an integer cycle, and the variation in the float ambiguity estimate within three consecutive filter updates is < 1% of an L1 cycle. If a cycle slip occurs for some pair of GPS satellites, the filter restimates the integer ambiguity for this pair. If there is a communication blackout, the filter will propagate its state using dynamic model.

24 [Leung, S., and Montenbruck, O., op cit] 24 GPS broadcast ephemeris errors: offsets of up to 5 m (2.5 m rms) in radial, tangential, and Normal direction; no multipath errors Ionosphere: Constant electron Density 20*10 16 e - /m 2 (3.2 m Vertical path delay) EKF update: 30 s

25 [Leung, S., and Montenbruck, O., op cit] 25

26 Conclusions [Leung, S., and Montenbruck, O., JGCD 2005, op cit] 26 Single-frequency GPS-based real-time navigation for formation flying of LEO satellites in a decentralized architecture, with inter-satellite communication, is feasible. An inertial nav accuracy of 3 m (3D) is achieved which is mostly caused by GPS ephemeris errors A superior relative nav accuracy of 1.5 mm and 5 μm/s is achieved for 1-10 km baseline in a simulated environment. Iono delay is eliminated with GRAPHIC and by accounting for GPS satellites elevation angles A rigorous relative motion model, double-difference integer ambiguity resolution Dual-frequency receiver would contribute to faster convergence of Kalman filter and integer ambiguity resolution Iono scintillation, total electron count gradients, multipath, spacecraft maneuvers or thruster firings for formation control are not considered.

27 Montenbruck, O., and Ramos-Bosch, P., Precision real-time navigation of LEO satellites using GPS measurements, GPS Solutions, vol. 12, 2008, pp Contemporary remote science such as altimetry, gravimetry, SAR interferometry, or atmospheric sounding requires sub-decimeter position accuracy and sub mm/s velocity knowledge of LEO satellites. To reduce the burden of ground-based navigation, autonomous navigation of LEO satellites is highly desired. Thus we require highly precise autonomous navigation of the LEO satellites. This can be achieved with dynamic orbit determination techniques using GPS signals and their onboard real-time processing to eliminate various sources of errors. Montenbruck and Ramos-Bosch, in the cited paper, provide a reference algorithm for real-time onboard orbit determination, tested with GPS measurements from various recent space missions. GPS broadcast ephemeris contribute significant nav errors (3 m, 3D rms). With real-time GPS ephemeris products such as TDRSS Augmentation Service for Satellites (TASS), the nav errors of LEO satellites are reduced to m realtime.

28 28

29 29

30 Montenbruck, O., and Ramos-Bosch, P., Precision real-time navigation of LEO satellites using GPS measurements, GPS Solutions, vol. 12, 2008, pp CHAMP: Challenging Minisatellite Payload GRACE: Gravity Recovery and Climate Experiment TerraSAR-X: Radar Satellite High Resolution Imagery ICEsat: Ice, Cloud, and land Elevation satellite SAC-C: NASA and Argentine mission MetOp: Meteorological Operations

31 Montenbruck, O., and Ramos-Bosch, P., Precision real-time navigation of LEO satellites using GPS measurements, GPS Solutions, vol. 12, 2008, pp

32 Montenbruck, O., and Ramos-Bosch, P., Precision real-time navigation of LEO satellites using GPS measurements, GPS Solutions, vol. 12, 2008, pp CODE: Center for Orbit Determination in Europe

33 D Amico, S., Ardaens, J.-S., and Montenbruck, O., Navigation of Formation Flying Spacecraft using GPS: The PRISMA Technology Demonstration, ION 22 nd International Meeting of the Satellite Division, Savannah, GA, September 22-25, PRISMA: Prototype Research Instruments and Space Mission technology Advancement

34 Courtesy: Mango (Main) and Tango (Target) 34

35 D Amico, S., et al., op. cit. [PRISMA] 35

36 D Amico, S., et al., op. cit. [PRISMA] 36

37 D Amico, S., et al., op. cit. 37

38 Conclusions [PRISMA] 38 A GPS-based navigation system for a two-satellite formation system is designed, implemented, and tested. Absolute real-time onboard positioning accuracy is ~3 m (3D, rms), mostly caused by GPS broadcast ephemeris errors and thruster activities This error can be mitigated with real-time GPS ephemeris Relative navigation accuracy depends critically on the attitude profile during specific mission phase, and may range from: 0.5 m if the GPS antennas of Main and Target point in different directions, Few cm if sufficient number of common GPS satellites is tracked by the two spacecraft Nav accuracy is limited by the restricted knowledge of Target attitude, and lack of knowledge of GPS antenna phase pattern variation in the s/c environment. For mm level accuracy, accurate attitude knowledge must be available on both s/c so as to enable real-time integer ambiguity resolution

39 Montenbruck, O., Wermuth, M., and Kahle, R., GPS Based Relative Navigation for the TanDEM-X Mission First Flight Results, Navigation: Journal of the ION, Vol. 58, No. 4, 2011, pp [with permission] 39 TanDEM-X: TerraSAR-X Add On Digital Elevation Mapping Synthetic aperture radar (SAR) mission, in close Formation flying with TerraSAR-X for bistatic SAR interferometry IGOR (Integrated GPS and Occultation Receiver)

40 Montenbruck, O., et al., op cit [with permission] 40 The objective of TanDEM-X is to produce a global map of high resolution digital elevation map with SAR interferometry. This requires baseline of a few hundred meters between the two spacecraft determined with mm accuracy. Both spacecraft are equipped with geodetic grade receivers. Polar dawn-dusk sun-synchronous orbit at a 515 km altitude, and an 11 day repeat period. The two spacecraft are in helix orbit which combines radial separation at the poles, with a lateral separation at the equator an e-i (eccentricityinclination) vector separation. This enables safe proximity operations in LEO. Mosaic GNSS receiver: single-frequency, for on-board navigation and timesynchronization Dual-frequency IGOR (Integrated GPS and Occultation Receiver) for offline orbit determination and reconstruction of the intersatellite separation

41 Moreira, A., Kreiger, G., Mittermayer, J, Satellite Configuration for Interferometric and/or Tomographic Remote Sensing by Means of Synthetic Aperture Radar, U.S. Patent No. 6,677,884 B2, Jan 13, Fig. 7 Orbits of two satellites having cross-track separation at equator and radial separation at the poles, and their planar projections to show the safe separation

42 Relative inclination and eccentricity vectors for LEO satellites 42 Montenbruck, et al, E/I-vector separation for safe switching of the GRACE formation, Aerospace Science and Technology, Vol. 10, 2006, pp D Amico, S., and Montenbruck, O., Proximity Operations of Formation-Flying Spacecraft Using an Eccentricity/Inclination Vector Separation, AIAA JGCD, Vol. 29, No. 3, pp

43 Perturbed and Controlled Motion of Relative Inclination and Eccentricity Vectors [D Amico, S., and Montenbruck, O., op. cit.] 43

44 Formation control of TanDEM-X (TDX) around TerraSAR-X (TSX): radial vs. cross-track motion [D Amico, S., and Montenbruck, O., op. cit.] 44

45 Formation control of TanDEM-X (TDX) around TerraSAR-X (TSX): radial vs. along-track motion [D Amico, S., and Montenbruck, O., op. cit.] 45

46 Formation control of TanDEM-X (TDX) around TerraSAR-X (TSX): tangential maneuvers [D Amico, S., and Montenbruck, O., op. cit.] 46

47 Conclusions [D Amico, S., and Montenbruck, O., op. cit.] 47 Orbital element differences simplify the formation flying relative dynamics and the design of autonomous control of perturbations caused by J 2. Relative eccentricity and inclination vectors their magnitudes and phases are related directly with the relative motion between the two satellites. This helps in designing safe, passive, J 2 -stable formation flying configurations (that is, the two orbits and the minute differences between their orbital elements). No-collision can be achieved, with desired navigation accuracies, by arranging and maintaining anti-parallel relative e/i vectors. This formation configuration design and control approach is suitable for SARinterferometry with a baseline of 1 km, or for longitude swap operation (GRACE satellites, for instance) with in-track separation of 200 km.

48 Montenbruck, O., D Amico, S., Ardaens, J.-S., and Wermuth, M., Carrier Phase Differential GPS for LEO Formation Flying The PRISMA and TanDEM-X Experience, AAS Astrodynamics Specialist Conference, July-August, 2010, Girdwood, U.S.A. 48 Both PRISMA and TanDEM-X use GPS as their primary means for absolute and relative navigation, but they use widely different GPS receivers, as the two missions are very different. PRISMA Low-cost single-frequency receiver Real-time navigation to provide instantaneous estimate of the relative state Real-time nav is compared with on-ground nav using CDGPS (single-difference carrier phase GPS) TanDEM-X No real-time solution required but a posteriori solution of rel nav of TDX-TSX SAR antenna required with ~1 mm (1D rms) accuracy (!) Geodetic-grade dual-frequency IGOR (integrated GPS occultation receiver, along with satellite laser ranging (SLR) reflectors The receiver is capable of L1 C/A code tracking, L1/L2 P(Y) tracking of up to 16 GPS satellites 12 channel of zenith looking choke ring antenna for precise orbit determination and relative navigation, 4 channels horizontal looking (parallel to velocity and antivelocity) for iono sounding

49 Offline (on-ground) Relative Navigation [Montenbruck, O., et al, AAS 2010, op cit] 49 Precise orbit determination with GPS High Precision Orbit Determination Software Tools (GHOST) PRISMA Single-frequency pseudorange and carrier phase measurements in a batch least-square estimation Determines epoch-wise clock offsets, the initial state vector, drag and radiation pressure coefficients, piece-wise constant empirical acceleration, and pass-by-pass ambiguities Precise GPS orbits and high rate (30 s) clock updates provided by CODE (Center for Orbit Determination in Europe) of the International GNSS Service (IGS) Iono errors eliminate with GRAPHIC (Group and Phase Ionospheric Correction) using L1 psudorange and carrier phase measurements Absolute position of Mango and Tango can be determined with 0.5 m accuracy in the absence of frequent orbit or attitude maneuvers TanDEM-X Dual-frequency carrier phase measurements enable ten times better orbit determination accuracy, ~ 5 cm; SLR predictions match

50 Offline (on-ground) Relative Navigation: Measurement models [Montenbruck, O., et al, AAS 2010, op cit] 50 To obtain relative nav accuracy of mm level, measurement models must also be of compatible accuracy. So GPS measurements on both spacecraft must be synchronized. For TanDEM-X, 1 μs mismatch causes 7.5 mm along-track position difference, so extrapolation required. Spacecraft attitude: GPS antennas are offset from the center-of-mass of the s/c Instantaneous attitude must be known with an accuracy of 0.5 mrad so proper sensors required Solar panel flexure Phase center offset and variation Center-of-mass location Phase wind up

51 Offline (on-ground) Relative Navigation Kalman Filter [Montenbruck, O., et al, AAS 2010, op cit] 51 For enhanced performance, the filter is operated in both forward and backward direction, so it is a filter/smoother For dual-frequency receiver (TanDEM-X), the filter estimates ΔI as well singledifference integer ambiguities ΔA 1 and ΔA 2, so for a 12 channel receiver the state vector is of the size 48x1 For single-frequency 12 channel receiver, the state vector shown below is 25x1 Integer ambiguities resolved by LAMBDA For dual-frequency receiver (TanDEM-X): For single-frequency:

52 Real-time Relative Navigation of PRISMA [Montenbruck, O., et al, AAS 2010, op cit] 52 Requirement: Provide absolute and relative navigation in all mission phases; the satellites don t necessarily maintain zenith orientation, and perform thruster firings for rendezvous and formation control Provide navigation even if only pseudorange and carrier phase measurements are from non-common GPS satellites (which means we can t difference the measurements from the two receivers) Fully symmetric treatment of both satellites; inertial (or ECEF) position and velocity of both satellites are estimated in a joint EKF. See the state vector below of the size ( )x1 for a 12-channel receiver; ΔV M is a delta velocity increment for the main satellite GRAPHIC is used with GPS satellites in view separately for Mango and Tango; this yields absolute nav accuracy of ~1 m for both satellites and ~ 0.5 m for relative nav After the use of GRAPHIC, single-difference carrier phase measurements for common GPS satellites in view are used Then, relative state, which would be accurate better than decimeter, would be obtained Onboard software does not insist on ambiguity fixing; float ambiguities are accepted to reduce load on flight computer High-fidelity acceleration model: 20x20 gravity, luni-solar gravity, atmospheric drag New measurements are process once every 30 s to manage the flight computer load, and trajectories are interpolated for 1 Hz navigation

53 [Montenbruck, O., et al, AAS 2010, op cit] 53

54 Summary and Conclusion [Montenbruck, O., et al, AAS 2010, op cit] 54 With single-difference carrier phase measurements, relative positions of two spacecraft can be reconstructed with the accuracy of a few mm to cm level. Achievable real-time accuracies are limited by phase center variation, and phase pattern distortion that may introduce unknown biases far greater than 1 mm carrier phase measurement noise level. Dual-frequency measurements are desirable for very precise navigation. For real-time applications, rel nav accuracy of PRISMA using single-difference carrier phase is sub-decimeter; but this is because of accepting float ambiguities to reduce load on onboard computer. In future formation flying missions, with moderate thruster activity, favorable spacecraft attitude, and a properly designed antenna system, 1 cm relative nav is possible.

55 55 Courtesy:

56 56

57 Concluding Remarks 57 The use of pseudorange and differential carrier phase GPS signals for real-time precise absolute navigation and precise relative navigation for formation control of LEO satellites has already been demonstrated. The on-orbit precision depends on the receivers and the way the signals are used, and the on-board computer resources. Further, it also depends on if real-time GPS satellites positions are made available with TDRSS Augmentation or International GNSS Service. Not sure if GAGAN would provide this service for India. This high nav accuracy has been achieved with both single-frequency and dualfrequency receivers, with accuracies of different levels. While EKF is used for on-orbit real-time navigation, batch least-square-error technique is used for on-ground post-facto navigation analysis for some remote sensing applications. Research on the use of IRNSS for precise absolute navigation (~0.2 m) and precise relative navigation (~1 mm) for formation control of SAR interferometry remote sensing LEO satellites will be very fruitful.