GPS Data Processing Methods for Satellite Formation Flying

1. M.Sc. in Advanced Communication and Navigation Satellite Systems Chapter of Rome AFCEA’s International Student Conference 2008 “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini Brussels, April 10 2008

2. Introduction to the study • Master of Science (M.Sc.) in Advanced Communications and Navigation Satellite Systems of the University of Rome “Tor Vergata” achieved in February 2008 • Internship in the Observation Systems & Radar B.U. – Satellite Systems Engineering – Integrated Control Systems of Thales Alenia Space Italy S.p.A. (TAS-I) based in Rome, Italy • Study of a future TAS-I/ASI (Italian Space Agency) Low Earth Orbit Satellite in Formation Flying with COSMO Sky-Med Constellation Satellites for Remote Sensing and Earth Observation • High Accuracy Levels in the Relative Baseline Determination between COSMO Sky-Med Satellites and the future Formation Flying Satellite for reasons of High Level of SAR images Resolution using Interferometric Techniques and GPS Carrier Phase Data Processing Methods

3. Main topics • Mission Requirements • High Accuracy Levels in the Relative Baseline Determination between COSMO Sky-Med Satellites and the future Formation Flying Satellite for reasons of High Level of SAR images Resolution using Interferometric Techniques • Main Arguments • Mission Accurate Baseline Determination On-Board Processing Models & Algorithms using GPS Carrier Phase Data • Theory and SW Tooling Implementation & Testing of the GPS Data Processing Methods • Overview & Synthesis of the GPS Orbital Receiver SW Simulator • GPS Receiver SW Simulator Architecture, Performances & Test Campaign Results • Simulations Numerical Results & Test Performances • Targets • Simulations Results near to Real On-Board GPS Receiver Physical behaviour • Simulations Results near to Real GPS Signal Degradation & Delay Sources • High level of Accuracy in the Formation Flying Satellites Receivers Baseline Determination • Next Steps • SW Tools integration in the Satellite System & Subsystems Platform SW Simulator • Algorithms Tests SW Performances: From Post-Processing to On-Board Real-Time SW implementation

4. Spacecraft formationflying missions • Spacecraft formation flying is commonly considered as: • a key technology for advanced space missions • The distribution of sensor systems to multiple platforms offers: • improved flexibility and redundancy • shorter times to mission • the prospect of being more cost-effective • compared to large individual spacecraft • Satellite formations in Low Earth Orbit provide: • advanced science opportunities that cannot (or less easily) be realized with single spacecraft (such as): • measuring small scale variations in the Earth’s gravity field • higher resolution imagery and interferometry

5. Spacecraft formationflying missions • Fundamental issues of spacecraft formation flying: • the determination of the relative state (position and velocity) between the satellite vehicles within the formation • knowledge of these relative states in (near) real-time is important for operational aspects • some of the scientific applications, such as high resolution interferometry, require an accurate post-facto knowledge of these states instead • therefore a suitable sensor system needs to be selected for each mission

6. Formation Flying forEarth Remote Sensing

7. Formation Flying forEarth Remote Sensing • Classification of active microwave formations

8. Mission Objectives & Scenario • The Program is an experimental Mission both for scientific contribution and for the innovative technological aspects • The Program shall operate in strict coordination with COSMO-SkyMed, without any impact at Space and Ground level • The Program will be developed in order to guarantee a maximum level of commonality with COSMO in terms of synergies, developments, operations and maintenance • The Mission objectives are: • to provide additional products wrt the COSMO-SkyMed ones • to realize a “demonstrator” for the testing of Interferometric, Bistatic, Radargrammetric techniques • to fly in formation with one satellite of the COSMO-SkyMed constellation, avoiding to interfere with COSMO-SkyMed mission and operations

9. Mission Objectives & Scenario • Selected Configurations for Interferometric and Bistatic acquisitions from the Reference COSMO-SkyMed orbit • Leader-Follower • Cartwheel • Pendulum

10. Mission Objectives & Scenario Reference: Hill’s coordinate frame

11. GPS Receiver SW Simulator Overview • Simulated Physical Quantities • The SW Simulator reproduces two different main scenarios: • The first one is represented by the Simulated Operative Behaviour Physics in which the GPS Receiver operates that is the Orbital Mechanics and the Physical Degradations and Delays which affect the In-Space GPS Signal transmitted from GPS Satellites to the In-Orbit GPS Receiver. • The second one is about the GPS Receiver Behaviour and Performances as far as: • Receiver estimations and measures of the GPS Signal Degradations due to the Received GPS Signal (Code and Phase) Acquisition and Tracking Processes; • Pseudo-range and Pseudo-range-Rate Equations Systems Resolution for the In-Orbit Receiver Position and Velocity determination;

12. GPS Receiver SW Simulator Overview SW Simulator Logical Scheme

13. GPS Receiver SW Simulator Overview 3D ECI Propagated Receiver Position & Velocity Dynamics Receiver 3DOrbital Velocity Receiver 3D Orbital Position

14. GPS Receiver SW Simulator Overview 3D ECI NORAD Propagated GPS Satellites Position & Velocity Dynamics GPS Satellites 3D Orbital Position GPS Satellites 3D Orbital Velocity

15. GPS Receiver SW Simulator Overview GPS Signal Degradation & Delay Models (1) Receiver Clock Bias Delay Effect Measures Dynamic Ionospheric Delay Effect Measures Dynamic GPS SAT PRN N°1 2nd Order Relativistic Delay Effect Measures Dynamic Receiver 1st Order Relativistic Delay Effect Measures Dynamic

16. GPS Receiver SW Simulator Overview GPS Signal Degradation And Delay Models (2) GPS SAT PRN N°1 C/A Code Gain Pattern Delay Effect Measures Dynamic GPS SAT L1 Carrier Frequency Multipath Delay Effect Measures Dynamic GPS SAT PRN N°1 L1 and L2 Carrier Frequencies Signal to Noise Ratio (SNR) Measures Dynamic GPS SAT L1 Carrier Frequency Relativistic Doppler Delay Effect Measures Dynamic

17. GPS Receiver SW Simulator Overview Receiver Measures Determination GPS SAT PRN N°1 Free Space GPS Signal Propagation Time Delay Dynamic GPS SAT PRN N°1 L1 Carrier Frequency Pseudo-range Measures Dynamic GPS SAT PRN N°1 L1 Carrier Frequency Integrated Pseudo-range Measures Dynamic GPS SAT PRN N°1 L1 Carrier Frequency Pseudo-range Rate Measures Dynamic GPS SAT PRN N°1 L1 Carrier Phase Integrated Doppler Measures Dynamic GPS SAT PRN N°1 L1 Carrier Phase Integrated Doppler Rate Measures Dynamic

18. GPS Receiver SW Simulator Overview GPS Satellites Visibility Determination Number of GPS Satellites Visibility Dynamic GPS PRN Satellites Visibility Dynamic Visibility: Mean Value and Standard Deviation

19. GPS Receiver SW Simulator Overview • Receiver SPS Position & Velocity Solutions Accuracy • Receiver SPS 3D ECI Position Components (X,Y,Z) Error Dynamics • Receiver SPS 3D ECI Velocity Components (U,V,W) Error Dynamics

20. GPS Receiver SW Simulator Overview Navigation Solution Performance Requirements (Laben Test Report)

21. GPS Observations & Relative Spacecraft Positioning • Relative positioning models: • - Single difference model • - Double difference model • Relative Spacecraft Positioning: • Integer ambiguity resolution: • Integer ambiguity estimation • Integer ambiguity validation • Proposed processing strategy: • Sequential kinematic filter (Real Time Kinematic/RTK approach)

22. GPS Observations & Relative Spacecraft Positioning • Relative positioning models: Single & Double difference models Overall viewing geometry for relative (spacecraft) positioning using differenced GPS observations. GPS satellites j and k are commonly observed by both receivers and thus SD and DD observations can be formed. This is not the case for GPS satellites h and m, which are only observed by one receiver

23. GPS Observations & Relative Spacecraft Positioning Integer ambiguity resolution (estimation & validation) Distribution of a double difference ambiguity as real-valued (float) and accompanying integer (fixed) solution. In the left figure the probability mass for the correct value (4) is still low, in the right figure this might already be high enough to neglect the stochastic nature of the ambiguity

24. GPS Observations & Relative Spacecraft Positioning • Overall Processing And Positioning Strategy: • • Complete initialization of all DD ambiguities • • Partial (re)initialization of new DD ambiguities • • Relative positioning with DD carrier phase observations and known integer ambiguities

25. GPS Observations & Relative Spacecraft Positioning • STEP 1: Measures initialization & acquisition processes • STEP 2: Observables double difference DD and covariance matrices construction • STEP 3: Initial differential ambiguities determination: the MLAMBDA method • - Floating point solution • - Reduction and de-correlation processes • - Search process • STEP 4: Ambiguities fixing & ionosphere free combination processes • STEP 5: Relative positioning & ambiguity-fixed-ionosphere free DD carrier phases

26. MLAMBDA: A Modified LAMBDA methodfor Integer Least-squares Estimation • The LAMBDA method: • Reduction process: • Integer Gauss transformations • Permutations • The reduction algorithm • Discrete search process • Modifying the LAMBDA method: (MLAMDA) • Modified reduction • Symmetric pivoting strategy • Greedy selection strategy • Lazy transformation strategy • Modified reduction algorithm • Modified search process

27. MLAMBDA: A Modified LAMBDA methodfor Integer Least-squares Estimation • Numerical simulations Satellite B Orbital Position 3D ECI components Baseline between sat A and B 3D ECI components

28. MLAMBDA: A Modified LAMBDA methodfor Integer Least-squares Estimation • Numerical simulations Satellite B Orbital Position X ECI component esteem solution accuracy Satellite B Orbital Position Y ECI component esteem solution accuracy Satellite B Orbital Position Z ECI component esteem solution accuracy

29. MLAMBDA: A Modified LAMBDA methodfor Integer Least-squares Estimation • Numerical simulations Baseline error X ECI component Baseline error Z ECI component Baseline error Y ECI component Baseline ECI error norm

30. MLAMBDA: A Modified LAMBDA methodfor Integer Least-squares Estimation • Numerical simulations Satellite B error norm PDOP for Satellite A ECI satellite B 3D vector components accuracy Mean Value and Standard Deviation PDOP for Satellite B

31. Conclusions & Future Developments • Conclusions • From a careful statistical study and from an accurate comparison between the SW Simulator Data Graphics and those reported in the Laben Lagrange Test Reports we can conclude that the GPS SW Simulator supplies statistically the same results of the real Lagrange Receiver (ENEIDE Mission) • The SW Simulator also reconstructs the Lagrange Mission Operative Environment simulating the physics which governs both the Receiver Orbital Dynamic and the GPS Constellation Orbital Dynamic considering all types of orbital perturbations • The simulations of the GPS data processing with the SW tools for the accurate baseline determination have reached the requested preliminary mission performances which are accuracies on each ECI component in space of the order of 1 cm as Standard Deviation in very short computational time for simulations time periods of 1 orbit

32. Conclusions & Future Developments • Future Developments • Now the work is to develop new strategies and algorithms to make more robust and accurate the data processing performances and integrate these SW tools in the Mission Satellite Platform SW Simulator in Matlab which will be used for the simulations of the Satellite System and Subsystems in the preliminary mission requirements design phase • The future step will be to decode all these SW tools from Fortran and Matlab to the ADA code in which the Satellite On-Board SW is implemented and try to reach the target of obtaining the same statistical real-time GPS data processing performances On-Board and higher level of accuracy (of the order of 1 mm) in the ground-based post-processing

33. Thank you very much for your attention!Do you have any question? Mobile: (0049)3382376754 E-mail: michelange.ambrosini@tiscali.it Public Profile URL: http://www.linkedin.com/in/michelangeloambrosini On-line Curriculum Vitae URL: http://ctif.uniroma2.it/mastercv/ambrosinim/CV_Ambrosini_ENG.pdf Michelangelo Ambrosini Thales Alenia Space Italia S.p.A. (TAS-I) Observation Systems & Radar Business Unit Satellite System Engineering Integrated Control Systems Via Saccomuro, 24 - 00131 - Rome, Italy Michelangelo Ambrosini Brussels, April 10 2008