1. April 10, 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 Template reference : 100181670S-EN All rights reserved, 2008, Thales Alenia Space Chapter of Rome M.Sc. in Advanced Communication and Navigation Satellite Systems 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” Brussels, April 10 2008 of Michelangelo Ambrosini

2. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 2 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Introduction to the study 1.Master of Science (M.Sc.) in Advanced Communications and Navigation Satellite Systems of the University of Rome “Tor Vergata” achieved in February 2008 2.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 3.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 4.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. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 3 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 Main topics

4. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 4 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 Spacecraft formation flying missions

5. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 5 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 Spacecraft formation flying missions

6. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 6 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Formation Flying for Earth Remote Sensing

7. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 7 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Classification of active microwave formations Formation Flying for Earth Remote Sensing

8. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 8 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 9 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Mission Objectives & Scenario Selected Configurations for Interferometric and Bistatic acquisitions from the Reference COSMO-SkyMed orbit Leader-Follower Cartwheel Pendulum

10. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 10 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Mission Objectives & Scenario Reference: Hill’s coordinate frame

11. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 11 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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; GPS Receiver SW Simulator Overview

12. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 12 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 SIMULATION STARTING DATA RECEIVERS SPS POSITION AND VELOCITY SOLUTION FORMATION SPS POSITION AND VELOCITY BASELINE SOLUTION RECEIVERS EXACT POSITION AND VELOCITY SOLUTIONS FORMATION EXACT POSITION AND VELOCITY BASELINE SOLUTION RECEIVERS ORBITAL PROPAGATION GPS SATELLITES ORBITAL PROPAGATION RECEIVERS SIGNAL DEGRADATIONS MEASUREMENTS RECEIVERS INNER LOOPS DEGRADATIONS MEASUREMENTS POST PROCESSING (RTK & MLAMBDA METHOD) FORMATION BASELINE ACCURACY RECEIVERS SIGNAL DEGRADATIONS ESTEEMS SW Simulator Logical Scheme GPS Receiver SW Simulator Overview

13. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 13 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 3D ECI Propagated Receiver Position & Velocity Dynamics Receiver 3D Orbital Position Receiver 3D Orbital Velocity GPS Receiver SW Simulator Overview

14. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 14 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 3D ECI NORAD Propagated GPS Satellites Position & Velocity Dynamics GPS Satellites 3D Orbital PositionGPS Satellites 3D Orbital Velocity GPS Receiver SW Simulator Overview

15. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 15 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 GPS Signal Degradation & Delay Models (1) Receiver Clock Bias Delay Effect Measures Dynamic Ionospheric Delay Effect Measures Dynamic Receiver 1st Order Relativistic Delay Effect Measures Dynamic GPS SAT PRN N°1 2nd Order Relativistic Delay Effect Measures Dynamic GPS Receiver SW Simulator Overview

16. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 16 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 GPS Signal Degradation And Delay Models (2) GPS SAT PRN N°1 L1 and L2 Carrier Frequencies Signal to Noise Ratio (SNR) Measures Dynamic GPS SAT L1 Carrier Frequency Multipath Delay Effect Measures Dynamic GPS SAT PRN N°1 C/A Code Gain Pattern Delay Effect Measures Dynamic GPS SAT L1 Carrier Frequency Relativistic Doppler Delay Effect Measures Dynamic GPS Receiver SW Simulator Overview

17. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 17 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 Pseudo-range Rate Measures Dynamic GPS SAT PRN N°1 L1 Carrier Frequency Integrated Pseudo-range 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 GPS Receiver SW Simulator Overview

18. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 18 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 GPS Satellites Visibility Determination GPS PRN Satellites Visibility Dynamic Visibility: Mean Value and Standard Deviation Number of GPS Satellites Visibility Dynamic GPS Receiver SW Simulator Overview

19. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 19 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Physical QuantitiesMean Value1σ CLOCK BIAS1.8005e-008 [sec]1.03937e-008 [sec] CLOCK BIAS RATE1.0e-011 [sec/sec]0.0[sec/sec] IONOSPHERE1.0081 [m]0.9904 [m] MULTIPATH0.1083 [m]0.1823 [m] GPS 1° ORDER RELATIVITY2.2203e+003 [m]3.9047e+003 [m] RECEIVER 1° ORDER RELATIVITY 9.2628e+003 [m]5.3478e+003 [m] RECEIVER 2° ORDER RELATIVITY 0.0226 [m]0.0081 [m] CARRIER DOPPLER EFFECT 6.6936 [m] 387.5065 [Hz] 213.9529 [m] 1.2307e+004 [Hz] GAIN PATTERN0.0045 [m]4.0079 [m] Receiver Measures Statistics: Mean Value and Standard Deviation GPS Receiver SW Simulator Overview

20. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 20 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 GPS Receiver SW Simulator Overview

21. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 21 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 ∆x, 1σ [m] ∆y, 1σ [m] ∆z, 1σ [m] ∆vx, 1σ [m/s] ∆vy, 1σ [m/s] ∆vz, 1σ [m/s] Pos, 1σ 3D [m] Vel 1σ 3D [m/s] 121.06480.38456.414.43810.5729.14434.9469.121 ∆x, 1σ [m] ∆y, 1σ [m] ∆z, 1σ [m] ∆vx, 1σ [m/s] ∆vy, 1σ [m/s] ∆vz, 1σ [m/s] Pos 1σ 3D [m] Vel 1σ 3D [m/s] 121.09480.45456.466.15614.41712.39435.11712.628 L1 Carrier Frequency ECI Position and Velocity Solutions Precision L2 Carrier Frequency ECI Position and Velocity Solutions Precision GPS Receiver SW Simulator Overview

22. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 22 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Navigation Solution Performance Requirements (Laben Test Report) GPS Receiver SW Simulator Overview

23. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 23 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 DOP Determination Receiver L1 Carrier Frequency GDOP Measures Dynamic Receiver L1 Carrier Frequency PDOP Measures Dynamic GDOP, PDOP and TDOP Mean Value and Sigma GPS Receiver SW Simulator Overview

24. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 24 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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) GPS Observations & Relative Spacecraft Positioning

25. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 25 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 GPS Observations & Relative Spacecraft Positioning

26. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 26 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 GPS Observations & Relative Spacecraft Positioning

27. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 27 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 GPS Observations & Relative Spacecraft Positioning

28. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 28 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 GPS Observations & Relative Spacecraft Positioning

29. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 29 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 The well-known LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) method has been widely used for the integer least-squares (ILS) estimation problems in positioning and navigation -The LAMBDA method consists of two stages: reduction and search -We presented a modified LAMBDA method (MLAMBDA) which improves both this two stages -The key to the algorithm is to compute the factorization with symmetric pivoting, de-correlate the parameters by greedy selection and lazy transformations, and shrink the ellipsoidal region during the search process -Numerical simulation showed that MLAMBDA can be much faster than LAMBDA implemented in Delft’s LAMBDA package for high dimensional problems -This will be particularly useful to integer ambiguity determination when there are more GNSS satellites visible simultaneously, with carrier phase observations on three frequencies in the future MLAMBDA: A Modified LAMBDA method for Integer Least-squares Estimation

30. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 30 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 MLAMBDA: A Modified LAMBDA method for Integer Least-squares Estimation

31. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 31 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Numerical simulations Average CPU running time for dimension 5 < n < 40 MLAMBDA: A Modified LAMBDA method for Integer Least-squares Estimation

32. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 32 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Numerical simulations Average CPU running time for dimension n = 40 MLAMBDA: A Modified LAMBDA method for Integer Least-squares Estimation

33. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 33 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Numerical simulations Satellite B Orbital Position 3D ECI components Baseline between sat A and B 3D ECI components MLAMBDA: A Modified LAMBDA method for Integer Least-squares Estimation

34. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 34 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 MLAMBDA: A Modified LAMBDA method for Integer Least-squares Estimation

35. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 35 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Numerical simulations Baseline error X ECI component Baseline error Y ECI component Baseline error Z ECI component Baseline ECI error norm MLAMBDA: A Modified LAMBDA method for Integer Least-squares Estimation

36. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 36 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Numerical simulations Satellite B error normPDOP for Satellite A PDOP for Satellite B ECI 3D error Components Mean values (meters) 1σ (meters) Δx (1°)0.01490.0138 Δy (2°)0.02370.0114 Δz (3°)0.03750.0460 ECI satellite B 3D vector components accuracy Mean Value and Standard Deviation MLAMBDA: A Modified LAMBDA method for Integer Least-squares Estimation

37. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 37 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 Conclusions & Future Developments

38. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 38 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 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 Conclusions & Future Developments

39. All rights reserved, 2008, Thales Alenia Space Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems Page 39 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini April 10, 2008 Michelangelo Ambrosini Thank you very much for your attention! Do you have any question? Brussels, April 10 2008 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 Mobile: (0049)3382376754 E-mail: michelange.ambrosini@tiscali. it michelange.ambrosini@tiscali. it Public Profile URL: http://www.linkedin.com/in/mic helangeloambrosini http://www.linkedin.com/in/mic helangeloambrosini On-line Curriculum Vitae URL: http://ctif.uniroma2.it/mastercv /ambrosinim/CV_Ambrosini_E NG.pdf http://ctif.uniroma2.it/mastercv /ambrosinim/CV_Ambrosini_E NG.pdf