Presentazione_stage_Ambrosini

Observation Systems & Radar Business Unit
February 4th, 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
All rights reserved, 2008, Thales Alenia Space
Templatereference:100181670S-EN
GPS DATA PROCESSING METHODS
USING SW TOOLS AND THE GPS
RECEIVER SW SIMULATOR FOR
PRECISE RELATIVE POSITIONING OF
FORMATION FLYING SATELLITES
of Michelangelo Ambrosini

Page 2
GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR
February 4th, 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

Page 3
February 4th, 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

Page 4
February 4th, 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

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February 4th, 2008
Formation Flying for Earth Remote Sensing

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February 4th, 2008
Classification of active microwave formations
Formation Flying for Earth Remote Sensing

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February 4th, 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

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February 4th, 2008
Selected Configurations for Interferometric and Bistatic acquisitions
from the Reference COSMO-SkyMed orbit
 Leader-Follower
 Cartwheel
 Pendulum

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February 4th, 2008
Reference: Hill’s coordinate frame

Page 10
February 4th, 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

Page 11
February 4th, 2008
SIMULATION
STARTING DATA
RECEIVERS SPS
POSITION AND VELOCITY SOLUTION
RECEIVERS
ORBITAL PROPAGATION
GPS SATELLITES
ORBITAL PROPAGATION
RECEIVERS SIGNAL
DEGRADATIONS MEASUREMENTS
RECEIVERS SIGNAL
DEGRADATIONS ESTEEMS
RECEIVERS INNER
LOOPS DEGRADATIONS
MEASUREMENTS
POST PROCESSING
(RTK & MLAMBDA METHOD)
FORMATION SPS
POSITION AND
VELOCITY
BASELINE SOLUTION
RECEIVERS EXACT
POSITION AND VELOCITY
SOLUTIONS
FORMATION EXACT
POSITION AND
VELOCITY
BASELINE SOLUTION
FORMATION
BASELINE ACCURACY
SW Simulator Logical Scheme

Page 12
February 4th, 2008
3D ECI Propagated Receiver Position & Velocity Dynamics
Receiver 3D Orbital Position Receiver 3D Orbital Velocity

Page 13
February 4th, 2008
3D ECI NORAD Propagated GPS Satellites Position &
Velocity Dynamics
GPS Satellites 3D Orbital Position GPS Satellites 3D Orbital Velocity

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February 4th, 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

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February 4th, 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

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February 4th, 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
Pseudo-range Rate Measures Dynamic
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

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February 4th, 2008
GPS Satellites Visibility Determination
GPS PRN Satellites Visibility Dynamic
Visibility: Mean Value and Standard Deviation
Number of GPS Satellites
Visibility Dynamic

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February 4th, 2008
Physical Quantities Mean Value 1σ
CLOCK BIAS 1.8005e-008 [sec] 1.03937e-008 [sec]
CLOCK BIAS RATE 1.0e-011 [sec/sec] 0.0[sec/sec]
IONOSPHERE 1.0081 [m] 0.9904 [m]
MULTIPATH 0.1083 [m] 0.1823 [m]
GPS 1° ORDER RELATIVITY 2.2203e+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 PATTERN 0.0045 [m] 4.0079 [m]
Receiver Measures Statistics: Mean Value and Standard Deviation

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February 4th, 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

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February 4th, 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]
121.06 480.38 456.41 4.438 10.572 9.144 34.946 9.121
∆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]
121.09 480.45 456.46 6.156 14.417 12.394 35.117 12.628
L1 Carrier Frequency ECI Position and Velocity Solutions Precision
L2 Carrier Frequency ECI Position and Velocity Solutions Precision

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February 4th, 2008
Navigation Solution Performance Requirements (Laben Test Report)

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February 4th, 2008
DOP Determination
Receiver L1 Carrier Frequency GDOP Measures Dynamic
Receiver L1 Carrier Frequency PDOP Measures Dynamic
Receiver L1 Carrier Frequency PDOP Measures Dynamic
GDOP, PDOP and TDOP Mean Value and Sigma

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February 4th, 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

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February 4th, 2008
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

Page 25
February 4th, 2008
Integer ambiguity resolution (estimation & validation)
Positioning
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

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February 4th, 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
Positioning

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February 4th, 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
Positioning

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February 4th, 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

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February 4th, 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

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February 4th, 2008
Numerical simulations (1)
Average CPU running time for dimension 5 < n < 40

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February 4th, 2008
Average CPU running time for dimension n = 40

Page 32
February 4th, 2008
Satellite B Orbital Position 3D
ECI components
Baseline between sat A and B
3D ECI components

Page 33
February 4th, 2008
Satellite B Orbital Position
X ECI component esteem
solution accuracy
Y ECI component esteem
solution accuracy
Z ECI component esteem
solution accuracy

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February 4th, 2008
Baseline error X ECI component
Baseline error Y ECI component
Baseline error Z ECI component
Baseline ECI error norm

Page 35
February 4th, 2008
Satellite B error norm PDOP for Satellite A
PDOP for Satellite B
ECI 3D error
Components
Mean values
(meters)
1σ
(meters)
Δx (1°) 0.0149 0.0138
Δy (2°) 0.0237 0.0114
Δz (3°) 0.0375 0.0460
ECI satellite B 3D vector components
accuracy Mean Value and Standard Deviation

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February 4th, 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

Page 37
February 4th, 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

Page 38
February 4th, 2008
Michelangelo Ambrosini
SABRINA Mission GPS Navigation
Thales Alenia Space Italia S.p.A.
Satellite System Engineering Division
Avionics Systems Subdivision
Via Saccomuro, 24 - 00131 Roma
Room: E2.24
Office: (0039)0641512431
Mobile: (0039)3382376754
E-mail (work): michelangelo.ambrosini@thalesaleniaspace.com
E-mail (home): michelange.ambrosini@tiscali.it

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