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GP-B Spacecraft
Redundant spacecraft processors, transponders. 16 Helium gas thrusters, 0-10 mN ea, for fine 6 DOF control.Roll star sensors for fine pointing.Magnetometers for coarse attitude determination.Tertiary sun sensors for very coarse attitude determination.Magnetic torque rods for coarse orientation control.Mass trim to tune moments of inertia.Dual transponders for TDRSS and ground station communications.Stanford-modified GPS receiver for precise orbit information. 70 A-Hr batteries, solar arrays operating perfectly.
6.4 m 3240 kg
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Challenges of Data Analysis
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Simple GP-B Data Analysis
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Three Cornerstones of Dynamic Estimation (Filtering)InformationTheoryFilter Implementation: Numerical TechniquesSQUID Readout Signal Structure: Measurement ModelsUnderlyingPhysics,Engineering
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Data Analysis Structure: Two-Floor ProcessingSQUID Readout ProcessingGyro Orientation Time HistoryData Analysis BuildingFirst FloorSecond FloorRelativityMeasurementFull Information Matrix
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Polhode Motion, Trapped Flux & CgActual London moment readout
Trapped magnetic fieldsLondon magnetic field at 80 Hz: 57.2 GGyro 1: 3.0 GGyro 2: 1.3 G Gyro 3: 0.8 GGyro 4: 0.2 G Scale factor Cg modulated at polhode frequency by trapped magnetic fluxTwo methods of determining Cg history- Fit polhode harmonics to LF SQUID signal- Direct computation by Trapped Flux Mapping
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Polhode Motion and Readout Scale Factor: Cg ModelGyro principle axes of inertiaand instant spin axis position Harmonic expansion in polhode phase with coefficients that depend on polhode angleTrapped Flux Mapping (TFM)UnknownsTrapped FluxJohn Conklin
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
First Floor: SQUID Readout Data ProcessingSQUID DataSQUID No-bias SignalNonlinear Least-Squares Estimator(No Torque Modeling)Roll PhaseDataAberrationDataData Grading
Batch length: 1orbit
Bias EstimatorCg (tk*)CT (tk*) (tk*)ResidualsPointing/Misalign. Computation Roll PhaseDataAberrationDataOUTPUT:PointingGSV/GSIPolhode PhaseDataPolhode AngleDataFull Information MatrixLets look at the gyro orientation profilesG/T Matching
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Inertial Orientation Time-history: Gyro 1 NS Direction De-trendedtimemilliarcsecm=42m=41NS DirectiontimemilliarcsecStrong Geodetic Effect
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Inertial Orientation Time-history: Gyro 2NS direction de-trendedmilliarcsecEW Direction
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Torque Modelingk(t), c+(t), c-(t) are modulated by harmonics of polhode frequency roll/polhode resonance: 2006-20072008
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Torque Coefficients: Polhode VariationRoll-resonance torque coefficients c+, c-:The same polhode structure as in Readout Scale Factor Model (1st Floor)
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
2nd Floor Roll-Resonance Torque Dynamic EstimatorFull 1st Floor Information is not yet used
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Gyro 2: Estimation Results(Modeled Orientation vs Measured Orientation)Subtracting the torque contributions 74 Resonances!
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Gyro 2: Reconstructed Relativistic TrajectoryFrame-dragging effect!
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Current Relativity Estimates for Gyros 1,2,3, and 4GR predictionGyro 1,2,3,4 combinedG1G3
GP-B/Aero-Astro*Data AnalysisSeptember 30, 2008 Stanford
Where we stand now Roll-Resonance Torque Modeling: reduced large part of systematic errors: previously unmodeled torque-related errors are now modeled properly dramatically enhanced the agreement between the gyroscopes The same torque model works for all 4 gyros over entire mission Developed estimator is not good enough: Orientation time step, currently 1-orbit (97min) should be made much less than 1 roll period (77 sec) Final improvement of Algebraic Method: 2-sec Filter: That is where we need your help!
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Two-Second Filter: Nonlinear Stochastic Optimization ProblemNew Filter is formulated as a Dynamic Nonlinear Estimation Problem:(!)SQUID Data307 days = 4605 orbits x 97 min x 30 (2-sec data points)Nonlinear Model Nonlinear Dynamic Gyro Motion Model Requires multiple cost-function minimum search iterations going through millions of data pointsFor 1 Gyro
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Main EquationsTr = 97 secGeodeticFrame-dragging
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Main Equaitions -cont
GP-B/ Aero-Astro*October 21, 2008 StanfordData Analysis
Challenges of 2-sec FilterDealing with several millions of measurement equations requires new assessment of numerical techniques and computational capabilitiesAnalyzing gyroscopes together and the nonlinear structure of the estimation problem probably will require parallel processing (in which we have no experience)Evaluation of the analysis results, given the complexity of 2-sec filter, will probably require the development of new truth model simulations
Get correct numbers for Geodetic effect (6623)Lipa: how does this tie to Einsteins GR put back prediction equations