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
