2second Filter: Software Development Review

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2-second Filter Software Development Review
M.Heifetz, J.Conklin
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Outline

• Fundamentals of 2-sec Filter
• Modular Software Structure
• Schedule of Tests

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• Four Cornerstones of Filter Development

SQUID Readout Signal Structure Measurement
Model(s)
Gyroscope Motion Torque Model(s)
Estimation Algorithms Numerical Techniques
Algebraic Method Machinery Development and
Experience
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SQUID Readout Signal Model

• Estimation performed for the data collected
  during Guide
• Star Valid (GSV) mode

• Pointing

Estimated (?) Torb 24.648770 days
known
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Scale Factor (Cg) 4 Approaches

• Use TFM scale factor variations as is
  (simplest)
• Algebraic filter will estimate constant CgLM
  only
• Use ?Cg model without TFM prior information
  (symmetric phase)
• Algebraic filter estimates full set of ?Cg
  coefficients ank, bnk and CgLM
• Use TFM scale factor and estimate correction via
  ?Cg
• Algebraic filter estimates subset of ?Cg
  coefficients amn, bmn, and CgLM

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4. Ideal Approach Exact Polhode Phase

• ?Cg Model using exact polhode phase ?p
• Algebraic filter will estimate CgLM, update TFM
  estimates of amn, bmn

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Gyroscope Motion Torque Model
Misalignment Torque
Roll-resonance Torque
Relativity
TFM
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• Explicit solution for orientation (Alex S.)

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Pointing Error Compensation (matching)

• - part of state
  vector
• (per gyro, per telescope side)

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GP-B Data Analysis Nonlinear Filtering Problem
Two main approaches

• Iterative Extended Kalman Filter (IEKF)
• widely used in post-flight data analysis
• drawbacks linearization and potentially biased
  state-vector estimate

• Sigma Point Filter (SPF)
• recently developed by the aero-astro community
  for spacecraft attitude estimation, nonlinear
  aerodynamic parameter estimation, and tracking
  applications
• claims that performance is better than EKF/IEKF
• drawbacks more computationally intensive than
  EKF

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Iterative Extended Kalman Filter (IEKF)

• Iterative linearization process

(1)
(2)
(3)
(4)
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• Apply linear least-squares estimator (e.g.
  square-root information filter)

Output and

• Difficulty Jacobian computation
• analytic
• numerical

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List of Modules
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List of Modules cont.

• Code for all methods exist and have been vetted
• Must be packaged into a single function with
  option to select method
• For Cg with exact polhode phase (method 4), ?p,
  ?p should be written to L3 (and L3 speedread) to
  drastically reduce execution time

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List of Modules cont.
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List of Modules cont.
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List of Modules cont.
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List of Modules cont.

• Module IEKF (Primary method)
• Input Z(t), ,
• Output State vector estimate, covariance
  matrix, P
• Method IEKF (uses Bierman library)
• Algorithm T.Holmes (20), V.Solomonik,
  M.Heifetz, J. Conklin
• Code V.Solomonik
• Readiness 0 (1 month)

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List of Modules cont.
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Two interwoven loops

• Guide Star Valid Data Loop (full mission)
• State vector parameters estimation
• Relativity (rNS, rEW)
• Gyro scale factor coefficients (CgLM, ank , bnk)
• Roll phase offset (d?)
• Telescope scale factor coeffs. (Gyro/Telescope
  Matching) (cTi)
• Roll-resonance torque parameters (c1mn, c2mn)
• Misalignment torque parameters (k1mn, k2mn)
• Initial orientation (sNS0, sWE0)

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List of Modules cont.

• Module Truth Model
• Algorithm M.Heifetz, KACST
• Code KACST
• Readiness 0

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List of Modules cont.

• Module Residuals Analysis
• Goodness-of-fit tests, Residual structure
  identification
• Algorithms T.Holmes, M.Heifetz, KACST
• Code KACST
• Readiness 0

• Module Geometric Method Integration
• Purpose Apply Geometric Method to s(t) with
  Roll-Resonance torque removed
• Algorithm M.Keiser, J.Conklin, K. Stahl
• Code K. Stahl
• Readiness 0

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Data Segmentation

• 10 Data Segments interrupted by anomalous events
• 1) September 13, 2004 September 23 (11 days)
• 2) September 25 November 10 (47 days)
• 3) November 12 December 04 (23 days)
• 4) December 05 December 09 (5 days)
• 5) December 10 January 20, 2005 (42 days)
• 6) January 21 March 04 (43 days)
• 7) March 07 March 15 (9 days)
• 8) March 16 March 18 (3 days)
• 9) March 19 May 27 (70 days)
• 10) May 31 July 23 (54days)

307 days of science data available
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Schedule of Tests

• Phase 1 Test of baseline configuration
  March - April
• - Data Segment 5 (or 6)
• - Module Mode 1 ( from TFM)
• - Module Initial profile, no
  iterative update
• - Matching based on known telescope scale
  factors (no update)

• Phase 2 Test of extended baseline configuration
  April-June
• - Data Segment 5 6
• - Module Mode 2 (Estimated
  parameters)
• - Module Initial profile, no
  iterative update
• - Matching estimation of telescope scale
  factors

• Phase 3 Full Mission Analysis Test July -
  August

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Modules where KACST can contribute

• Module Residuals Analysis
• Goodness-of-fit tests, Residual model
  identification
• Algorithms T.Holmes, M.Heifetz, KACST
• Code KACST

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• Module Truth Model
• Simulate SQUID data and test Estimation Methods
• Algorithms M.Heifetz, KACST
• Code KACST

• Module Optimization
• Interface between optimization package and GP-B
  data analysis software
• Study optimization package that will be used as a
  part of estimation process
• This package exploits subroutines written in C
  and/or Fortran, and GP-B analysis software is
  written in Matlab therefore some interface is
  needed for communication between various modules
• Algorithm A. Bradley (Stanford Optimization
  Lab), J.Conklin
• Code K. Stahl, KACST

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• Module SPF (for Phase 3)
• Investigate alternative nonlinear estimation
  techniques Sigma-point filters
• Algorithms T.Holmes, M.Heifetz, J. Conklin,
  KACST
• Code KACST