Gravity Probe B Science Data Analysis: Filtering Strategy

Nonlinear filtering provides one component of the data analysis strategy to determine the relativistic precession of GP-B science gyroscopes. The filtering methodology is based on: 1) models of the gyroscope motion, 2) models of the science signal readout electronics and 3) numerical filtering techniques. A ``two-floor'' process has been developed. The first floor focuses on modeling of the readout system: gyroscopes' scale factor polhode variations, telescope signals, matching of the gyroscope and telescope scale factors/bias, and SQUID calibration signal modeling. Nonlinear parameter estimation is performed for a set of independent batches that generates state vector covariance matrices for each batch. The second floor separates the relativistic precessions from the torque-induced motion of the science gyroscopes. Batch-based estimates from the first-floor filter are treated as ``measurements'' of the second floor state vector and connected through the torque model and other constraints. Estimates of relativistic precession and its covariance are obtained from the ``second-floor'' filters. Supporting validation tools such as spectral and statistical analyses of the filter residuals were developed to interface with the filter outputs for multiple sensitivity analyses.