Attitude estimation without rate gyros using generalized multiple model adaptive estimation

A generalized multiple model adaptive estimation (GMMAE) scheme is derived to determine the attitude of a spacecraft without the use of rate information provided by gyros. Multiple model adaptive estimation (MMAE) uses several extended Kalman filters (EFKs) running in parallel, each representing a hypothesis of the actual system, to generate enhanced state and parameter estimates. The estimates of each parallel filter are combined based on the likelihood that each hypothesis is correct, which is determined from measurement residuals. GMMAE is an extension of this approach wherein a window of previous-time data is used via the autocorrelation matrix to perform the adaptive update. This approach shows significant improvement over both the standard EKF and standard MMAE approaches in both accuracy and convergence of the estimates. Each of the multiple models within the filter makes a separate hypothesis as to the process noise covariance of the system, and the combination of these separate filters allows it to be adaptively estimated. The filter formulation is based on the standard equations of attitude dynamics, with global attitude parameterization given by a quaternion. A multiplicative quaternion-error approach is used to guarantee that quaternion normalization is maintained in the filters. A Markov model approach for modeling the angular rates, which requires no torque input, is considered. Simulation results are provided to show the effectiveness of the GMMAE scheme.