A Stochastic H∞ Filter for Spacecraft Attitude Estimation

A filter for estimating spacecraft attitude quaternion and gyro drift from vector measurements in the presence of white noises in the gyro error, in the drift dynamics, and in the line-of-sight measurement error is developed. The variance parameters of the white noises are unknown, and are modeled as non-anticipative second order stochastic processes. The approach taken in this work consists in estimating the attitude quaternion and the gyro drift while attenuating the transmission from the unknown variances to the estimation error. The resulting H∞ filter involves the solution of a set of (differential) linear matrix inequalities. In the case of gyro white noises, extensive Monte-Carlo simulations were run showing that the proposed filter performs well from the standpoint of attitude estimation per se, in a wide range of gyro noise and line-of-sight noise intensities. The guaranteed disturbance attenuation level seems to be slightly dependent on the noises intensities. The actual level of disturbance attenuation is improving when the noises levels increase and admits as worst scenario the case of(ideal) noise-free sensors, as expected from the analysis. When compared with a matched quaternion Kalman filter, the H∞ filter produces higher Monte-Carlo standard deviations of the estimation error, but lower Monte-Carlo means. The higher the level of noises are, the less obvious the advantage of the Kalman filter is. When estimating the quaternion only, and as opposed to standard quaternion Kalman filters, the H∞ filter’s gains can be computed independently from the quaternion estimates, which makes it insensitive to estimation errors. This favorable feature is further emphasized when comparing its performances with those of unmatched Kalman filters. When provided with too high or too low noise covariances, the Kalman filter is outperformed by the H∞ filter, which delivers essentially identical levels of errors within a wide range of noise intensities.