Spacecraft attitude estimation via stochastic H _∞ filtering

A filter for estimating spacecraft attitude quaternion from line-of-sight (LOS) measurements in the presence of white noises in the gyro output and in the attitude sensing is developed. The variance parameters of the white noises are assumed unknown and modeled as non-anticipative second order stochastic processes. The approach taken in this work consists in estimating the attitude quaternion while attenuating the transmission gain from the unknown variances to the estimation error. The resulting H _∞ filter involves the solution of a set of (differential) linear matrix inequalities, which do not depend on the estimated quaternion. 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 and LOS 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 two different matched quaternion Kalman filters (KF), 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 to the Kalman filters is. As opposed to standard quaternion Kalman filters, the H _∞ filter's gain process can be computed independently from the quaternion estimate process, which makes it unsensitive to estimation errors. This nice 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.