Quaternion estimation from vector observations using a matrix Kalman filter

This paper presents a novel quaternion estimator from vector observations, which is a synthesis between Wahba's approach and the Kalman filtering approach. It considers the particular case where, at each sampling time, the same physical vectors are measured. The proposed algorithm has two stages. The first stage, which is the original contribution of the paper, consists of a linear Kalman filter of the so-called K-matrix. A matrix Kalman filter is used here in order to preserve the natural formulation of the matrix plant equations. A linearly constrained matrix Kalman filter is also designed. This constrained filter optimally enforces the symmetry and zero-trace properties in the matrix estimate. The constraints are here incorporated to the estimation process by using the concept of pseudo-measurement. The filters developed in this work estimate the attitude only; however, additional dynamic parameters can easily be incorporated in the estimation process. The second stage of the algorithm consists of extracting the quaternion from the updated estimate of the K-matrix using the known q-method. Extensive Monte-Carlo simulations, with a spinning and nutating spacecraft as a case study, show that the proposed algorithm outperforms an earlier algorithm, named Optimal-REQUEST. This result is corroborated by analysis. The simulation results also show that the constrained matrix Kalman filter becomes relatively efficient, with respect to the unconstrained algorithm, when the constraints are perturbed in the course of the estimation process.