Suboptimal receding horizon estimation via noise blocking

Abstract

For discrete-time linear systems, we propose a suboptimal approach to constrained estimation so that the associated computation burden is reduced. This is achieved by enforcing a move blocking (MB) structure in the estimated process noise sequence (PNS). We show that full information estimation (FIE) and receding horizon estimation (RHE) with MB are both stable in the sense of an observer. The techniques in proving stability are inspired by those that have been proposed for standard RHE. To be specific, stability results are mainly achieved by (i) carefully embellishing the general assumptions for standard RHE to accommodate the MB requirement; (ii) exploiting the principle of optimality, as well as convexity of the quadratic programs (QPs) associated with FIE and RHE; (iii) relying on the fact that the Kalman filter is the best linear estimator in the least-squares sense. A crucial requirement in achieving stability for MB RHE is that the segment structure (SS) of the PNS of MB FIE for the optimization steps within the receding horizon (i.e., steps between T−N and T−1) has to be enforced in the MB RHE optimization. As a result, the MB RHE strategy becomes a dynamic estimator with a periodically varying computational complexity. The theoretical results have been illustrated with examples.