Stability Analysis of Kalman Filter by Orthonormalized Compressed Measurement
Hyung Keun Lee, Jang Gyu Lee · 2002
In this paper, we propose the concept of orthonormalized compressed measurement for the stability analysis of discrete linear time-varying Kalman filters. Compared with the previous studies that deals with the homogeneous portion of Kalman filters, the proposed Lyapunov method directly deals with the stochastically-driven system. The orthonormalized compressed measurement provides information on the a priori state estimate of the Kalman filter at the k -th step that is propagated from the a posteriori state estimate at the previous block of time. Since the complex multiple-step propagations of a candidate Lyapunov function by process and measurement noises can be simplified to a one-step Lyapunov propagation by the orthonormalized compressed measurement, a stochastic radius of attraction can be derived that would be practically difficult to obtain by the conventional multiple-step Lyapunov method.