Stability Analysis of Kalman Filter by Orthonormalized Compressed Measurement

  • Hyung Keun Lee (School of Electrical Engineering and Computer Science and the Automatic Control Research Center, Seoul National University) ;
  • Jang Gyu Lee (School of Electrical Engineering and Computer Science and the Automatic Control Research Center, Seoul National University)
  • 발행 : 2002.02.01

초록

In this paper, we propose the concept of orthonormalized compressed measurement for the stability analysis of discrete linear time-varying Kalman filters. Unlike previous studies that deal with the homogeneous portion of Kalman filters, the proposed Lyapunov method directly deals with the stochastically-driven system. The orthonorrmalized 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 with 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 impractically difficult to obtain by the conventional multiple-step Lyapunov method.

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