论文信息 - A necessary and sufficient condition for semi-stability of the recursive Kalman filter

A necessary and sufficient condition for semi-stability of the recursive Kalman filter

This paper studies semi-stability for Kalman filters in the context of linear time-varying systems with incorrect noise information. Semi- stability is a key property, as it ensures that the actual estimation error does not diverge exponentially. As the main result of the paper we present a necessary and sufficient condition for the recursive Kalman filter to be semi-stable, relying on the relevant data of the system and noise. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist.

A. Astolfi | E.F. Costa | A. Astolfi | E. F. Costa

[1] S. Sangsuk-Iam,et al. Analysis of discrete-time Kalman filtering under incorrect noise covariances , 1990 .

[2] Joseph J. Winkin,et al. Convergence of the Time-Invariant Riccati Differential Equation towards Its Strong Solution for Stabilizable Systems , 1995 .

[3] G. Goodwin,et al. Riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices , 1986 .

[4] C. Price. An analysis of the divergence problem in the Kalman filter , 1968 .

[5] A. Astolfi,et al. On the stability of the recursive Kalman filter for linear time-invariant systems , 2008, 2008 American Control Conference.

[6] H. Abou-Kandil,et al. Matrix Riccati Equations in Control and Systems Theory , 2003, IEEE Transactions on Automatic Control.

[7] N. F. Toda,et al. Divergence in the Kalman Filter , 1967 .

[8] Jacques L. Willems,et al. Divergence of the stationary Kalman filter for correct and for incorrect noise variances , 1992 .

[9] D. Sworder,et al. Introduction to stochastic control , 1972 .

[10] Harald K. Wimmer. Intervals of solutions of the discrete-time algebraic Riccati equation , 1999 .

[11] Harald K. Wimmer. A Parametrization of Solutions of the Discrete-time Algebraic Riccati Equation Based on Pairs of Opposite Unmixed Solutions , 2006, SIAM J. Control. Optim..