IMPLICIT KALMAN FILTERING

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation schem e is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows fo r generalization to descriptor systems. The implementation of the impl icit filter depends on the solution of the congruence matrix equation A(1)P(x)A(1)(T) = P-F. We develop a general iterative method for the s olution of this equation, and prove necessary and sufficient condition s for convergence. It is shown that when the system matrices of an imp licit system are sparse, the implicit Kalman filter requires significa ntly less computer time and storage to implement as compared to the tr aditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.