OPTIMAL FIR FILTERS FOR TIME-VARYING STATE-SPACE MODELS

An optimal finite-impulse response (FIR) filter and an optimal FIR smoother are introduced for time-varying state-space models. The suggested filter not only possesses an FIR structure but also utilizes a finite observation. It is shown that the impulse response of the optimal FIR filter can be obtained by a simple Riccati-type matrix differential equation. Especially for time-invariant systems, this FIR filter is reduced to the previously known simple forms. For implementation, a recursive form of the optimal FIR filter and smoother is derived by using adjoint variables, and computational algorithms are suggested. It is also shown by sensitivity analysis that the proposed optimal FIR filter alleviates potential divergence characteristics of the standard Kalman filter. © 1990 IEEE