Optimal FIR filters for time-varying state-space models
Woong Kwon, K.S. Lee, Oakyoung Kwon · IEEE Transactions on Aerospace and Electronic Systems · 1990
An optimal FIR (finite impulse response) filter and smoother is introduced for the time-varying state-space model. The suggested filter has an FIR structure and utilizes 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 reduces to 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.>