Abstract
Abstract An FIR (finite impulse response) filter and an FIR smoother are introduced for discrete-time state-space models with system noises, since the FIR structure not only guarantees both the BIBO (bounded input/bounded output) stability and the robustness to some parameter changes, but also improves the filter divergence problem. It is shown in this paper that impulse responses of both the FIR filter and the FIR smoother are given by a Riccati-type difference equation. Especially for time-invariant systems, they are also to be time-invariant and determined by simpler equations on a finite interval once and for all. For implementational purpose, recursive forms of the FIR filter and smoother are derived using each other as adjoint variables. The improved characteristics of the FIR filter in the divergence problem is demonstrated via a simulation.
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