Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing
Kalman filters are commonly used to estimate the states of a dynamic system. However, Kalman filters have an infinite impulse response, which can lead to instability in the presence of unmodeled dynamics. Finite impulse reponse (FIR) filters thus provide a robust alternative to Kalman filters. This paper derives a unified form for the Kalman filter and Kalman smoother, derives a unified form for an FIR filter and smoother, and compares the filters and smoothers via simulation results. The examples in the paper below can be replicated with the below m-files, which can be run in the MATLAB environment.
RTSEq1.m illustrates the equivalence
of the unified Kalman filter/smoother and the RTS smoother
RTSEq4.m was used to derive the results of Example 1 in the paper.
FIRNopt.m was used to derive the results of Example 2 in the paper.
RTSFIRMonte.m was used to derive the results of Example 3 in the paper.
Last Revised: December 14, 2013