Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

Dan Simon
Department of Electrical Engineering
Cleveland State University

Cleveland, Ohio
 

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.

References

  1. D. Simon and Y. Shmaliy, “Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing,” Automatica, vol. 49, no. 6, pp. 1892-1899, June 2013

Professor Simon’s Home Page

Department of Electrical and Computer Engineering

Cleveland State University


Last Revised: December 14, 2013