The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances.
Simon, Daniel J. and Shmaliy, Yuriy S., "Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing" (2013). Electrical Engineering & Computer Science Faculty Publications. 206.
D. Simon and Y. S. Shmaliy, "Unified forms for Kalman and finite impulse response filtering and smoothing," Automatica, vol. 49, pp. 1892-1899, 2013.
NOTICE: this is the author’s version of a work that was accepted for publication in Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Automatica, 49, 6, (06-01-2013); 10.1016/j.automatica.2013.02.026