Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

Daniel J. Simon; Yuriy S. Shmaliy

doi:10.1016/j.automatica.2013.02.026

Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

Daniel J. Simon
, Yuriy S. Shmaliy

Universidad de Guanajuato

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Journal	Automatica
Volume	49
DOIs	https://doi.org/10.1016/j.automatica.2013.02.026
State	Published - Jun 1 2013

Keywords

Kalman filters; Unbiased FIR filters; Smoothing; Filtering; Robust estimation

Disciplines

Electrical and Computer Engineering

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10.1016/j.automatica.2013.02.026License: CC BY

Unified Forms for Kalman and Finite Impulse Response Filtering anFinal published version, 1.55 MBLicense: CC BY

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title = "Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing",

abstract = " 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.",

keywords = "Kalman filters; Unbiased FIR filters; Smoothing; Filtering; Robust estimation",

author = "Simon, \{Daniel J.\} and Shmaliy, \{Yuriy S.\}",

note = "D. Simon and Y. S. Shmaliy, {"}Unified forms for Kalman and finite impulse response filtering and smoothing,{"} Automatica, vol. 49, pp. 1892-1899, 2013.",

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AU - Shmaliy, Yuriy S.

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Y1 - 2013/6/1

N2 - 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.

AB - 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.

KW - Kalman filters; Unbiased FIR filters; Smoothing; Filtering; Robust estimation

UR - https://engagedscholarship.csuohio.edu/enece_facpub/206

U2 - 10.1016/j.automatica.2013.02.026

DO - 10.1016/j.automatica.2013.02.026

M3 - Article

VL - 49

JO - Automatica

JF - Automatica

ER -

Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

Abstract

Keywords

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