Central difference Kalman smoother

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Abstract

A central difference Kalman smoother (CDKS) is designed to solve the nonlinear state-smoothing problem for a class of nonlinear discrete-time systems. Optimal smoothing recursive formulas for estimating nonlinear system states are derived on the basis of minimum mean-square-error estimation; and the central difference transformation is used to calculate the posterior mean and covariance of nonlinear states. Compared with the standard central difference Kalman filter (CDKF), the proposed CDKS effectively improves the estimation precision of the nonlinear system states, and extends the applications of the central difference transformation. Simulations example shows the feasibility and effectiveness of the proposed smoother.

Original languageEnglish
Pages (from-to)361-367
Number of pages7
JournalKongzhi Lilun Yu Yingyong/Control Theory and Applications
Volume29
Issue number3
StatePublished - Mar 2012

Keywords

  • Central difference Kalman smoother
  • Central difference transformation
  • Minimum mean square error estimation
  • Nonlinear discrete-time systems

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