Optimal solution of the two-stage Kalman estimator

Chien Shu Hsieh*, Fu-Chuang Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

196 Scopus citations


The two-stage Kalman estimator was originally proposed to reduce the computational complexity of the augmented state Kalman filter. Recently, it was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term. Except in certain restrictive conditions, the conventional two-stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter. In this paper, the authors propose a new two-stage Kalman estimator, i.e., new structure, which is an extension of Friedland's estimator and is optimal in general conditions. In addition, we provide some analytic results to demonstrate the computational advantages of two-stage estimators over augmented ones.

Original languageEnglish
Article number739135
Pages (from-to)194-199
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - Jan 1999


  • Augmented state Kalman filter
  • Bias-free filter
  • Dynamical bias
  • Optimal filter
  • Two-stage Kalman estimator


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