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This chapter discusses the extensions of the Kalman filtering technique to solve a problem that was not directly designed to solve. In Sect. 8.1 it is shown how to use the linear Kalman filtering approach with minor modifications to solve the colored-noise-source problems. Nonlinear estimators, using the linearized and extended Kalman filters, are developed in Sect. 8.2, as well. Finally, in Sect. 8.3, linear state estimators are improved by simultaneously estimation of the uncertain system parameters and/or noise statistics together with the system states. This results in simultaneously parameter estimation and noise-adaptive filtering.

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Extensions of the Optimum Recursive (Kalman) Filter

  • 章节

  • 发表日期：

    2026年

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  • Branko Kovačević,
  • Željko Đurović,
  • Zoran Banjac

摘要

This chapter discusses the extensions of the Kalman filtering technique to solve a problem that was not directly designed to solve. In Sect. 8.1 it is shown how to use the linear Kalman filtering approach with minor modifications to solve the colored-noise-source problems. Nonlinear estimators, using the linearized and extended Kalman filters, are developed in Sect. 8.2, as well. Finally, in Sect. 8.3, linear state estimators are improved by simultaneously estimation of the uncertain system parameters and/or noise statistics together with the system states. This results in simultaneously parameter estimation and noise-adaptive filtering.