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Kalman Filtering

In: Kalman Filtering Under Information Theoretic Criteria

Author

Listed:
  • Badong Chen

    (National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, National Key Laboratory of Human-Machine Hybrid Augmented Intelligence)

  • Lujuan Dang

    (National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, National Key Laboratory of Human-Machine Hybrid Augmented Intelligence)

  • Nanning Zheng

    (National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, National Key Laboratory of Human-Machine Hybrid Augmented Intelligence)

  • Jose C. Principe

    (University of Florida, Electrical and Computer Engineering Department)

Abstract

Estimation of system parameters and system states has been one of the most important issues in signal processing, communications, optimal control, and robotics, with an enormous importance in the industry. The actual applications include parameter estimation, system identification, target tracking, simultaneous localization, and many others. The purpose of this chapter is to briefly review the foundations of statistical estimation. For linear dynamic systems, the estimation problem is usually solved by the Kalman filter (KF). In order to solve the nonlinear filtering problem, researchers have made many additions to the KF family, including the extended Kalman filter (EKF), the unscented Kalman filter (UKF), the cubature Kalman filter (CKF), and many others. At the same time, robust Kalman filters were also studied. Typical examples include the H-infinity filter (HIF), adaptive Kalman filter (AKF), robust student’s t-based Kalman filter (RSTKF), particle filter (PF), and Huber-based Kalman filter (HKF), etc. In this chapter, the detailed derivation about these methods is presented.

Suggested Citation

  • Badong Chen & Lujuan Dang & Nanning Zheng & Jose C. Principe, 2023. "Kalman Filtering," Springer Books, in: Kalman Filtering Under Information Theoretic Criteria, chapter 0, pages 11-51, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-33764-2_2
    DOI: 10.1007/978-3-031-33764-2_2
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