Additional Topics in Kalman Filtering Under Information Theoretic Criteria

Badong Chen, Lujuan Dang, Nanning Zheng and Jose C. Principe
Additional contact information
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

Chapter Chapter 8 in Kalman Filtering Under Information Theoretic Criteria, 2023, pp 229-284 from Springer

Abstract: Abstract Besides the previously mentioned Kalman filters, some other Kalman type filters are derived based on information-theoretic criteria for specific cases. For example, to address the problem of state estimation under equality constraints, the maximum correntropy Kalman filter with state constraints (MCKF-SC) was developed, which combines the MCC and constrained estimation methodology. In addition, two novel nonlinear filters, the correntropy-based first-order divided difference (CDD1) filter and the correntropy-based second-order divided difference (CDD2) filter, are derived to solve the problem of numerical instability due to the propagation of a non-positive definite covariance matrix. When the parameters of system model are unknown a priori or varying with time, the dual Kalman filtering under minimum error entropy with fiducial points (MEEF-DEKF) provides an effective tool in estimating the model parameters and the hidden states under non-Gaussian noises. For nonlinear time-series prediction, the kernel Kalman filtering based on conditional embedding operator and maximum correntropy criterion (KKF-CEO-MCC) was also derived, which shows significant performance improvements over traditional filters in noisy nonlinear time-series prediction. In this chapter, the detailed derivation about these methods is presented.

Keywords: Maximum correntropy Kalman filter with state constraints; Correntropy-based first-order divided difference; Correntropy-based second-order divided difference; Dual Kalman filtering under minimum error entropy with fiducial points; Kernel Kalman filtering based on conditional embedding operator and maximum correntropy criterion (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/978-3-031-33764-2_8

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