期刊
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
卷 66, 期 11, 页码 4265-4277出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2019.2920773
关键词
Kernel; Kalman filters; Noise measurement; Cost function; Random variables; Predictive models; Estimation; Hilbert space embedding; kernel Kalman-type filter; conditional embedding operator; maximum correntropy criterion; Nystrom approximation
资金
- 973 Program [2015CB351703]
- National NSF of China [91648208, U1613219]
The Hilbert space embedding provides a powerful and flexible tool for dealing with the nonlinearity and high-order statistics of random variables in a dynamical system. The kernel Kalman filtering based on the conditional embedding operator (KKF-CEO) shows significant performance improvements over the traditional Kalman filters in the noisy nonlinear time-series prediction. However, KKF-CEO based on the minimum mean-square-error (MMSE) criterion is sensitive to the outliers or heavy-tailed noises. In contrast to the MMSE criterion, the maximum correntropy criterion (MCC) can achieve more robust performance in the presence of outliers. In this paper, we develop a novel kernel Kalman-type filter based on MCC, referred to kernel Kalman filtering with conditional embedding operator and maximum correntropy criterion (KKF-CEO-MCC). The proposed KKF-CEO-MCC can capture higher order statistics of errors and is robust to outliers. In addition, two simplified versions of KKF-CEO-MCC are developed, namely, KKF-CEO-MCC-O and KKF-CEO-MCC-NA. The former is an online approach and the latter is based on Nystrom approximation. Simulations on noisy nonlinear time-series prediction confirm the desirable accuracy and robustness of the new filters.
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