Abstract
The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.
Highlights
The state estimation problem in dynamic systems is an important research topic in engineering applications and scientific research
This paper is organized as follows: In Section 2, we review the concept of correntropy and existing maximum correntropy Kalman filter (MCKF)
The kernel parameters of Gaussian correntropy determine the filtering performance of the MCKF, and an improper kernel bandwidth might lead to filtering performance degradation or even diverge
Summary
The state estimation problem in dynamic systems is an important research topic in engineering applications and scientific research. As an excellent optimal state-space estimator, the Kalman filter (KF) is commonly applied in various fields like control systems and signal processing. The optimality of KF requires exact system models and ideal noise conditions as summarized in [1]. The widely used KF, which usually refers to the Kalman filter based on the Hidden. Markov Models (HMM), has rigorous requirements for the noise models. Both process and measurement noise are assumed as ideal independent Gaussian noise sequences. In practical applications, ideal noise conditions are not likely, and model uncertainties such as system structure changes and environmental disturbances are generally inevitable
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