Maximum weighted correntropy filters for nonlinear non-Gaussian systems

In this paper, we focus on the filtering issue for nonlinear non-Gaussian systems. Considering the limitations of the Gaussian function with a single kernel bandwidth, we design a novel extended version called weighted Gaussian function, which consists of a weighting coefficient and two distinct kernel bandwidths. The additional coefficient can directly balance two kernel bandwidths, which improves the flexibility and performance of the correntropy. We develop a cost function utilizing the suggested weighted Gaussian function and statistical linearization method, followed by deriving a maximum weighted correntropy filter based on the maximum correntropy criterion. The proposed algorithm is demonstrated to converge to a Gaussian filter as the kernel bandwidths approach infinity. In addition, we derive the corresponding information filter, which takes the form of information matrix and information vector. It is computationally efficient and easier to generalize to multisensor systems. The performance of the proposed algorithms is compared with other filters based on the third-order spherical cubature rule and the fixed point iteration technique in a target tracking system. Simulation results confirm the effectiveness of the new approaches.