Distributed Maximum Correntropy Linear Filter Based on Rational Quadratic Kernel Against Non-Gaussian Noise

This paper investigates the distributed state estimation problem for the linear system against non-Gaussian noise, where every sensor commutates information only within its adjacent sensors without the need for a fusion center. Correntropy is a similarity metric based on a kernel function that has symmetry. Symmetry means that for any two data points, the output value of the kernel function does not depend on the order of the data points. By adopting a correntropy cost function based on the rational quadratic kernel function approximation to restrain non-Gaussian heavy-tailed noise, a centralized maximum correntropy Kalman filter is first derived for the linear sens+or network system at first. Then the corresponding centralized maximum correntropy information filter is attained by employing the information matrices, which is a foundation for further designing distributed information algorithms under multi-sensor networks. Thirdly, the distributed rational quadratic maximum correntropy information filter and distributed adaptive rational quadratic maximum correntropy information filter are designed by exploiting the weighted census average to solve the non-Gaussian heavy-tailed noise interference in sensor networks. Finally, the performance of the proposed algorithms is illustrated through numerical simulations on the sensor network system.