Maximum mixture correntropy based outlier-robust nonlinear filter and smoother.

• The novel robust recursive filter and smoother for the nonlinear non-Gaussian system based on the cost functions induced by maximum mixture correntropy criterion are proposed. • The statistical linear regression method is used to linearize the nonlinear dynamic model and measurement function. • Two extra weights are introduced into the proposed robust recursive filter and smoother to modify the filtering and smoothing gains, respectively. • Simulation results of manoeuvring target tracking under different non-Gaussian noise scenarios illustrate the effectiveness of the proposed robust recursive filter and smoother. In this paper, we are dedicated to studying the robust filtering and smoothing problem for a nonlinear non-Gaussian system. Considering the advantage of mixture correntropy with two kernel bandwidths in dealing with non-Gaussian noise, we propose the novel robust recursive filter and smoother based on the cost functions induced by the maximum mixture correntropy criterion, where the nonlinear dynamic model function and measurement model function are linearized by using the statistical linear regression (SLR) method. In the proposed robust recursive filter and smoother, we apply a third-order spherical cubature rule to obtain the prior estimation of the state and covariance matrix, and approximate the multi-dimensional Gaussian integrals encountered in the SLR method. Furthermore, two additional weights are introduced into the proposed robust recursive filter and smoother to modify the filtering and smoothing gains, respectively. The simulation results of manoeuvring target tracking under different non-Gaussian noise scenarios illustrate the effectiveness of the proposed robust recursive filter and smoother. [ABSTRACT FROM AUTHOR]