We propose a new robust recursive fixed-interval smoother for nonlinear systems under non-Gaussian process and measurement noises, i.e., the nominal Gaussian noise is polluted by large noise from unknown distributions. Taking advantage of correntropy in handling non-Gaussian noise, a robust Rauch-Tung-Striebel (RTS) smoother is derived according to the maximum-correntropy-criterion-based cost functions with nonlinear functions linearized by their first-order Taylor series expansions, where two weights are utilized to adjust the estimation gains of forward filtering and backward smoothing, respectively. Simulation results demonstrate the effectiveness of the proposed smoother in the presence of various non-Gaussian process and measurement noises, especially the shot sequences and multimodal noise.

In this brief, we investigate the robust state estimation of nonlinear systems with heavy-tailed noise. Based on the fact that the multivariate Laplace (ML) distribution has heavier tails than Gaussian distribution but is only determined by its mean and covariance, we utilize the ML distribution to model the heavy-tailed measurement noise. Based on the Gaussian mixture form of ML distribution, the system state and the covariance of ML distribution are inferred by variational Bayesian method, and then a closed recursive robust nonlinear Kalman filter is obtained with the nonlinear integrations calculated by numerical integration methods. Simulation results demonstrate that the proposed algorithm is insensitive to its free parameters and can obtain better estimation accuracy than related robust algorithms.