A Gaussian-multivariate Laplacian mixture distribution based robust cubature Kalman filter

In this paper, the state estimation problems of nonlinear systems with outlier-corrupted measurements are investigated. First, to model the non-Gaussian noises caused by the randomly occurring measurement outliers, we propose a new Gaussian-multivariate Laplacian mixture (GMLM) distribution and analyze its distribution characteristics. Then, the measurement likelihood probability density function (PDF) is formulated as the GMLM distribution and further expressed as a hierarchical Gaussian expression. Furthermore, by variational Bayesian (VB) method, a robust cubature Kalman filter is derived (GMLMRCKF). Finally, simulation test and real date are utilized to evaluate the effectiveness of our GMLMRCKF, the results illustrate that the proposed filter has better estimation accuracy and consistence in the case of non-stationary heavy-tailed noises than the existing robust filters, i.e., it has almost the same performance as the standard CKF in the absence of outliers and better robust performance in the presence of unknown outliers.