This paper explores the problem of nonlinear state estimation in the presence of outlier-contaminated measurements. First, to deal with the non-stationary non-Gaussian noises caused by randomly occurring measurement outliers, we propose a new Gaussian-multivariate Laplacian mixture (GMLM) distribution and construct it as a hierarchical Gaussian expression. Next, utilizing the GMLM distribution and existing variational Bayesian (VB) method, a robust cubature Kalman filter is derived (VB-GMLMRCKF). Then, considering the high computational complexity of the existing VB inference process, a new partial VB (PVB) method is developed, which can separately estimate state vector and mismatched measurement noise covariance matrix. Building upon the VB-GMLMRCKF and PVB approach, a novel robust cubature Kalman filter is derived (PVB-GMLMRCKF). Finally, a target tracking model is utilized to evaluate the PVB-GMLMRCKF in terms of estimation accuracy, estimation consistency and computational efficiency.

In the integrated inertial navigation system (INS) and celestial navigation system (CNS), the attitudes and positions of probes are estimated based on the auxiliary measurement of an infrared Earth sensor. The poor accuracy of the infrared Earth sensor compared to that of the star sensor significantly limits the navigation accuracy of the integrated navigation system. This paper proposes a novel INS/CNS integrated navigation system that uses the specific force with noncumulative error to correct infrared Earth measurements. The probe azimuth angle and elevation angle relative to the Earth's inertial frame are first estimated according to the specific force provided by the INS to filter the infrared Earth sensor's measurement error. Then, the corrected infrared Earth measurement assists the CNS to obtain accurate celestial measurements. The integrated INS/CNS navigation system in the tightly coupled mode finally estimates the accurate probe attitude and position. Compared to the integrated navigation system, which directly uses the uncorrected infrared Earth measurement, the yaw, pitch, and roll angle are improved under the proposed method by 76.73%, 77.64%, and 75.39% on average, respectively; the latitude and longitude estimation errors improve under the proposed method by 70.44% and 61.92% on average, respectively. In short, the proposed method is a feasible and highly accurate approach to the INS/CNS integrated navigation system.

A method based on low rank and sparse decomposition is proposed for moving object detection by the fusion of visual and infrared video. The visual and infrared image sequences are decomposed into the joint low rank background term, the uncorrelated sparse moving nonobject term, and the common sparse moving object term via a joint minimization cost of nuclear norm, $F$ norm, and $l_1$ norm. This method provides a flexible framework that can easily fuse information from visual and infrared video. The prior fusion strategies are not required. The complementary information on visual and infrared images can be naturally fused in the procedure of object detection. The experimental results show that the proposed algorithm is effective.

This paper investigates the nonlinear state estimation under heavy-tailed process and measurement noises (PAMNs), the noises may be induced by sensor failures, measurement loss, modeling errors, environmental changes, or malicious cyberattacks. Considering that the multivariate Laplacian (ML) distribution has obvious heavy-tailed characteristic, we employ the distribution to describe heavy-tailed PAMNs. Furthermore, to improve the computational efficiency of the existing variational Bayesian (VB) iteration process, we design an improved VB iteration method, which can separately calculate the posterior distributions of the state vector and unknown noise parameters. Employing the ML distribution and improved VB inference process, a computationally efficient robust cubature Kalman filter (CEMLRCKF) is derived. Simulation and vehicle experiment results illustrate the superiority of the proposed filter.