This paper addresses robust adaptive state estimation for a linear dynamical system subject to measurement outliers and Gaussian noises with unknown time-varying covariances. The proposed method relies on a Bernoulli-Gaussian (BG) model of measurement noise as well as on a variational Bayesian-moving horizon estimation (VB-MHE) approach that allows to jointly estimate the state trajectory on a moving window of fixed size along with the noise parameters (outlier probability, process noise and measurement noise covariances). A centralized robust adaptive filter is first derived and then extended to the distributed multi-sensor case by exploiting a distributed variational Bayesian (DVB) approach. It is shown, via simulation experiments, how the performance of both proposed, centralized and distributed, robust adaptive filters is very close to the ideal one achievable by a Kalman filter with perfect outlier detection and full knowledge of noise covariances.

Aiming at the problem that the performance of adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement of the noise matrices are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of multi-fading factor and an updated monitoring strategy adaptive Kalman filter-based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model and the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the updated monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices.

We focus on state estimation in linear systems characterized by Gaussian process noise and heavy-tailed measurement noise. In the state space model, we assume that process noise obeys a Gaussian distribution with known covariance, while measurement noise obeys a Normal-Exponential-Gamma (NEG) distribution with unknown parameters. Therefore, Gaussian and NEG distributions are used to model predicted and likelihood probability density functions, respectively. We then employ joint posterior density and variational Bayesian methods to approximately obtain the state and parameters estimated results. The results of the target tracking simulation and loosely coupled inertial measurement unit (IMU)/Ultra-Wideband (UWB) positioning experiment verify the superiority of the proposed algorithm.

This article focuses on centralized and distributed state estimations with measurement outliers and inaccurate noise covariance matrices. To capture the heavy-tailed nature introduced by measurement outliers, the measurement noise is modeled using an elliptical distribution (ED). To guarantee the conjugate, the inaccurate scale matrix of ED and the covariance matrix of the Gaussian process noise are modeled as inverse Wishart distributions, respectively. In the centralized filtering algorithm, enabling robust multisensor fusion at a central node, the state and parameters are jointly estimated based on the variational Bayesian (VB) approach. In the distributed case, a distributed VB (DVB) algorithm is proposed in a fully distributed way, which includes the natural gradient ascent, consensus averaging, and VB updates. Simulation results demonstrate that the proposed algorithms substantially outperform existing state-of-the-art filters in terms of robustness and estimation accuracy.