In this paper, a novel variational Bayesian (VB) based adaptive Kalman filter (VBAKF) for linear Gaussian state-space models with inaccurate process and measurement noise covariance matrices is proposed. By choosing inverse Wishart priors, the state together with the predicted error and measurement noise covariance matrices are inferred based on the VB approach. Simulation results for a target tracking example illustrate that the proposed VBAKF has better robustness to resist the uncertainties of process and measurement noise covariance matrices than existing state-of-the-art filters.

A novel robust Student's t-based Kalman filter is proposed by using the variational Bayesian approach, which provides a Gaussian approximation to the posterior distribution. Simulation results for a manoeuvring target tracking example illustrate that the proposed filter has smaller root mean square error and bias than existing filters.

In this paper, a novel Gaussian-Student's t mixture (GSTM) distribution is proposed to model non-stationary heavy-tailed noises. The proposed GSTM distribution can be formulated as a hierarchical Gaussian form by introducing a Bernoulli random variable, based on which a new hierarchical linear Gaussian state-space model is constructed. A novel robust GSTM distribution based Kalman filter is proposed based on the constructed hierarchical linear Gaussian state-space model using the variational Bayesian approach. The Kalman filter and robust Student's t based Kalman filter (RSTKF) with fixed distribution parameters are two existing special cases of the proposed filter. The novel GSTM distributed Kalman filter has the important advantage over the RSTKF that adaptation of the mixing parameter is much more straightforward than learning the degrees of freedom parameter. Simulation results illustrate that the proposed filter has better estimation accuracy than the Kalman filter and RSTKF for a linear state-space model with non-stationary heavy-tailed noises.

To solve the problem of unknown noise covariance matrices inherent in the cooperative localization of autonomous underwater vehicles, a new adaptive extended Kalman filter is proposed. The predicted error covariance matrix and measurement noise covariance matrix are adaptively estimated based on an online expectation-maximization approach. Experimental results illustrate that, under the circumstances that are detailed in the paper, the proposed algorithm has better localization accuracy than existing state-of-the-art algorithms.

In this paper, a new robust Kalman filtering framework for a linear system with non-Gaussian heavy-tailed and/or skewed state and measurement noises is proposed through modeling one-step prediction and likelihood probability density functions as Gaussian scale mixture (GSM) distributions. The state vector, mixing parameters, scale matrices, and shape parameters are simultaneously inferred utilizing standard variational Bayesian approach. As the implementations of the proposed method, several solutions corresponding to some special GSM distributions are derived. The proposed robust Kalman filters are tested in a manoeuvring target tracking example. Simulation results show that the proposed robust Kalman filters have a better estimation accuracy and smaller biases compared to the existing state-of-the-art Kalman filters.

In this paper, a new outlier-robust Student's t based Gaussian approximate filter is proposed to address the heavy-tailed process and measurement noises induced by the outlier measurements of velocity and range in cooperative localization of autonomous underwater vehicles (AUVs). The state vector, scale matrices, and degrees of freedom (DOF) parameters are jointly estimated based on the variational Bayesian approach by using the constructed Student's t based hierarchical Gaussian state-space model. The performances of the proposed filter and existing filters are tested in the cooperative localization of an AUV through a lake trial. Experimental results illustrate that the proposed filter has better localization accuracy and robustness than existing state-of-the-art outlier-robust filters.