A Novel Robust Kalman Filtering Approach Based on Time-Dependent Structure

In this article, we consider the Kalman filtering problem in the presence of non-Gaussian measurement noise contaminated by time-correlated outliers. A novel robust filtering approach integrating a time-dependent outlier rejection structure into the hierarchical statistic model is proposed to address the sequential outliers in the Bayesian framework. The Gaussian-Gamma prior is first used to model the contaminated measurements, and a weight for each measurement is estimated online to assess the contribution of the current measurement in the state estimation. Furthermore, a novel structured Beta-Bernoulli prior is developed to model the continuous occurrence sequence pattern of outliers by imposing an
${l}$
th-order time-dependent structure and to identify and exclude outliers automatically. The mean-field variational Bayesian (VB) inference method is then utilized to estimate approximate posterior distributions of the state of interest iteratively at each time instant. The superiority of the proposed method over state-of-the-art algorithms is demonstrated by both numerical and experimental datasets.