Distributed Student's t filtering algorithm for heavy‐tailed noises

Abstract

In this paper, a distributed Student's t filtering algorithm to deal with heavy-tailed noises is developed. In the traditional Kalman filter, the distribution of the signal is assumed. However, in reality, outliers in the signal are often encountered for which the assumption of Gaussian distribution is no longer valid. The Student's t distribution can describe noises in the presence of outliers.As a result, the weight on each data point within the filter adapts to the data quality so that the filter becomes insensitive to the outliers. We first derive the distributed filtering algorithm from the centralized Student's t filter, which is able to handle heavy-tailed noises such as outliers and then analyze properties of the proposed method. It is shown that the proposed algorithm provides the same accuracy as the centralized Student's t filtering with no performance loss. Furthermore, the distributed Student's t filtering with feedback is developed, which is in accordance with centralized filtering, and the local error covariance is reduced as expected. Two numerical examples support the theoretical results and illustrate the validity of the proposed method.

Robust algorithm for attack detection based on time‐varying hidden Markov model subject to outliers

“…Therefore, to deal with outliers that follow a non-Gaussian distribution, the Student's t distribution has been implemented. 19,20 A distributed Student's t filtering algorithm is developed to deal with noise process in the presence of heavy-tailed noises. 19 In process monitoring and diagnosis, a robust approach 21 with multivariate Student's t distribution has been proposed to adapt to different data quality in various operating points.…”

“…19,20 A distributed Student's t filtering algorithm is developed to deal with noise process in the presence of heavy-tailed noises. 19 In process monitoring and diagnosis, a robust approach 21 with multivariate Student's t distribution has been proposed to adapt to different data quality in various operating points. In addition, a robust probabilistic model with Student's t mixture output is proposed for fault classification in dynamic industrial processes.…”

“…Although Gaussian distribution has been widely used in attack detection due to its convenient mathematical properties, 18 such as the straightforward maximum likelihood estimation. However, Xu et al 19 point out that the performance of Gaussian distribution‐based methods will be significantly deteriorated when dealing with heavy‐tailed non‐Gaussian distribution noises. Therefore, to deal with outliers that follow a non‐Gaussian distribution, the Student's t distribution has been implemented 19,20 .…”

“…However, Xu et al 19 point out that the performance of Gaussian distribution‐based methods will be significantly deteriorated when dealing with heavy‐tailed non‐Gaussian distribution noises. Therefore, to deal with outliers that follow a non‐Gaussian distribution, the Student's t distribution has been implemented 19,20 . A distributed Student's t filtering algorithm is developed to deal with noise process in the presence of heavy‐tailed noises 19 .…”

Robust filter design for asymmetric measurement noise using variational Bayesian inference

“…In order to deal with heavy tailed noises caused by outliers, the Student's t distribution has been commonly used in the state estimation problems [17–20]. Under the condition that process and measurement noises are both heavy tailed, a linear Student's t filter is proposed by calculating the posterior density in [19], which is further extended to non‐linear systems [20].…”