Distributed Kalman Filter With Faulty/Reliable Sensors Based on Wasserstein Average Consensus

Abstract

This brief considers distributed Kalman filtering problem for systems with sensor faults. A trust-based classification fusion strategy is proposed to resist against sensor faults. First, the local sensors collect measurements and then update their state estimations and estimation error covariance matrices. Then, sensors exchange the information (state estimations and estimation error covariance matrices) with their neighboring sensors. After obtaining the estimation information from neighboring sensors, an iterative classification/clustering algorithm, which contains three steps ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Initialization Step</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Assignment Step</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Update Step</i> ), is proposed to classify the collected estimations into two clusters (trusted and untrusted clusters). Third, the fused states and error covariance matrices are computed by Wasserstein average algorithm. Finally, the time update is performed on the basis of fusion information. Stability and convergence of the proposed filter are analyzed. A target tracking simulation example is provided to verify the effectiveness of the proposed distributed filter in a wireless sensor network.