Design of distributed recursive filters based on data compression for sensor networks

• Published in: Signal processing 2023-06, Vol.207, p.108937, Article 108937
• Main Authors: Shen, Yuqing, Sun, Shuli
• Format: Article
• Language: English
• Subjects: Cross-covariance matrix; Data compression; Distributed recursive filter; Exponential boundedness in the mean square; Sensor network
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2023.108937

•Measurements and estimates of sensors are compressed, respectively.•An optimal distributed recursive filter is presented in the LUMV criterion.•A suboptimal distributed recursive filter is presented to avoid CCMs.•The filtering error is exponentially bounded in the mean square. This paper is concerned with the distributed filtering problem based on data compression for linear discrete time-varying systems over sensor networks. Two kinds of sensors are considered: one kind only has a measuring capability and communicates measurements, while the other adds a calculating capability and communicates estimates. At each sensor node with calculating capability, a weighted measurement fusion algorithm is employed to compress the measurements of the sensor and its neighbor nodes with only measuring capability; and a weighted state fusion algorithm is employed to compress the estimates from neighbor nodes with calculating capability. Using compressed data, an optimal distributed recursive filter with a Kalman consensus filter form is devised in the linear unbiased minimum variance (LUMV) criterion. Cross-covariance matrices (CCMs) of the filtering errors between sensor nodes are derived. To avoid calculating CCMs, a suboptimal distributed recursive filter is presented, where a covariance intersection fusion algorithm is employed to compress the estimates from neighbor nodes with calculating capability. The filtering and consensus gains are solved to minimize an upper bound of covariance matrix (CM) of the filtering error. It is proved that the filtering error is exponentially bounded in the mean square. Simulations illuminate the effectiveness of proposed algorithms.