Distributed recursive filtering for multi-rate uniform sampling systems with packet losses in sensor networks

ABSTRACT

The distributed filtering problem is studied for a multi-rate uniform sampling linear discrete system over sensor networks, where packet losses may occur during data exchange between nodes. The multi-rate system is transformed into a single-rate system by using a virtual measurement method. At each sensor node, the estimates received from neighbour nodes are fused by matrix or scalar weighting according to their different estimation accuracy. A distributed recursive filter with the Kalman consensus filter structure is devised based on the fused estimate, where the filtering gain and consensus gain are solved by locally minimising an upper bound of the filtering error covariance. The obtained gains and the upper bound of the covariance depend on a group of free positive scalar parameters. The scalar parameters are optimised by minimising the upper bound of the covariance. It is proved that the upper bound of the covariance of the filter with optimal gains and parameters is smaller than the covariance of the local filter based on sensor measurements. It avoids calculating cross-covariance matrices between nodes and has small computational burden. The exponential boundedness in the mean square of the filtering error is analysed. A target tracking system verifies the effectiveness of the algorithm.

KEYWORDS:

• Sensor network
• distributed recursive filter
• multi-rate uniform sampling system
• packet loss
• exponential boundedness in mean square

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Key Project of the Natural Science Foundation of Heilongjiang Province, China under grant number ZD2021F003, and Information Fusion Estimation and Detection Key Laboratory in Heilongjiang Province, China.

Notes on contributors

Yuqing Shen

Yuqing Shen was born in Qiqihaer, China in 1997. He received the B.S. degree in department of automation from Heilongjiang University, in 2020. Now, she is a Master degree candidate in control science and engineering from Heilongjiang University. His research interests are in the areas of state estimation, information fusion, and sensor network.

Shuli Sun

Shuli Sun was born in Heilongjiang, China, in 1971. He received the B.S. degree in applied mathematics from the department of mathematics, Heilongjiang University, Harbin, China, in 1996, the M.E. degree in control theory and control engineering from the department of automation, Heilongjiang University, in 1999, and the Ph.D. degree in aircraft design from the School of Astronautics, Harbin Institute of Technology, Harbin, China, in 2004. He was a Research Fellow with Nanyang Technological University, Singapore, from 2006 to 2007. Since 2006, he has been a Professor with the School of Electronic Engineering, Heilongjiang University. His research interests are in the areas of state estimation, signal processing, information fusion, and networked systems.