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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.

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