Distributed Recursive Filtering with Bit Rate Constraints and Cross-Correlated Noises over Sensor Networks

This paper focuses on the distributed filtering issue for a type of discrete-time systems with cross-correlated measurement noises under constrained bit rate. The system under consideration is subject to cross-correlated measurement noises, that is, for different sensor nodes, the measurement noises are a-step cross-correlated. For digital communication, the binary encoding scheme is employed to encode the signals into binary bit strings, in which the random bit errors induced by the channel noise may occur during the propagation of the binary bit string via the memoryless binary symmetric channel. To characterize the occurrence of the bit errors, a set of Bernoulli distributed random variables is adopted. Furthermore, to better reflect the practice, the time delays in the coding-decoding process is incorporated in the filter design. Considering the impacts of the cross-correlated noises, constrained bit rates and bit errors, an upper bound of the filtering error covariance matrix is obtained and the filter parameters are acquired by minimizing the upper bound. Finally, a simulation example is conducted to demonstrate the effectiveness of the proposed algorithm.