Recursive Filtering for Discrete-Time Stochastic Complex Networks under Bit-Rate Constraints: A Locally Minimum Variance Approach

In this article, the recursive filtering problem is investigated for a class of discrete-time stochastic dynamical networks where the data delivery from the sensors to the filter is implemented by a digital communication channel. With the help of the uniform quantization method, an improved encoding–decoding mechanism associated with measurement outputs is first put forward where the decoding error is guaranteed to be stochastically bounded under a certain bit-rate constraint condition. Based on the obtained decoded measurement outputs, sufficient conditions are then established such that the filtering error variance is constrained by an optimized upper bound at each sampling instant. The desired filter parameters are recursively calculated by solving two coupled Riccati difference equations. Moreover, the monotonicity for the filtering error variance with respect to the bit-rate of the communication channel is analytically discussed. Finally, an illustrative numerical simulation is provided to verify the obtained theoretical results.