Distributed Kalman Filtering Under Two-Bitrate Periodic Coding Strategies

Abstract

This paper is concerned with the problem of distributed Kalman filtering over sensor networks under two-bitrate periodic coding strategies. Initially, the optimal estimates for sensor individuals are acquired using the conventional Kalman filter. Subsequently, the information pair, consisting of the local estimate and the corresponding covariance, is exchanged among their immediate neighbors to achieve cooperative estimation. Due to the constrained network bandwidth, a vector/matrix quantization approach is formulated to quantize the information pair. The output of this quantization establishes a conservative bound for the actual covariance. A two-bitrate periodic coding strategy is proposed, where the encoded bits of the quantizer outputs are divided into two separate parts, namely the most significant and least significant bits, following a periodic transmission principle. It is demonstrated that the estimation preserves a consistency property over the sensor networks as the reported error covariance always serves as an upper bound for the actual error covariance. It is shown that the mean-square estimation errors are bounded when certain conditions regarding collective observability and network connectivity are satisfied. Finally, the effectiveness of the proposed algorithm is verified through a numerical example.