An adaptive quantization scheme for distributed consensus

The problem of distributed average consensus with quantized data is considered in this paper. We firstly propose a simple modification to the classical consensus protocol. Under a condition that the quantization noise variance converges to zero, the proposed protocol achieves a consensus in a mean squared sense and the consensus value is equal to the average of the initial state. Based on this result, we develop an adaptive quantization scheme which can adaptively adjust its quantization threshold and step-size by learning from previous runs, in a way such that the quantization noise variance at each sensor decreases to zero. Simulation results are presented to illustrate the effectiveness of the proposed algorithm.