Polynomial filter design for quantized consensus

We consider the problem of distributed average consensus where sensors exchange quantized data with their neighbors. We deploy a polynomial filtering approach in the network nodes in order to accelerate the convergence of the consensus problem. The quantization of the values computed by the sensors however imposes a careful design of the polynomial filter. We first study the impact of the quantization noise in the performance of accelerated consensus based on polynomial filtering. It occurs that the performance is clearly penalized by the quantization noise, whose impact directly depends on the filter coefficients. We then formulate a convex optimization problem for determining the coefficients of a polynomial filter, which is able to control the quantization noise while accelerating the convergence rate. The simulation results show that the proposed solution is robust to quantization noise while assuring a high convergence speed to the average value in the network.