A novel approach to design of local quantizers for distributed estimation

In distributed estimation where each node can collect only partial information on the parameter of interest without communication between nodes and quantize it before transmission to a fusion node which conducts estimation of the parameter, we consider a novel quantization technique employed at local nodes. It should be noted that the performance can be greatly improved if each node can transmit its measurement to one designated node (namely, head node) which can quantize its estimate using the total rate available in the system. For this case, the best strategy at the head node would be simply to partition the parameter space using the generalized Lloyd algorithm, producing the global codewords, one of which is closest to the estimate is transmitted to a fusion node. In this paper, we propose an iterative design algorithm that seeks to efficiently assign the codewords into each of quantization partitions at nodes so as to achieve the performance close to that of the system with the head node. We show through extensive experiments that the proposed algorithm offers a performance improvement in rate-distortion perspective as compared with previous novel techniques.