Quantization For Distributed Estimation in Large Scale Sensor Networks

We study the problem of quantization for distributed parameter estimation in large scale sensor networks. Assuming a Maximum Likelihood estimator at the fusion center, we show that the Fisher Information is maximized by a score-function quantizer. This provides a tight bound on best possible MSE for any unbiased estimator. Furthermore, we show that for a general convex metric, the optimal quantizer belongs to the class of score function quantizers. We also discuss a few practical applications of our results in optimizing estimation performance in distributed and temporal estimation problems.