Distributed estimation under the minimax criterion

In this paper, the problem of distributed estimation using one-bit quantization in the presence of non-ideal transmission links is revisited. Previous results have shown that the estimation performance highly depends on the selection of local quantization thresholds. Both the identical threshold scheme and the non-identical threshold scheme are investigated under the minimax criterion. Specifically, local sensor thresholds are uniformly distributed in the known range of the parameter under estimation for the non-identical threshold scheme. By comparing the Cramer-Rao bounds (CRBs), the uniform thresholding scheme outperforms the identical threshold scheme when the parameter range is large relative to the standard deviation of the observation noise. Using the uniform thresholding scheme, maximum likelihood estimator (MLE) as well as a more practical estimator is developed. The comparison of these two thresholding schemes is conducted by adopting the proposed simple estimator and our previously proposed mean estimator. The results further confirm the superiority of the non-identical threshold scheme for a large parameter range.