Robust distributed maximum likelihood estimation with dependent quantized data

In this paper, distributed maximum likelihood estimation (MLE) with quantized data is considered under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic parameters. The parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe dependence of observations across sensors. We first discuss the regularity conditions which should be satisfied by the pdf and vector quantizers such that the MLE with quantized data is asymptotically efficient. Then, the relationship between the asymptotic variance of the MLE and the number of quantization bits is analytically derived. Since the optimal MLE scheme based on quantized data cannot be obtained when the joint pdf of observations is not completely known, a robust distributed MLE scheme is designed for a fixed number of quantization bits. Its asymptotic efficiency is proved under some regularity conditions and the asymptotic variance is derived so that the robustness can be analytically assessed. A numerical example with a bivariate Gaussian pdf is considered. Simulations show that the robustness of the proposed MLE scheme. keywords: Maximum likelihood estimation; distributed estimation; quantized data; asymptotic variance; Fisher information matrix; wireless sensor networks