Non-Bayesian Estimation with Partially Quantized Observations

In this paper, we consider non-Bayesian parameter estimation in wireless sensor networks (WSNs) with multiple sensors that have different quantization resolutions. Quantized measurements provide improved performance in the sense of energy consumption, communication bandwidth, and hardware complexity, but are less informative than analog, unquantized measurements and may lead to poor estimation performance. In this paper we assume that the WSN contains two types of sensor nodes: 1-bit, quantized measurements and infinity-bit, unquantized measurements. We introduce the maximum-likelihood (ML) estimator for this case and derive the Fisher scoring method in order to implement it. The Cramer-Rao lower bound (CRB) has been developed for the considered model. In addition, we characterize the sample allocation rule that determines how many sensors are selected for quantized and unquantized measurements in order to minimize the sum of the CRB and linear sensors costs. Finally, we present simulations that show for the linear Gaussian model the ML estimator achieves the CRB and examine the use of additional analog measurements as a tool for improving robustness.