Optimal Identical Binary Quantizer Design for Distributed Estimation

Abstract

We consider the design of identical one-bit probabilistic quantizers for distributed estimation in sensor networks. We assume the parameter-range to be finite and known and use the maximum Crameŕ–Rao lower bound (CRB) over the parameter-range as our performance metric. We restrict our theoretical analysis to the class of antisymmetric quantizers and determine a set of conditions for which the probabilistic quantizer function is greatly simplified. We identify a broad class of noise distributions, which includes Gaussian noise in the low-SNR regime, for which the often used threshold-quantizer is found to be minimax-optimal. Aided with theoretical results, we formulate an optimization problem to obtain the optimum minimax-CRB quantizer. For a wide range of noise distributions, we demonstrate the superior performance of the new quantizer—particularly in the moderate to high-SNR regime

Optimal quantizers for distributed Bayesian estimation

“…Identical quantizers at the sensors have traditionally been used by researchers as it simplifies the design problem [3] [6]. However, relatively little research has focused on the optimality of these identical quantizers.…”

Distributed estimation for moving target under switching interconnection network

“…Recent years have witnessed increasing attention in multisensor networks for its broad application, e.g., [1], [2], [3], [4], [5]. One of an important problems in the sensor network is distributed estimation, that is, to estimate constants or variables in a distributed way.…”

One-Bit Quantization and Distributed Detection with an Unknown Scale Parameter

“…In the context of wireless sensor networks (WSNs), the detection of unknown parameters by using a multitude of sensor nodes has been of significant interest over the past few decades (e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13] and the references therein). The widely-deployed sensors are designated to provide measurements of a given physical process (temperature, humidity, etc.…”

“…In practice, especially to meet bandwidth/energy constraints, there is a need to reduce the dimension of raw measurements from each sensor to the FC by using one-bit quantization [1][2][3][4][5][6][7][8][9][10][11]. In [4], a fixed quantization (FQ) approach was examined for distributed estimation of a mean parameter (i.e., the mean of observations).…”

“…To overcome this difficulty, a distributed adaptive quantization (AQ) approach was proposed in [5,6], where the threshold is dynamically regulated from one sensor to another, in such a way that the threshold converges to the optimum threshold. In [7], the design of the binary antisymmetric quantizer was studied by the minimization of the worst case of the Cramér-Rao bound (CRB). Using a generalized likelihood ratio test (GLRT) framework, joint estimation and detection of an unknown mean parameter based on one-bit quantization was considered in [8].…”