Nonparametric Density Estimation, Hypotheses Testing, and Sensor Classification in Centralized Detection

In distributed sensing, the statistical model of the data collected by the sensor elements is often unavailable. In addition, these statistics may vary among the sensors and over time, for instance due to: 1) hardware variations; 2) the sensors' geographical locations; 3) different noise statistics; 4) diverse channel conditions between the sensor elements and the fusion center (FC); and 5) the presence of misbehaving sensors sending false data to the FC. In this paper, we consider the problem of centralized binary hypothesis testing in a wireless sensor network consisting of multiple classes of sensors, where the sensors are classified according to the probability density function (PDF) of their received data (at the FC) under each hypothesis. The sensor nodes transmit their observed data to the FC, which must classify the nodes and detect the state of nature. To optimally fuse the data, the FC must also estimate the PDFs of the sensors' observations. We develop a method based on the expectation maximization (EM) algorithm to estimate the PDFs for each sensor class, to classify the sensors, and to detect the underlying hypotheses. The estimation of PDFs is nonparametric in that no prior model is assumed. Simulation results using fewer than three iterations of the EM algorithm demonstrate the efficacy of the proposed method.