Nonparametric Probability Density Estimation for Sensor Networks Using Quantized Measurements

We develop a nonparametric method for estimating the probability distribution function (pdf) describing the physical phenomenon measured by a sensor network. The measurements are collected by sensor-processor elements (nodes) deployed in the region of interest; the nodes quantize these measurements and transmit only one bit per observation to a fusion center. We model the measurement pdf as a Gaussian mixture and develop a Fisher scoring algorithm for computing the maximum likelihood (ML) estimates of the unknown mixture probabilities. We also estimate the number of mixture components as well as their means and standard deviation. Numerical simulations demonstrate the performance of the proposed method.