Separating Function Estimation Test for Binary Distributed Radar Detection With Unknown Parameters

This paper addresses the problem of distributed detection in the case where, under the signal-present hypothesis, the signal-to-noise ratio (SNR) is unknown and/or observations are correlated. We assume that each local detector makes a (binary) decision while meeting a local false alarm constraint; it then transmits its decision to a fusion center. The unknown SNR at each local detector induces an unknown probability of detection and, hence, the optimal detector at the fusion center does not exist. We begin with the case most often considered in the literature: independent observations. In this case, we derive the asymptotically optimal separating function estimation test (AOSFET) and the generalized likelihood ratio test (GLRT). Moreover, we propose a method to set the local false alarm rates to achieve the maximum probability of detection at the fusion center (while meeting a constraint on the global probability of false alarm). The second part of this paper considers the case of correlated observations. We show that the AOSFET for this problem does not exist. As alternatives, we propose three suboptimal SFETs: based on an approximation to the AOSFET, the Kullback–Leibler divergence, and the Euclidean distance of the estimated probability mass function (pmf) of the observations under each hypotheses. Finally, we propose two methods to improve the performance of the estimation of the pmfs using a library of training labeled data based on the maximum likelihood estimation and expected maximization methods.