A Chi-squared Approximation-based Weighting Method for Distributed Detection

In the distributed radar, signal fusion-based detection can exploit more information from local radars to yield higher detection performance, but most of existing signal fusion-based detection algorithms implicitly demand that the local test statistics to be fused have an identical kind of statistical distributions. Meanwhile, in the distributed generalized likelihood ratio test (GLRT), the weights over local test statistics dismiss after replacing unknown parameters with their maximum likelihood estimates and thus lead to an inappropriate equal-weighting test. In this paper, we consider how to fuse heterogeneous local test statistics with linear weights for a global test statistic in the distributed radar system. The global test statistic is approximated as a Chi-square distributed random variable and local weights are designed to maximize the probability of detection under a given false alarm rate. Numerical results show that better detection performance is achieved through this weighting method. Meanwhile, the Chi-square approximation performs well even in the right tail part of its distribution and thus the false alarm rate can be accurately and conveniently controlled.