General First-Order Framework for Passive Detection with Two Sensor Arrays

In this paper we establish a general framework for deriving two-channel detectors for passively detecting sources of acoustic or electromagnetic radiation. The framework is based on a first-order model for multivariate normal measurements at two spatially separated arrays, each consisting of L sensors that record M snapshots. The question to be answered is whether or not these measurements contain a signal common to both sensor arrays, indicating the existence of a radiating source. Generalized likelihood ratios (GLRs) aim to maximize the output signal-to-noise ratio (SNR) of a two-channel receiver. Quite generally, the GLRs are maximum eigenvalues of variance-normalized covariance matrices constructed from spacetime measurements at the two arrays. So, while the underlying measurement model is a first-order model, the resulting GLR statistics are decidedly nonlinear functions of the measurements.