Generalized likelihood ratio test for distributed targets in heterogeneous environments

Adaptive detection for distributed target or targets in non-homogeneous environments is studied in this paper. It is assumed that the covariance matrix of the secondary data M_s is a random matrix following inverse Wishart distribution with its conditional expectation proportional to that of the primary data, i.e. E(M_s | M_p)= γM_p. Firstly, the maximum likelihood estimator (MLE) of M_p, γ and target amplitudes are given and the generalized likelihood ratio test (GLRT) are proposed subsequently, which turns out to be in the form of the summed adaptive coherence estimator (ACE). The detector is coincident with the generalized adaptive subspace detector (GASD) based on deterministic unknown covariance matrix and it has CFAR property. When the target exists only in one range bin, the detector is boiled down into the ACE based on the partial homogeneous environments.