Adaptive detection for distributed target and multiple point targets in non-homogeneous environments is studied in this paper, where it is assumed that the covariance matrix of the secondary data follows inverse Wishart distribution conditioned on that of the primary data with its expectation proportional to it. The Maximum Likelihood Estimator (MLE) of the covariance matrix of the primary data, scale factor and target amplitude are firstly given and subsequently a detector is proposed based on Bayesian theory and Generalized Likelihood Ratio Test (GLRT) decision rule. The detector is coincident with the Adaptive Coherence Estimator (ACE) when the target exists in one range bin and it is consistent with the Generalized Adaptive Subspace Detector (GASD) when target extends more than one range bin. However, what makes it different is that the ACE and GASD are both based on unknown deterministic covariance matrix. Additionally, the detector has Constant False Alarm Rate (CFAR) and bears good performance.
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