Distributed Target Detection in Partially Homogeneous Environment When Signal Mismatch Occurs

This paper investigates the problem of detecting a distributed target in the presence of signal mismatch in a partially homogeneous environment. To design a selective detector, we modify the original hypothesis test by injecting a fictitious interference under the null hypothesis test. The fictitious interference is assumed to be orthogonal to the nominal signal in the whitened subspace. Then, according to the generalized likelihood ratio criterion, we obtain a detector that has the constant false alarm rate property and is more selective than existing detectors. However, the proposed detector works only in the case of large number of training data. To overcome this limitation, we introduce a tunable detector, which is parameterized by a tunable parameter. It can work under a very loose constraint on a number of training data. More importantly, the directivity property (robustness and selectivity) of the tunable detector can be flexibly adjusted through the tunable parameter. In addition, the tunable detector can achieve roughly the same detection performance as the corresponding generalized likelihood ratio test when no signal mismatch occurs. Numerical examples are given to demonstrate the effectiveness of the proposed detectors.