Adaptive Matched Filter Using Non-Target Free Training Data

The problem of detecting a subspace signal in colored Gaussian noise with unknown covariance matrix is investigated when the training data may contain samples with target signal. The target signal is assumed that it lies in a subspace spanned by columns of a known matrix. To develop the test, an ad hoc approach, similar to the classical adaptive matched filter (AMF) is used where instead of the maximum likelihood (ML) estimator of the covariance, the minimum alpha-divergence based estimator is substituted in the likelihood ratio. This test just depends on the single parameter alpha and as a special case can be turned to the AMF. For a range of alpha, the proposed test has the benefits of being robust to outliers and the existence of other targets in the training data. Numerical examples illustrating that the proposed detector can achieve better detection rates in such a scenario while providing almost the same performance in a target free scenario are presented.