Normalized matched filter - a low rank approach

This paper presents the performance of the normalized matched filter (NMF) test in a background of disturbance consisting of clutter having a covariance matrix with known structure and unknown scaling plus background white Gaussian noise. Specifically, it is shown that when the clutter covariance matrix is low rank, the NMF test retains invariance with respect to the unknown scaling as well as the background noise level and is approximately CFAR. Performance of the test depends only upon the number of elements, number of pulses processed in a coherent processing interval and the rank of the clutter covariance matrix. Analytical expressions for calculating the false alarm and detection probabilities are presented. Performance of the method is shown to degrade with increasing clutter rank especially for low false alarm rates.