Modified GLRT and AMF Framework for Adaptive Detectors

The well-known general problem of signal detection in background interference is addressed for situations where a certain statistical description of the interference is unavailable, but is replaced by the observation of some secondary (training) data that contains only the interference. For the broad class of interferences that have a large separation between signal-and noise-subspace eigenvalues, we demonstrate that adaptive detectors which use a diagonally loaded sample covariance matrix or a fast maximum likelihood (FML) estimate have significantly better detection performance than the traditional generalized likelihood ratio test (GLRT) and adaptive matched filter (AMI') detection techniques, which use a maximum likelihood (ML) covariance matrix estimate. To devise a theoretical framework that can generate similarly efficient detectors, two major modifications are proposed for Kelly's traditional GLRT and AMF detection techniques. First, a two-set GLRT decision rule takes advantage of an a priori assignment of different functions to the primary and secondary data, unlike the Kelly rule that was derived without this. Second, instead of ML estimates of the missing parameters in both GLRT and AMF detectors, we adopt expected likelihood (EL) estimates that have a likelihood within the range of most probable values generated by the actual interference covariance matrix. A Gaussian model of fluctuating target signal and interference is used in this study. We demonstrate that, even under the most favorable loaded sample-matrix inversion (LSMI) conditions, the theoretically derived EL-GLRT and FL-AMF techniques (where the loading factor is chosen from the training data using the EL matching principle) gives the same detection performance as the loaded AMF technique with a proper a priori data-invariant loading factor. For the least favorable conditions, our EL-AMF method is still superior to the standard AMF detector, and may be interpreted as an intelligent (data-dependent) method for selecting the loading factor.