Adaptive detectors in the Krylov subspace

The validity of the application of the Krylov subspace techniques in adaptive filtering and detection is investigated. A new verification of the equivalence of two well-known methods in the Krylov subspace, namely the multistage Wiener filters (MWF) and the auxiliary-vector filtering (AVF), is given in this paper. The MWF and AVF are incorporated into two well-known detectors, namely, the adaptive matched filter (AMF) and Kelly's generalized likelihood ratio test (GLRT) including their diagonally loaded versions, which form new detectors. Compared to the conventional AMF, GLRT, and their diagonally loaded versions as well as the reduced-rank AMF and GLRT, the probabilities of detection (PDs) of the new detectors are improved especially when the sample support is low. More importantly, the new detectors are robust of the rank selection of the clutter subspace compared to the reduced-rank AMF and GLRT. These new detectors all possess asymptotic constant false alarm rate (CFAR) property.