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.摘要验证了Krylov子空间技术在信号检测和滤波中的有效性。 提出了一种新的多级维纳滤波器(MWF)和辅助向量滤波器(AVF)等价性的证明方法。 把MWF和AVF与两种检测器(自适应匹配滤波检测器(AMF)和广义似然比检测器(GLRT))及对角加载(DL)技术相结合, 形成了新的检测器。 与传统AMF和GLRT检测器相比, 新检测器具有更高的检测概率(PD), 尤其是训练样本数较低时。 更重要的是, 新检测器对杂波子空间秩的选取不敏感。 此外, 新检测器具有渐近恒虚警(CFAR)特性。