This dissertation examines the problem of detecting a multichannel signal in spatially and temporally colored disturbances. First, a parametric Rao test is developed by modeling the disturbance signal as a multichannel autoregressive (AR) process. Interestingly, the well-known parametric adaptive matched filter (PAMF) detector is shown to be equivalent to the parametric Rao detector. The equivalence offers new insights into the performance and implementation of the PAMF detector. Specifically, the parametric Rao detector is asymptotically a parametric generalized likelihood ratio test (GLRT), due to an asymptotic equivalence between the Rao test and the GLRT. The asymptotic distribution of the test statistic is obtained in closed-form. In addition, the parametric Rao detector is shown to asymptotically achieve constant false alarm rate (CFAR).; Second, a parametric GLRT is developed by exploiting a multichannel AR model for the disturbance. Maximum likelihood (ML) parameter estimation underlying the parametric GLRT is also examined. It is shown that the ML estimator for the alternative hypothesis is non-linear and there exists no closed-form expression. To address this issue, an asymptotic ML (AML) estimator is presented, which yields asymptotically optimum parameter estimates at reduced complexity. The performance of the parametric GLRT is studied by considering challenging cases with limited or no training data. Such cases are of great interest in detecting signals in heterogeneous or dense-target environment, but generally cannot be handled by most existing multichannel detectors which rely more heavily on training at an adequate level. The parametric Rao and GLRT detectors use the test and training data for parameter estimation and can handle the training-free case.; Third, the performance of these parametric detectors are examined using airborne data from the Multi-Channel Airborne Radar Measurement (MCARM) database, which show that they significantly outperform the conventional non-parametric detectors.; Finally, we present recursive versions of the aforementioned parametric detectors by integrating the multichannel Levinson algorithm, which is employed for recursive and computationally efficient parameter estimation, with a generalized Akaike Information Criterion (GAIC) for model order selection. Numerical results show that these recursive parametric detectors yield a detection performance nearly identical to that of their non-recursive counterparts at significantly reduced complexity.
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