Abstract-In this paper, we use the theory of generalized likelihood ratio tests (GLRTs) to adapt the matched subspace detectors (MSDs) of [1] and [2] to unknown noise covariance matrices. In so doing, we produce adaptive MSDs that may be applied to signal detection for radar, sonar, and data communication. We call the resulting detectors adaptive subspace detectors (ASDs). These include Kelly's GLRT and the adaptive cosine estimator (ACE) of [6] and [19] for scenarios in which the scaling of the test data may deviate from that of the training data. We then present a unified analysis of the statistical behavior of the entire class of ASDs, obtaining statistically identical decompositions in which each ASD is simply decomposed into the nonadaptive matched filter, the nonadaptive cosine or -statistic, and three other statistically independent random variables that account for the performance-degrading effects of limited training data.

Abstract-The constant false alarm rate (CFAR) matched subspace detector (CFAR MSD) is the uniformly most-powerful-invariant test and the generalized likelihood ratio test (GLRT) for detecting a target signal in noise whose covariance structure is known but whose level is unknown. Recently, the CFAR adaptive subspace detector (CFAR ASD), or adaptive coherence estimator (ACE), was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data. We show here that the CFAR ASD is GLRT when the test measurement is not constrained to have the same noise level as the training data. As a consequence, this GLRT is invariant to a more general scaling condition on the test and training data than the well-known GLRT of Kelly.

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The constant false alarm rate (CFAR) matched subspace detector (CFAR MSD) is the uniformly most-powerful-invariant test and the generalized likelihood ratio test (GLRT) for detecting a target signal in noise whose covariance structure is known but whose level is unknown. Recently, the CFAR adaptive subspace detector (CFAR ASD), or adaptive coherence estimator (ACE), was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data. We show here that the CFAR ASD is GLRT when the test measurement is not constrained to have the same noise level as the training data. As a consequence, this GLRT is invariant to a more general scaling condition on the test and training data than the well-known GLRT of Kelly.

[1] Estimation of the range-and height-dependent index of refraction over the sea surface facilitates prediction of ducted microwave propagation loss. In this paper, refractivity estimation from radar clutter returns is performed using a Markov state space model for microwave propagation. Specifically, the parabolic approximation for numerical solution of the wave equation is used to formulate the refractivity from clutter (RFC) problem within a nonlinear recursive Bayesian state estimation framework. RFC under this nonlinear state space formulation is more efficient than global fitting of refractivity parameters when the total number of range-varying parameters exceeds the number of basis functions required to represent the height-dependent field at a given range. Moreover, the range-recursive nature of the estimator can be easily adapted to situations where the refractivity modeling changes at discrete ranges, such as at a shoreline. A fast range-recursive solution for obtaining range-varying refractivity is achieved by using sequential importance sampling extensions to state estimation techniques, namely, the forward and Viterbi algorithms. Simulation and real data results from radar clutter collected off Wallops Island, Virginia, are presented which demonstrate the ability of this method to produce propagation loss estimates that compare favorably with ground truth refractivity measurements.