102 research outputs found

    Detection of a signal in linear subspace with bounded mismatch

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    We consider the problem of detecting a signal of interest in a background of noise with unknown covariance matrix, taking into account a possible mismatch between the actual steering vector and the presumed one. We assume that the former belongs to a known linear subspace, up to a fraction of its energy. When the subspace of interest consists of the presumed steering vector, this amounts to assuming that the angle between the actual steering vector and the presumed steering vector is upper bounded. Within this framework, we derive the generalized likelihood ratio test (GLRT). We show that it involves solving a minimization problem with the constraint that the signal of interest lies inside a cone. We present a computationally efficient algorithm to find the maximum likelihood estimator (MLE) based on the Lagrange multiplier technique. Numerical simulations illustrate the performance and the robustness of this new detector, and compare it with the adaptive coherence estimator which assumes that the steering vector lies entirely in a subspace

    Adaptive detection of a signal known only to lie on a line in a known subspace, when primary and secondary data are partially homogeneous

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    This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known

    Adaptive detection in nonhomogeneous environments using the generalized eigenrelation

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    This letter considers adaptive detection of a signal in a nonhomogeneous environment, more precisely under a covariance mismatch between the test vector and the training samples, due to an interference that is not accounted for by the training samples, e.g., a sidelobe target or an undernulled interference. We assume that the covariance matrices of the test vector and the training samples verify the so-called generalized eigenrelation. Under this assumption, we derive the generalized likelihood ratio test and show that it coincides with Kelly’s detector

    Adaptive detection with bounded steering vectors mismatch angle

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    We address the problem of detecting a signal of interest (SOI), using multiple observations in the primary data, in a background of noise with unknown covariance matrix. We consider a situation where the signal signature is not known perfectly, but its angle with a nominal and known signature is bounded. Furthermore, we consider a possible scaling inhomogeneity between the primary and the secondary noise covariance matrix. First, assuming that the noise covariance matrix is known, we derive the generalized-likelihood ratio test (GLRT), which involves solving a semidefinite programming problem. Next, we substitute the unknown noise covariance matrix for its estimate obtained from secondary data, to yield the final detector. The latter is compared with a detector that assumes a known signal signature

    A novel approach to robust radar detection of range-spread targets

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    This paper proposes a novel approach to robust radar detection of range-spread targets embedded in Gaussian noise with unknown covariance matrix. The idea is to model the useful target echo in each range cell as the sum of a coherent signal plus a random component that makes the signal-plus-noise hypothesis more plausible in presence of mismatches. Moreover, an unknown power of the random components, to be estimated from the observables, is inserted to optimize the performance when the mismatch is absent. The generalized likelihood ratio test (GLRT) for the problem at hand is considered. In addition, a new parametric detector that encompasses the GLRT as a special case is also introduced and assessed. The performance assessment shows the effectiveness of the idea also in comparison to natural competitors.Comment: 28 pages, 8 figure

    Matched subspace detection with hypothesis dependent noise power

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    We consider the problem of detecting a subspace signal in white Gaussian noise when the noise power may be different under the null hypothesis—where it is assumed to be known—and the alternative hypothesis. This situation occurs when the presence of the signal of interest (SOI) triggers an increase in the noise power. Accordingly, it may be relevant in the case of a mismatch between the actual SOI subspace and its presumed value, resulting in a modelling error. We derive the generalized likelihood ratio test (GLRT) for the problem at hand and contrast it with the GLRT which assumes known and equal noise power under the two hypotheses. A performance analysis is carried out and the distributions of the two test statistics are derived. From this analysis, we discuss the differences between the two detectors and provide explanations for the improved performance of the new detector. Numerical simulations attest to the validity of the analysis

    An improved adaptive sidelobe blanker

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    We propose a two-stage detector consisting of a subspace detector followed by the whitened adaptive beamformer orthogonal rejection test. The performance analysis shows that it possesses the constant false alarm rate property with respect to the unknown covariance matrix of the noise and that it can guarantee a wider range of directivity values with respect to previously proposed two-stage detectors. The probability of false alarm and the probability of detection (for both matched and mismatched signals) have been evaluated by means of numerical integration techniques

    A bayesian approach to adaptive detection in nonhomogeneous environments

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    We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter

    An ABORT-like detector with improved mismatched signals rejection capabilities

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    In this paper, we present a GLRT-based adaptive detection algorithm for extended targets with improved rejection capabilities of mismatched signals. We assume that a set of secondary data is available and that noise returns in primary and secondary data share the same statistical characterization. To increase the selectivity of the detector, similarly to the ABORT formulation, we modify the hypothesis testing problem at hand introducing fictitious signals under the null hypothesis. Such unwanted signals are supposed to be orthogonal to the nominal steering vector in the whitened observation space. The performance assessment, carried out by Monte Carlo simulation, shows that the proposed dectector ensures better rejection capabilities of mismatched signals than existing ones, at the price of a certain loss in terms of detection of matched signals
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