A bayesian approach to adaptive detection in nonhomogeneous environments

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

Detection of a signal in linear subspace with bounded mismatch

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

A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes.Comment: submitted for journal publicatio

An improved adaptive sidelobe blanker

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

Design of Customized Adaptive Radar Detectors in the CFAR Feature Plane

The paper addresses the design of adaptive radar detectors with desired behavior, in Gaussian disturbance with unknown statistics. Specifically, based on detection probability specifications for chosen signal-to-noise ratios and steering vector mismatch levels, a methodology for the design of customized constant false alarm rate (CFAR) detectors is devised in a suitable feature plane obtained from two maximal invariant statistics. To overcome the analytical and numerical intractability of the resulting optimization problem, a novel general reduced-complexity algorithm is developed, which is shown to be effective in providing a feasible solution (i.e., fulfilling a constraint on the probability of false alarm) while controlling the behavior under both matched and mismatched conditions, so enabling the design of fully customized adaptive CFAR detectors

Toward Data-Driven Radar STAP

Catalyzed by the recent emergence of site-specific, high-fidelity radio frequency (RF) modeling and simulation tools purposed for radar, data-driven formulations of classical methods in radar have rapidly grown in popularity over the past decade. Despite this surge, limited focus has been directed toward the theoretical foundations of these classical methods. In this regard, as part of our ongoing data-driven approach to radar space-time adaptive processing (STAP), we analyze the asymptotic performance guarantees of select subspace separation methods in the context of radar target localization, and augment this analysis through a proposed deep learning framework for target location estimation. In our approach, we generate comprehensive datasets by randomly placing targets of variable strengths in predetermined constrained areas using RFView, a site-specific RF modeling and simulation tool developed by ISL Inc. For each radar return signal from these constrained areas, we generate heatmap tensors in range, azimuth, and elevation of the normalized adaptive matched filter (NAMF) test statistic, and of the output power of a generalized sidelobe canceller (GSC). Using our deep learning framework, we estimate target locations from these heatmap tensors to demonstrate the feasibility of and significant improvements provided by our data-driven approach in matched and mismatched settings.Comment: 39 pages, 24 figures. Submitted to IEEE Transactions on Aerospace and Electronic Systems. This article supersedes arXiv:2201.1071

Adaptive Radar Detection of a Subspace Signal Embedded in Subspace Structured plus Gaussian Interference Via Invariance

This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna. The problem is solved via the Principle of Invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant. A maximal invariant statistic, which completely characterizes the class of invariant decision rules and significantly compresses the original data domain, as well as its statistical characterization are determined. Thus, the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules. At the analysis stage, the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions

Mismatched Filter Effects on Synthetic Aperture Radar Image Quality Metrics

Detection of targets across a wide dynamic range is an enduring challenge in radar. This work formulates a modified least-squares mismatched filter that greatly reduces these sidelobes in order to enable the detection of small radar cross section targets in the presence of considerably larger scatterers, increasing the dynamic range. Unlike previous mismatched filters, the proposed filter is applicable to noisy, oversampled signals with no requirements on signal structure. Range profiles and images are presented to demonstrate the superior sidelobe suppression of the modified least-squares mismatched filter in comparison to the commonly employed matched filter. Various weighting vectors are introduced to further increase sidelobe suppression for particular scene geometries. The modified mismatched filter created with the addition of a noise compensation term is shown to have superior sidelobe suppression to that of the matched filter across all signal-to-noise ratios, coming at the relatively low expense of a small degree of mainlobe energy loss and widening, as well as increased processing time