In this paper, we deal with the problem of adaptive detection of distributed targets embedded in colored noise modeled in terms of a compound-Gaussian process and without assuming that a set of secondary data is available. The covariance matrices of the data under test share a common structure while having different power levels. A Bayesian approach is proposed here, where the structure and possibly the power levels are assumed to be random, with appropriate distributions. Within this framework we propose GLRT-based and ad-hoc detectors. Some simulation studies are presented to illustrate the performances of the proposed algorithms. The analysis indicates that the Bayesian framework could be a viable means to alleviate the need for secondary data, a critical issue in heterogeneous scenarios.

In the present paper, we focus on the design of adaptive decision schemes for point-like targets; the proposed algorithms can take advantage of the possible spillover of target energy between consecutive matched filter samples. To this end, we assume that the received useful signal is known up to a complex factor modeled as a deterministic parameter; moreover, it is embedded in correlated Gaussian noise with unknown covariance matrix. Finally, for estimation purposes we assume that a set of secondary data, free of signal components, but sharing the same covariance matrix of the noise in the cells containing signal returns, up to a possibly different scale factor, is available. Remarkably, the proposed decision schemes can provide accurate estimates of the target position within the cell under test and ensure the desirable constant false alarm rate property with respect to the unknown noise parameters.

We address adaptive detection of Swerling 2 pulse trains by an array of antennas. The disturbance is modeled in terms of a state space model and the ideas of subspace identification are used to come up with a GLRT-based detector. Such detector is compared by Monte Carlo simulation with a Kelly's detector derived assuming that returns are temporally uncorrelated (but spatially correlated) and that a proper set of secondary data is available

We address adaptive discrimination between the signal of interest and a sidelobe interferer. To this end, we propose a detector derived resorting to a GLRT implementation of the generalized Neyman-Pearson rule and a two-stage detection scheme. The adaptive detectors rely on secondary data, free of signal components, but sharing the statistical characterization of the noise in the cell under test, in order to guarantee the CFAR property

We consider the problem of detecting a signal of interest in the presence of compound-Gaussian clutter, without resorting to secondary data in order to infer the clutter covariance matrix. Towards this end, we assume that both the texture τ and the speckle covariance matrix R are random variables with some a priori distributions. Marginalizing with respect to these variables, the probability density function of the observed primary data is derived, leading to a closed-form expression for the generalized likelihood ratio test (GLRT) of the problem at hand. Accordingly, the GLRT assuming that τ is deterministic is also derived. The two detectors are assessed through numerical simulations

We address adaptive detection of coherent signals backscattered by possible point-like targets or originated from electronic countermeasure (ECM) systems in presence of thermal noise, clutter, and possible noise-like interferers. In order to come up with a class of decision schemes capable of discriminating between targets and ECM signals, we resort to generalized likelihood ratio test (GLRT) implementations of a generalized Neyman-Pearson rule (i.e., for multiple hypotheses). The adaptive detectors rely on secondary data, free of signal components, but sharing the statistical characterization of the noise in the cell under test. The performance assessment focuses on an adaptive beamformer orthogonal rejection test (ABORT)-like detector; analytical expressions for the probability of false alarm, the probability of detection of the target, and the probability of blanking the ECM (coherent) signal are given. More remarkably, it guarantees the constant false alarm rate (CFAR) property. The performance assessment shows that it can outperform the adaptive sidelobe blanker (ASB) in presence of ECM systems.

We address the problem of estimating a covariance matrix R using K samples z k whose covariance matrices are τ kR, where τ k are random variables. This problem naturally arises in radar applications in the case of compound-Gaussian clutter. In contrast to the conventional approach which consists in considering R as a deterministic quantity, a knowledge-aided (KA) approach is advocated here, where R is assumed to be a random matrix with some prior distribution. The posterior distribution of R is derived. Since it does not lead to a closed-form expression for the minimum mean-square error (MMSE) estimate of R, both R and τ k are estimated using a Gibbs-sampling strategy. The maximum a posteriori (MAP) estimator of R is also derived. It is shown that it obeys an implicit equation which can be solved through an iterative procedure, similarly to the case of deterministic τ ks, except that KA is now introduced in the iterative scheme. The new estimators are shown to improve over conventional estimators, especially in small sample support.

We address the problem of adaptive detection of a signal of interest embedded in colored noise modeled in terms of a compound-Gaussian process. The covariance matrices of the primary and the secondary data share a common structure while having different power levels. A Bayesian approach is proposed here, where both the power levels and the structure are assumed to be random, with some appropriate distributions. Within this framework we propose MMSE and MAP estimators of the covariance structure and their application to adaptive detection using the NMF test statistic and an optimized GLRT herein derived. Some results, also in comparison with existing algorithms, are presented to illustrate the performances of the proposed detectors. The relevant result is that the solutions presented herein allows to improve the performance over conventional ones, especially in presence of a small number of training data.

In this correspondence, we focus on the design and the analysis of schemes aimed at estimating the position of multiple point-like targets that fall among three adjacent samples of the matched filter output (typically present in the processing chain of a radar). To this end, we exploit spillover of targets’ energy to adjacent range cells. The number of targets (and the corresponding Doppler frequency shifts) is assumed to be known. Moreover, we suppose that received useful signals can be modeled in terms of vectors known up to deterministic parameters and that they are embedded in correlated Gaussian noise with unknown covariance matrix. For estimation purposes we assume that a set of secondary data, free of signal components, but sharing the same covariance matrix of the noise in the cells containing signal returns, is available. The analysis, also in comparison to a possible competitor, proves the superiority of multitarget schemes with respect to single target ones, even under reasonably mismatched scenarios.

We present a statistical analysis of the laser ranging data of LAGEOS and LAGEOS 2 satellites which have provided a test of dragging of inertial frames, or frame-dragging, by rotating mass as predicted by General Relativity. As a result, the analysis of the residuals, after filtering out the periodic effects, is consistent with a Gaussian model, with a nonzero mean in agreement with the one predicted by Lense–Thirring effect.

We propose and assess new algorithms for adaptive detection and tracking based on space-time data. At design stage we take into account possible spillover of target energy to adjacent range cells and assume a target kinematic model. Then, resorting to the generalized likelihood ratio test (GLRT) we derive track-before-detect (TBD) algorithms that can operate in scan-to-scan varying scenarios and, more important, that ensure the constant false track acceptance rate (CFTAR) property with respect to the covariance matrix of the disturbance. Moreover, we also propose CFTAR versions of the maximum likelihood-probabilistic data association (ML-PDA) algorithm capable of working with data from an array of sensors. The preliminary performance assessment, conducted resorting to Monte Carlo simulation, shows that the proposed TBD structures outperform the ML-PDA implementations especially in terms of probability of track detection (and for low signal-to-noise ratio (SNR) values).