Two-step Generalized Likelihood Ratio Test Research Articles

Persymmetric Subspace Detectors With Multiple Observations in Homogeneous Environments

In this article, a target detection problem in homogeneous Gaussian noise with unknown covariance matrix is examined using multiple observations, which may be collected from multiple range cells, bands, and/or coherent processing intervals. In order to take into consideration mismatches of the target steering vector, we adopt a subspace model where the target steering vector is assumed to lie in a subspace spanned by the column vectors of a known matrix with unknown target coordinates. By exploiting persymmetric structures, we propose several adaptive detectors according to ad hoc modifications of generalized likelihood ratio test (GLRT), Rao test, and Wald test. It is found that the Rao test does not exist, whereas the two-step Wald test shares the same form as the two-step GLRT. Numerical examples show that the robustness of the proposed detectors is better than that of their counterparts in general. In particular, the proposed one-step GLRT is the most robust in most cases, and the proposed two-step GLRT and one-step Wald test can be more robust than the one-step GLRT in the case where the number of training data is small.

P.580 The impact of mental disorders on sexual health: a retrospective study

In this paper, we consider the range distributed target detection in partially homogeneous (PH) clutter which displays different statistical properties in adjacent range cells. We propose a group method that adjacent cells with slightly varying statistics are divided into a group. Given the cells group effects on deducing the generalized likelihood ratio test (GLRT), three detectors: one-step group GLRT (1S-G-GLRT), maximum a posteriori estimation group GLRT (MAP-G-GLRT) and two-step group GLRT (2S-G-GLRT) are developed. It is verified that the 1S-G-GLRT and 2S-G-GLRT are constant false alarm rate (CFAR) with respect to the scale parameter of texture and the estimated speckle covariance matrix. The experiments show that, in the simulated clutter, the three proposed detectors behave approximately similarly, all of them outperforming three existing detectors remarkably despite the effects of target models and group strategies. In the real clutter, the 1S-G-GLRT and MAP-G-GLRT have advantages over the detectors without grouping in PH real clutter.

Adaptive Target Detection in Gaussian Clutter Edges

This paper addresses the adaptive target detection problem in Gaussian clutter edges. We employ a two-step generalized likelihood ratio test (GLRT) for the detection problem. Our main contribution lies in devising an iterative algorithm in the second step of the GLRT to obtain the maximum likelihood estimation of the unknown clutter-plus-noise covariance matrix, with all available secondary samples in the clutter edge (including the homogeneous and heterogeneous ones). We prove that the proposed iterative algorithm has guaranteed convergence of the objective value. At the analysis stage, we evaluate the performance of the proposed detector and show the superiority over its counterparts.

Adaptive detection of point-like targets based on a reduced-dimensional data model

Abstract This paper approaches the problem of detecting a point-like target in Gaussian background. The useful signal lies in an one-dimensional subspace spanned by a known steering vector. The Gaussian disturbance fills the whole observation space. Since the disturbance outside the signal subspace is unrelated to the decision result, it is eliminated by pre-multiplying the recorded data by the conjugate transpose of the steering vector in this paper. This preprocessing is not applied in the classical detectors, such as the generalized likelihood ratio test (GLRT), the adaptive matched filter (AMF), etc. This preprocessing results in a new scalar data model where the useful signal and disturbance lie in the same space. Based on this scalar data model, two new detectors are designed through the one-step and two-step GLRT, respectively. Their probabilities of false alarms and detections are derived analytically. The one- (two-) step GLRT-based detector has the (approximately) constant false alarm rate feature in the Gaussian background. Simulation results show that the proposed detectors outperform those classical ones when finite training data is available. The one-step GLRT-based detector is more robust to mismatched signals than those classical detectors.

Adaptive subspace detection of range-spread target in compound Gaussian clutter with inverse Gaussian texture

In this paper, we investigate the adaptive subspace detection of range-spread target embedded in compound Gaussian clutter. The inverse Gaussian distribution is considered to describe the texture of the clutter in order to match the non-Gaussian characteristic of sea clutter. Moreover, the range-spread target's energy is assumed to be spread not only in range dimension but also in Doppler dimension, which is more suitable for the practical situation. Thus, the range-spread target is modeled as a subspace signal which describes the range-spread and Doppler-spread. In this paper, an adaptive detector for a subspace range-spread target is derived by using two-step generalized likelihood ratio test (GLRT). Finally, the detection performance of the proposed detector is verified by experiments based on measured data and simulation data. The experimental results show that the detection performance of the proposed detector is better than that of the existing detectors.

Adaptive Radar Detection Using Two Sets of Training Data

This paper deals with adaptive radar detection of a point-like target in a homogeneous environment characterized by the presence of clutter, jamming, and radar internal noise. At the design stage, two training datasets, whose gathering is carefully motivated in the paper, are considered to get receiver adaptation. Hence, the maximum likelihood estimator of the interference covariance matrix for the cell under test is computed exploiting both the available secondary sets. This estimate is then used to build two adaptive decision rules based on the two-step generalized likelihood ratio test and Rao test criteria. Remarkably, they are not limited by the conventional constraint on the cardinality of the classic training dataset. At the analysis stage, the detection performances of the newly proposed detectors are compared with those of the analogous conventional counterparts and the interplay among the different parameters of the problem is thoroughly studied.

Generalized Likelihood Ratio Test for Detection of Gaussian Rank-One Signals in Gaussian Noise With Unknown Statistics

We consider the classical radar problem of detecting a target in Gaussian noise with unknown covariance matrix. In contrast to the usual assumption of deterministic target amplitudes, we assume here that the latter are drawn from a Gaussian distribution. The generalized likelihood ratio test (GLRT) is derived based on multiple primary data and a set of secondary data containing noise only. The new GLRT is shown to be the product of Kelly's GLRT and a corrective, data dependent term. We also investigate two-step approaches where the GLRT for a known disturbance covariance matrix is first derived. In order to come up with detectors that provide a good tradeoff between detection of matched signals and rejection of mismatched signals, we also investigate the two-step GLRT when a fictitious signal is included in the null hypothesis. The constant false alarm rate properties of the detectors are analyzed. Numerical simulations are presented, which show that for small sample sizes the newly-proposed GLRT can outperform Kelly's GLRT and, in addition, that detectors including a fictitious signal are very powerful, at least for low-to-intermediate clutter to noise ratio values.

Three GLRT detectors for range distributed target in grouped partially homogeneous radar environment

In this paper, we consider the range distributed target detection in partially homogeneous (PH) clutter which displays different statistical properties in adjacent range cells. We propose a group method that adjacent cells with slightly varying statistics are divided into a group. Given the cells group effects on deducing the generalized likelihood ratio test (GLRT), three detectors: one-step group GLRT (1S-G-GLRT), maximum a posteriori estimation group GLRT (MAP-G-GLRT) and two-step group GLRT (2S-G-GLRT) are developed. It is verified that the 1S-G-GLRT and 2S-G-GLRT are constant false alarm rate (CFAR) with respect to the scale parameter of texture and the estimated speckle covariance matrix. The experiments show that, in the simulated clutter, the three proposed detectors behave approximately similarly, all of them outperforming three existing detectors remarkably despite the effects of target models and group strategies. In the real clutter, the 1S-G-GLRT and MAP-G-GLRT have advantages over the detectors without grouping in PH real clutter.

Adaptive detection of range-spread targets in compound Gaussian clutter with the square root of inverse Gaussian texture

The compound Gaussian clutter with the square root of inverse Gaussian texture component has been successfully used for modeling the heavy-tailed non-Gaussian clutter measured by high-resolution radars. In high-resolution radars, the targets may extend along multiple consecutive range cells, which are called range-spread targets. In this paper, we consider the range-spread target detection problem in the compound Gaussian clutter with the square root of inverse Gaussian texture. Three adaptive detectors are proposed based on Bayesian one-step generalized likelihood ratio test, maximum a posteriori generalized likelihood ratio test and Bayesian two-step generalized likelihood ratio test, respectively. Finally, the detection performances of the proposed detectors are evaluated by the Monte Carlo simulation. The simulation results show that the proposed detectors have better detection performance of range-spread target than the conventional generalized likelihood ratio test detector.

Radar detection and range estimation using oversampled data

In this work, we propose two adaptive receivers achieving enhanced range estimation capability through a joint exploitation of the oversampling and the spillover of target energy in adjacent range samples. To this end, a proper discrete-time model for the received signal is introduced. Then, the generalized likelihood ratio test (GLRT) and the so-called two-step GLRT are derived and assessed. The performance analysis, conducted using both simulated data and real recorded datasets, is aimed at assessing the effectiveness of proposed solutions, also in comparison with existing detectors sharing range estimation capabilities. The illustrative examples highlight that better detection performance and increased range estimation accuracy can be achieved by exploiting the oversampling at the price of an additional processing cost.

An Invariant Approach to Adaptive Radar Detection Under Covariance Persymmetry

In this paper, we propose a systematic and unifying framework to deal with adaptive radar detection in the presence of Gaussian interference sharing a persymmetric covariance structure. First, we determine the group of transformations which leaves the considered hypothesis testing problem unaltered; then, after reduction by sufficiency, we determine a maximal invariant statistic which is a four dimensional vector and significantly compresses the original observation space. Its first two components are the one-step and the two-step Generalized Likelihood Ratio Test decision statistics, respectively, whereas its last two entries represent an ancillary statistic. We provide also the exact statistical characterization of the maximal invariant which is exploited to synthesize both the optimum and the locally optimum (in the low Signal-to-Interference-plus-Noise Ratio regime) invariant receivers. Finally, some sub-optimum decision rules based on theoretically solid design criteria are discussed and their performances are analyzed in comparison with the benchmark invariant test.

Rao and Wald Tests for Distributed Targets Detection With Unknown Signal Steering

In this letter, we consider the problem of detecting a distributed target with unknown signal steering in the Gaussian noise. We derive the Rao and Wald tests. It is found that the Rao test coincides with the so-called modified two-step generalized likelihood ratio test (M2S-GLRT), while the Wald test is equivalent to the plain two-step GLRT (2S-GLRT). We also give some intuitive interpretations about the Rao and Wald tests, as well as other existing detectors.

Persymmetric adaptive detection of distributed targets in partially-homogeneous environment

In this paper we deal with the problem of detecting distributed targets in the presence of Gaussian noise with unknown but persymmetric structured covariance matrix. In particular, we consider the so-called partially-homogeneous environment, where the cells under test (primary data) and the training samples (secondary data), which are free of signal components, share the same structure of the interference covariance matrix but different power levels. Under the above assumptions, we derive the generalized likelihood ratio test (GLRT) and the so-called two-step GLRT. Remarkably, the new receivers ensure the constant false alarm rate property with respect to both the structure of the covariance matrix as well as the power level. The performance assessment, conducted by resorting to both simulated data and real recorded dataset, highlights that the proposed detectors can significantly outperform their unstructured counterparts, especially in a severely heterogeneous scenario where a very small number of secondary data is available.

ADAPTIVE DETECTION IN COMPOUND-GAUSSIAN CLUTTER WITH INVERSE GAUSSIAN TEXTURE

This paper mainly deals with the problem of target detection in the presence of Compound-Gaussian (CG) clutter with the Inverse Gaussian (IG) texture and the unknown Power Spectral Density (PSD). The traditional CG distributions, in particular the K distribution and the complex multivariate t distribution, are widely used for modeling the real clutter data from the High-Resolution (HR) radars. Recently, the novel CG distribution with the IG texture is described as the IG-CG distribution and validated to provide the better flt with the recorded data of the HR clutter than the mentioned two competitors. Within the IG-CG framework, the detector is flrstly proposed here in terms of the two-step Generalized Likelihood Ratio Test (GLRT) criterion, and the empirical estimation method is resorted to estimate the unknown PSD in order to adapt the realistic scenario. The proposed detector is tested on the real-life HR clutter data, in comparison with the Adaptive Normalized Matched Filter (ANMF) processor, and the detection results illustrate that it outperforms the ANMF.

Real-time change detection of steady-state evoked potentials

Steady-state evoked potentials (SSEP) are the electrical activity recorded from the scalp in response to high-rate sensory stimulation. SSEP consist of a constituent frequency component matching the stimulation rate, whose amplitude and phase remain constant with time and are sensitive to functional changes in the stimulated sensory system. Monitoring SSEP during neurosurgical procedures allows identification of an emerging impairment early enough before the damage becomes permanent. In routine practice, SSEP are extracted by averaging of the EEG recordings, allowing detection of neurological changes within approximately a minute. As an alternative to the relatively slow-responding empirical averaging, we present an algorithm that detects changes in the SSEP within seconds. Our system alerts when changes in the SSEP are detected by applying a two-step Generalized Likelihood Ratio Test (GLRT) on the unaveraged EEG recordings. This approach outperforms conventional detection and provides the monitor with a statistical measure of the likelihood that a change occurred, thus enhancing its sensitivity and reliability. The system's performance is analyzed using Monte Carlo simulations and tested on real EEG data recorded under coma.

Adaptive detection of distributed targets in compound-Gaussian clutter with inverse gamma texture

The problem of coherent detection for distributed target in compound-Gaussian clutter with inverse gamma texture is studied and three detectors. One-step generalized likelihood ratio test (GLRT), maximum a-posteriori GLRT and two-step GLRT, are proposed respectively in a Bayesian architecture. Resultantly, these detectors have similar detection structures with their test statistics modulated by the shape and scale parameters of the texture. Alternatively, they can be reformulated into another form with their test statistics associated with the scale parameter and detection thresholds related with the shape parameter. And this detection structure can be seen as a matched filter form with a shape-parameter-dependent threshold like the detectors for point target. Subsequently, the proposed detectors are compared with two-step GLRT based on compound-Gaussian clutter without considering texture model, their detection performances are evaluated, and their robustness are analyzed via Monte Carlo simulations. Results enlighten us that: (1) the three Bayesian detectors bear pretty much the same detection performances; (2) the detection performances fluctuate more intensely when the shape parameter or the scale parameter is smaller; (3) the shape parameter has more influences on the detection performances than the scale parameter, as it is an indication of the clutter impulsiveness.

Cascaded Detector for Range-Spread Target in Non-Gaussian Clutter

The work presented here addresses adaptive range-spread target detection in spherically invariant random vector (SIRV) clutter based on two-step generalized likelihood ratio test (GLRT) design procedure. Firstly, with known normalized clutter covariance matrix (NCCM), a robust detector with constant false alarm rate (CFAR) property is proposed, which cascades a detector based on the GLRT for target scatterer in each range cell and two binary integrators. Subsequently, the optimum parameters for the cascaded detector are obtained. Furthermore, by replacing the ideal NCCM with the approximate maximum likelihood (ML) estimated matrix based on secondary data only, the corresponding adaptive detector with approximate CFAR property is also devised. Moreover, the formulas relating the probability of false alarm to the detection threshold are deduced. The performance assessment conducted by Monte Carlo simulation confirms the effectiveness and robustness of the proposed detectors.

PERFORMANCE ANALYSIS OF MULTIPLE-SCAN DETECTION IN HEAVY HETEROGENEOUS SEA CLUTTER

Traditional detection approaches for the dim moving target are addressed under the background of homogeneous sea clutter. However, the realistic clutter commonly appears inhomogeneous, resulting in the low detectability. A heterogeneous multiple-scan detection framework is described in this paper, which combines the inhomogeneous coherent integration in the dwell of single scan and the non-coherent integration of the results from single-scan process across the multiple scans. In the inhomogeneous coherent integration, the Heterogeneous Single-scan Coherent Detector (HSCD) is derived, resorting to the two-step Generalized Likelihood Ratio Test (GLRT) criterion and a hybrid covariance matrix estimation scheme, where the nonhomogeneous Kelly detector and the inhomogeneous Adaptive Matched Filter (AMF) are also considered. Additionally, the Viterbi- Like (VL) algorithm is employed as the non-coherent integration strategy. Finally, the numerical simulations with Monte Carlo method analyze the performance of the nonhomogeneous multiple-scan detectors under amplitude and distribution clutter heterogeneity.

Adaptive Detection and Interference Rejection of Multiple Point-Like Radar Targets

We present an adaptive algorithm aimed at detecting multiple point-like radar targets embedded in correlated Gaussian noise. The proposed detector modifies and improves the adaptive beamformer orthogonal rejection test (ABORT) idea to address detection of multiple targets. More precisely, it relies on the so-called two-step generalized likelihood ratio test (GLRT) design procedure implemented without assignment of a distinct set of secondary data. The newly proposed detector can guarantee the constant false alarm rate (CFAR) property and the performance assessment, conducted resorting to simulated data, has shown that it exhibits better rejection capabilities of mismatched signals than previously proposed detectors, at the price of an acceptable performance loss for matched signals

A computationally efficient two-step implementation of the GLRT

In this paper, the performance of a new two-step adaptive detection algorithm is analyzed. The two-step GLRT consists of an initial adaptive matched filter (AMF) test followed by a generalized likelihood ratio test (GLRT). Analytical expressions are provided for the probability of false alarm (P/sub FA/) and the probability of detection (P/sub D/) in unknown complex Gaussian interference. The analysis shows that the two-step GLRT significantly reduces the computational load over the GLRT while maintaining detection and sidelobe rejection performance commensurate with the GLRT. The two-step GLRT detection algorithm is also compared with another two-step detection algorithm: the adaptive sidelobe blanker (ASB). Both the two-step GLRT and the ASB are characterized in terms of the mainbeam detection performance and the rejection of sidelobe targets. We demonstrate that for a given P/sub FA/, the two-step GLRT has a broad range of threshold pairs (one threshold for the AMF test and one for the GLRT) that provide performance identical to the GLRT. This is in contrast with the ASB, where the threshold pairs that maximize the P/sub D/ are a function of the target's signal-to-interference-plus-noise ratio (SINR). Hence, for a fixed pair of thresholds, the two-step GLRT can provide slightly better mainbeam detection performance than the ASB in the transition region from low to high detection probabilities.