Performance of the GLRT for adaptive vector subspace detection

Abstract-In this paper, we consider the problem of detecting a random spatially distributed signal source by an array of sensors. We start with an approximate likelihood ratio (LR) detector and analyze its performance. Using the generalized likelihood ratio (GLR) approach, we then derive detectors under several assumptions on the available statistics. The performance of these detectors is evaluated, and the effect of the angular spread of the source is investigated. The detection performance behaves differently under different scenarios. We notice that the degrees of freedom (DOF) of the distributions of the detection statistics depend on both the signal angular spread and the number of data snapshots. Specifically, at a high SNR level and with small degrees of freedom, an increase of angular spread improves the detection performance. However, with large degrees of freedom, the increase of angular spread reduces detection performance. We provide a detailed discussion of the behavior of detection performance under various conditions. A comparison between the GLR detectors and conventional beamformer detectors is made by computer simulations. The results indicate that the GLR detectors perform better as the angular spread becomes large than that of the conventional beamformer detectors.Index Terms-Detection, distributed source, generalized likelihood ratio (GLR), sensor array.

Section: Introductionmentioning

confidence: 99%

Detection of Distributed Sources Using Sensor Arrays

Jin

Friedlander

2004

“…At low SNR one tends to gain slightly in while at high SNR one looses slightly. This trend can actually be deduced from (17). Note that it is quite possible to outperform locally the optimal detector, the one one would have designed if the true/simulated model had been known.…”

Section: ) Behavior With Respect To False Values Of the Drmentioning

confidence: 99%

“…This is a scenario that is of interest in a radar context, for instance, where one will at best implement the test aiming to detect a target for directions belonging to a grid [16], [17]. It is well suited for the MSD since there is no privileged direction and the RMD should be able to handle it for small cells.…”

Section: ) a Ricean Channelmentioning

confidence: 99%

“…A subspace model is a useful way to model uncertainty in numerous situations as, for instance, in radar or sonar signal processing. When the signature is a steering vector and one wants to test for targets on a fixed regular grid [11], [15]- [17], a low dimensional subspace is used to model the steering vector within each cell in the grid. Similarly when the direction of look is not perfectly known, a subspace can be used to model the first few terms in the Taylor series expansion around the expected direction.…”

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confidence: 99%

See 1 more Smart Citation

A Robust Matched Detector

Fuchs

2007

Abstract-We address the matched detector problem in the case the signal to be detected is imperfectly known. While in the standard detector the signal is known to lie along a particular direction, we consider the case where this direction is known up to additive white Gaussian noise. This somehow amounts to assuming that the signal lies in a cone the aperture of which depends upon the level of uncertainty. We build the associated generalized likelihood ratio (GLR), analyze its statistical properties, indicate how to set the threshold to achieve a given false alarm rate, and how to predict the associated probability of detection. The so-obtained detector reduces to the conventional one when the uncertainty vanishes and we analyze its behavior when the level of uncertainty, which has to be known a priori, is mis-evaluated. It appears that the sensitivity of the detector is quite low with respect to this kind of errors. More importantly several realistic examples are presented that indicate that the proposed detector remains quite efficient when the true signals are far from being of the assumed model and whatever the model of the uncertainty actually is. It is this robustness that makes the detector valuable.Index Terms-Detection, generalized likelihood ratio test (GLRT), hypothesis testing, matched filter, robustness, total least squares. I. PROBLEM STATEMENT IN MANY applications it is desired to detect the presence of a signal whose observation is perturbed by interferences and noiseThe signal is the product of the magnitude and a signature . The interferences lie in a known -dimensional subspace of that is spanned by the column vectors of the matrix and represents the additive broadband noise. Observing , the problem is to decide if is equal to zero or different from zero. This is one of the problems considered in [1] that is known as the matched detector or matched filter detector. If is perfectly known, the difficulties induced by the presence of the interferences are marginal [2] and we will ignore them in the sequel to simplify the exposition.We extend this model to the case where is not exactly known. Indeed exact knowledge of the signature may seem unrealistic since many factors such as bad calibration, distorted antenna shape, jitter, local scattering, source spreading, or errors in the localization to cite a few, give rise to uncertainties about . A difference between the assumed and the actual signatures leads to performance loss unless this possibility has been taken into account in the design of the test. According to the scenario one considers, there are different solutions. One can, for instance, model the uncertainty to circumvent its effect, identify the signature prior to the detection, somehow combine estimation and detection in a unique scheme, or develop robust approaches, i.e., tests that are somehow immune to uncertainties without requiring to model them precisely.Robust adaptive beamforming somehow belongs to this last set of solutions. It has attracted a lot of attention recently [3]- [5]...

“…The detection problem of this type of model has a wide application in active radar and sonar, space-time adaptive processing (STAP), mobile communication systems, and many other multi-sensor or time series applications (see e.g. [6], [7], [12], [26], [31]). …”

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confidence: 99%

A CFAR adaptive subspace detector for second-order Gaussian signals

Jin

Friedlander²

2005

In this paper we study the problem of detecting subspace signals described by the Second Order Gaussian (SOG) model in the presence of noise whose covariance structure and level are both unknown. Such a detection problem is often called Gauss-Gauss problem in that both the signal and the noise are assumed to have Gaussian distributions. We propose adaptive detectors for the SOG model signals based on a single observation and multiple observations. With a single observation, the detector can be derived in a manner similar to that of the generalized likelihood ratio test (GLRT), but the unknown covariance structure is replaced by sample covariance matrix based on training data. The proposed detectors are constant false alarm rate (CFAR) detectors. As a comparison, we also derive adaptive detectors for the First Order Gaussian (FOG) model based on multiple observations under the same noise condition as for the SOG model.With a single observation, the seemingly ad hoc CFAR detector for the SOG model is a true GLRT in that it has the same form as the GLRT CFAR detector for the FOG model. We give an approximate closed form of the probability of detection and false alarm in this case. Furthermore, we study the proposed CFAR detectors and compute the performance curves.