Kelly's Generalized Likelihood Ratio Research Articles

A two‐stage tunable detector with enhanced rejection capabilities

This paper focuses on the method of an adaptive detector which works against Gaussian background with unknown parameters, such as covariance matrix. The authors design a tunable detector for point-like targets by mixing the Kelly's generalized likelihood ratio test and the enhanced Rao test. The analytical expression of the false alarm probability and detection probability of the proposed detector are derived. The performances of the new scheme are assessed, and analysed in comparison with its natural counterparts. The results show that it can provide enhanced rejection capabilities of mismatched signals, at the price of a limited detection loss for matched signals.

A Tunable Detector for Distributed Target Detection in the Situation of Signal Mismatch

This letter investigates the problem of distributed target detection with signal mismatch in homogeneous environment. Precisely, the actual signal steering vector is not aligned with the nominal one which is assumed by radar system. Within this framework, we propose a tunable detector which can adjust its directivity (robustness or selectivity) flexibly and effectively by changing a tunable parameter. Moreover, this tunable detector encompasses the generalized Kelly's generalized likelihood ratio test (GKGLRT) and the generalized adaptive matched filter (GAMF) as its two special cases. Finally, to test the effectiveness of this detector, the real data received by the IPIX radar are used for experiments. The results illustrate the superiority of the proposed detector both in simulation environment and realistic environment.

The adaptive coherence estimator: a uniformly most-powerful-invariant adaptive detection statistic

We show that the Adaptive Coherence Estimator (ACE) is a uniformly most powerful (UMP) invariant detection statistic. This statistic is relevant to a scenario appearing in adaptive array processing, in which there are auxiliary, signal-free, training-data vectors that can be used to form a sample covariance estimate for clutter and interference suppression. The result is based on earlier work by Bose and Steinhardt, who found a two-dimensional (2-D) maximal invariant when test and training data share the same noise covariance. Their 2-D maximal invariant is given by Kelly's Generalized Likelihood Ratio Test (GLRT) statistic and the Adaptive Matched Filter (AMF). We extend the maximal-invariant framework to the problem for which the ACE is a GLRT: The test data shares the same covariance structure as the training data, but the relative power level is not constrained. In this case, the maximal invariant statistic collapses to a one-dimensional (1-D) scalar, which is also the ACE statistic. Furthermore, we show that the probability density function for the ACE possesses the property of total positivity, which establishes that it has monotone likelihood ratio. Thus, a threshold test on the ACE is UMP-invariant. This means that it has a claim to optimality, having the largest detection probability out of the class of detectors that are also invariant to affine transformations on the data matrix that leave the hypotheses unchanged. This requires an additional invariance not imposed by Bose and Steinhardt: invariance to relative scaling of test and training data. The ACE is invariant and has a Constant False Alarm Rate (CFAR) with respect to such scaling, whereas Kelly's GLRT and the AMF are invariant, and CFAR, only with respect to common scaling.

An Efficient Adaptive Polarimetric Processor with an Embedded CFAR

To improve the detection performance of surveillance radars with polarization diversity, we developed an adaptive polarimetric processor and compared it with other polarimetric processors. We derived our adaptive polarimetric processor, called the polarization discontinuity detector (PDD), from the generalized likelihood ratio (GLR) test principle for the unspecified target component. We derived closed-form expressions of its probabilities of detection and false alarm, and compared its performance to that of the adaptive polarization canceller (APC) and Kelly's GLR processor. The PDD had a performance similar to Kelly's GLR in Gaussian clutter, and both the PDD and Kelly's GLR, which have embedded constant false alarm rates (CFARs), outperformed the APC, especially when the target polarization state was close to the clutter's polarization state. The important difference is that the PDD is much simpler than Kelly's GLR for hardware/software implementation, because the PDD does not require a costly two-parameter filter bank to cover the unknown target polarization state as Kelly's GLR does.

Performance analysis of two adaptive radar detectors against non-Gaussian real sea clutter data

The performance of two adaptive detection schemes developed in the literature, Kelly's generalized likelihood ratio test (GLRT) and the adaptive linear-quadratic (ALQ) detector, are tested on real sea clutter data recorded by the IPIX experimental radar. The results of first- and second-order statistical analyses performed on two data sets are reported. Amplitude analysis has been carried out by checking the fitting to Weibull, log-normal, K, and generalized K models. The results show good agreement between performance prediction based on the generalized K model, with texture strongly correlated among primary and secondary data, and the performance obtained by processing the real sea clutter data.

Suboptimum approach to adaptive coherent radar detection in compound-Gaussian clutter

Adaptive detection of fluctuating radar targets in unknown correlated Gaussian clutter has received considerable attention in the past. On the other hand, the problem of adaptive detection in non-Gaussian environments is still under investigation. Adaptive coherent radar detection of Swerling I targets against compound-Gaussian clutter is addressed. Our contribution is (1) to present a detection algorithm, called the adaptive linear-quadratic (ALQ) detector, with constant false-alarm rate (CFAR) behavior with respect to the clutter amplitude probability density function (apdf) and that is quite insensitive to the clutter correlation structure, and (2) to investigate and compare the performance of the ALQ detector and Kelly's generalized likelihood ratio test (GLRT) against K-distributed clutter.

Optimum array detector for a weak signal in unknown noise

We study the design of constant false-alarm rate (CFAR) tests for detecting a rank-one signal in the presence of background Gaussian noise with unknown spatial covariance. We look at invariant tests, i.e., those tests whose performance is independent of the nuisance parameters, like the background noise covariance. Such tests are shown to have the desirable CFAR property. We characterize the class of all such tests by showing that any invariant decision statistic can be written as a function of two basic statistics which are in fact the adaptive matched filter (AMF) statistic and Kelly's generalized likelihood ratio statistic. Further, we establish an optimum test in the limit of low signal-to-noise ratio (SNR), the locally most powerful invariant (LMPI) test. We also derive the bound for the probability of detection of any invariant detector, at a fixed false-alarm rate, and compare the LMPI and the published detectors (Kelly and AMF) to it.

A maximal invariant framework for adaptive detection with structured and unstructured covariance matrices

We introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing. This involves calculating a low-dimensional basis set of functions called the maximal invariant, the statistics of which are often tractable to obtain, thereby making analysis feasible and facilitating the search for tests with some optimality property. Using this approach, we obtain a locally most powerful invariant test for the unstructured covariance case and show that all invariant tests can be expressed in terms of the previously published Kelly's generalized likelihood ratio (GLRT) and Robey's adaptive matched filter (AMF) test statistics. Applying this framework to structured covariance matrices, corresponding to stochastic interferers in a known subspace, for which the GLRT is unavailable, we obtain the maximal invariant and propose several new invariant detectors that are shown to perform as well or better than existing ad-hoc detectors. These invariant tests are unaffected by most nuisance parameters, hence the variation in the level of performance is sharply reduced. This framework facilitates the search for such tests even when the usual GLRT is unavailable. >

The effects of signal contamination on two adaptive detectors

Two schemes for adaptive detection Kelly's generalized likelihood ratio test (GLRT) and the mean level adaptive detector (MLAD), are analyzed with respect to the deleterious effect of desired-signal contamination of the data used to compute the sampled covariance matrix for the two detectors. The detection probability P/sub D/ and false alarm performance (ghosting probability P/sub G/) are predicted for the two schemes under the assumptions that the input noises are Gaussian random variables that are temporally independent but spatially correlated; and the amplitude of the desired signal is Rayleigh distributed. P/sub D/ and P/sub G/ are computed as a function of the false alarm probability P/sub F/ with no contamination, the number of input channels, the number of independent samples-per-channel, the matched filtered output signal-to-noise (S/N) power ratio, and the S/N power ratio of the contaminating desired signal. It is shown that both P/sub D/ and P/sub G/ decrease with increasing levels of contamination. The P/sub G/ performance is is almost identical for the GLRT and MLAD. The P/sub D/ performance shows similar relative performance trends. Significantly, it is shown that the ghosting probability does not exceed P/sub F/ in the presence of contamination. >

A comparison of two adaptive detection schemes

Two schemes for adaptive detection are compared: Kelly's generalized likelihood ratio test (GLRT) and the mean level adaptive detector (MLAD). Detection performance, P/sub D/, is predicted for the two schemes under the assumptions that the input noises are zero-mean complex Gaussian random variables that are temporally independent but spatially correlated; and the amplitude of the desired signal is Rayleigh distributed. P/sub D/ is computed as a function of the false alarm probability, the number of input channels, the number of independent samples per channel, and the matched filtered output signal-to-noise (S/N) power ratio. In this analysis the GLRT is shown to have better detection performance than the MLAD. The difference in detection performance increases as one uses fewer input samples. However, the required number of samples necessary to have only a 3 dB detection loss for both detection schemes is approximately the same. This is significant since for the present, the MLAD is considerably less complex to implement than the GLRT.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>