Gaussian Clutter Research Articles

Statistical analysis of the covariance matrix MLE in K-distributed clutter

In the context of radar detection, the clutter covariance matrix estimation is an important point to design optimal detectors. While the Gaussian clutter case has been extensively studied, the new advances in radar technology show that non-Gaussian clutter models have to be considered. Among these models, the spherically invariant random vector modelling is particularly interesting since it includes the K-distributed clutter model, known to fit very well with experimental data. This is why recent results in the literature focus on this distribution. More precisely, the maximum likelihood estimator of a K-distributed clutter covariance matrix has already been derived. This paper proposes a complete statistical performance analysis of this estimator through its consistency and its unbiasedness at finite number of samples. Moreover, the closed-form expression of the true Cramér–Rao bound is derived for the K-distribution covariance matrix and the efficiency of the maximum likelihood estimator is emphasized by simulations.

Non-Gaussian clutter characterization applied to OTHR using a mixture of two Rayleigh probability density functions

A practical technique for characterizing non-Gaussian radar clutter is specified and demonstrated using Over The Horizon Radar (OTHR) data, as an example. The technique employs maximum likelihood to fit the probability density of the clutter amplitude returns to a mixture of two Rayleigh probability densities instead of the single Rayleigh density typically used for Gaussian clutter. This model for non-Gaussian clutter is fully specified for any set of clutter amplitudes by a log likelihood, two Rayleigh parameters, and a mixing coefficient. A 3D plot of these values yields an easily-visualized clutter characterization, as is illustrated using OTHR data. This technique is a demonstration of clutter characterization using OTHR data, but the method can be applied to characterize other types of clutter data.

Radar detection based on Bayesian estimation of target amplitude

A new approach to detect a target with an unknown amplitude in clutter is proposed. The received signal models under two hypotheses, H 0 and H 1 , are assumed to be the same, except that the target amplitude is zero under H 0 . Using the Bayesian approach, it is shown that the likelihood ratio can be calculated as the ratio of the prior to posterior probabilities of the target amplitude. Based on this relation, a new method for target detection in Gaussian clutter is presented. This method is applied to cases with both known and unknown clutter statistics and in each case, white and coloured clutters are considered. Simulation results show that the proposed detector has a much better performance compared with conventional generalised likelihood ratio test detectors.

Subspace Selection for Quadratic Detector of Random Signals in Unknown Correlated Clutter

The Letter deals with constant false alarm rate (CFAR) detection of random Gaussian target signals embedded in Gaussian clutter with unknown covariance. The proposed detector is analyzed on the assumption that clutter covariance is not known and a random target signal has low-rank property. The low-dimensional subspace-based approach leads to a robust false alarm rate (RFAR) detector. The detection performance loss and the false alarm stability loss to unknown clutter covariance have been evaluated for example scenario.

Energy Efficient Distributed Filtering With Wireless Sensor Networks

We consider a wireless sensor network (WSN) that monitors a physical field and communicates pertinent data to a distant fusion center (FC). We study the case of a binary valued hidden natural field observed in a significant amount of Gaussian clutter, which is relevant to applications like detection of plumes or oil slicks. The considerable spatio-temporal dependencies found in natural fields can be exploited to improve the reliability of the detection/estimation of hidden phenomena. While this problem has been previously treated using kernel-regression techniques, we formulate it as a task of delay-free filtering on a process observed by the sensors. We propose a distributed scalable implementation of the filter within the network. This is achieved by i) exploiting the localized spatio-temporal dependencies to define a hidden Markov model (HMM) in terms of an exponential family with O(N) parameters, where N is the size of the WSN, ii) using a reduced- state approximation of the propagated probability mass function, and iii) making a tractable approximation of model marginals by using iterated decoding algorithms like the Gibbs sampler (GS), mean field decoding (MFD), iterated conditional modes (ICM), and broadcast belief propagation (BBP). We compare the marginalization algorithms in terms of their information geometry, performance, complexity and communication load. Finally, we analyze the energy efficiency of the proposed distributed filter relative to brute force data fusion. It is demonstrated that when the FC is sufficiently far away from the sensor array, distributed filtering is significantly more energy efficient and can increase the lifetime of the WSN by one to two orders of magnitude.

Probabilities of False Alarm and Detection for the NAMF Operating in Gaussian Clutter

Performance analysis of the normalized adaptive matched filter (NAMF) operating in homogeneous Gaussian clutter has received considerable attention in the recent years (see ). In this letter, for the first time, exact and explicit expressions are derived for the associated probability of false alarm and the probability of detection. The practical advantages of using the derived expressions are established.

Non-coherent radar CFAR detection based on goodness-of-fit tests

This paper considers the problem of constant false alarm rate (CFAR) detection of radar targets using multiple observations. In the Gaussian clutter scenario, the structure of the optimum (uniformly most powerful) CFAR detector is rather simple, but when the clutter is heavy-tailed, that is non-Gaussian distributed, the derivation of the optimal detector becomes infeasible. For this latter relevant case, a new CFAR algorithm is porposed based on goodness-of-fit (GoF) tests. The performance of the proposed detector is numerically investigated through Monte Carlo simulations assuming heavy-tailed Weibull and Lognormal distributed clutter. Numerical results shown that, in heavy-tailed clutter and also when several interfering targets exist, the proposed detector outperforms the conventional CFAR detector based on binary integration. Performance is also tested processing real sea clutter data collected by a non-coherent navigation radar.

A GLRT for multichannel radar detection in the presence of both compound Gaussian clutter and additive white Gaussian noise

Motivated by multichannel radar detection applications in the presence of both white Gaussian noise and Gaussian clutter with unknown power, we develop maximum likelihood parameter estimates for the disturbance process. Both cases with known and unknown white noise variance are treated. As the estimators do not admit closed-form solutions, numerical iterative procedures are developed that are guaranteed to at least converge to the local maximum. The developed estimates allow us to construct a generalized likelihood ratio test (GLRT) for the detection of a signal with constant but unknown amplitude. This GLRT has important applications in multichannel radar detection involving both white Gaussian noise and spherically invariant random process clutter and is shown to have better detection performance and CFAR property compared with existing statistics.

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.

Information-theoretic bounds on target recognition performance based on degraded image data

This paper derives bounds on the performance of statistical object recognition systems, wherein an image of a target is observed by a remote sensor. Detection and recognition problems are modeled as composite hypothesis testing problems involving nuisance parameters. We develop information-theoretic performance bounds on target recognition based on statistical models for sensors and data, and examine conditions under which these bounds are tight. In particular, we examine the validity of asymptotic approximations to probability of error in such imaging problems. Problems involving Gaussian, Poisson, and multiplicative noise, and random pixel deletions are considered, as well as least-favorable Gaussian clutter. A sixth application involving compressed sensor image data is considered in some detail. This study provides a systematic and computationally attractive framework for analytically characterizing target recognition performance under complicated, non-Gaussian models and optimizing system parameters.

Multiframe detector/tracker: optimal performance

We develop the optimal Bayes multiframe detector/tracker for rigid extended targets that move randomly in clutter. The performance of this optimal algorithm provides a bound on the performance of any other suboptimal detector/tracker. We determine by Monte Carlo simulations the optimal performance under a variety of scenarios including spatially correlated Gaussian clutter and non-Gaussian (K and Weibull) clutter. We show that, for similar tracking performance, the optimal Bayes tracker can achieve peak signal-to-noise ratio gains possibly larger than 10 dB over the commonly used combination of a spatial matched filter (spatial correlator) and a linearized Kalman-Bucy tracker. Simulations using real clutter data with a simulated target suggest similar performance gains when the clutter model parameters are unknown and estimated from the measurements.

Detection performance of an adaptive MTD with WVD as a Doppler filter bank

The Wigner–Ville Distribution (WVD) has been gaining importance in the recent years for the analysis of time varying signals (B. Boashash, in: Simon Haykin (Ed.), Advances in Spectrum Analysis and Array Processing, Prentice-Hall, Englewood Cliffs, NJ, 1991). In this paper, an adaptive moving target detector (AMTD) based on WVD as a Doppler filter bank has been introduced. The proposed AMTD processor has been simulated in the presence of Gaussian and non-Gaussian clutter environments. The preliminary investigations reveal that the proposed processor performs better in terms of probability of detection than the existing moving target detector (MTD) processors.

Note on "Optimum and mismatched detection against K-distributed plus Gaussian clutter"

We derive the optimum radar receiver to detect fluctuating and non-fluctuating targets against a disturbance which is modeled as a mixture of coherent K-distributed and Gaussian-distributed clutter. In addition, thermal noise, which is always present in the radar receiver, is considered. We discuss the implementation of the optimum coherent detector, which derives from the likelihood ratio test under the assumption of perfectly known disturbance statistics, and evaluate its performance via a numerical procedure, when possible, and via Monte Carlo simulation otherwise. Moreover, we compare the performance of the optimum detector with those of two detectors which are optimum for totally Gaussian and totally K-distributed clutter respectively, when they are fed with such a mixed disturbance. We conclude that, though the optimum detector has a larger computational cost, it provides sensibly better detection performance than the mismatched detectors in a number of operational situations. Thus, there is a need to derive suboptimum target detectors against the mixture of disturbances which trade-off the detection performance and the implementation complexity.

Adaptive polarimetric target detection with coherent radar. II. Detection against non-Gaussian background

The derivation of a completely adaptive polarimetric coherent scheme to detect a radar target against a Gaussian background is presented. A previously proposed Generalized Likelihood Ratio Test (GLRT) polarimetric detector is extended to the case of a general number of channels; this exploits the polarimetric characteristics of the received radar echoes to improve the detection performance. Together with the fully adaptive scheme, a model-based detector is derived that has a lower estimation loss. A complete theoretical expression is derived for the detection performance of both proposed polarimetric detectors. They are shown to have Constant False Alarm Rate (CFAR) when operating against Gaussian clutter, but to be sensitive to deviations from the Gaussian statistic. The application to recorded radar data demonstrates the performance improvement achievable in practice.

Comparison of GLR and invariant detectors under structured clutter covariance

This paper addresses a target detection problem in radar imaging for which the covariance matrix of unknown Gaussian clutter has block diagonal structure. This block diagonal structure is the consequence of a target lying along a boundary between two statistically independent clutter regions. Here, we design adaptive detection algorithms using both the generalized likelihood ratio (GLR) and the invariance principles. There has been considerable interest in applying invariant hypothesis testing as an alternative to the GLR test. This interest has been motivated by several attractive properties of invariant tests including: exact robustness to variation of nuisance parameters and possible finite-sample min-max optimality. However, in our deep-hide target detection problem, there are regimes for which neither the GLR nor the invariant tests uniformly outperforms the other. We discuss the relative advantages of GLR and invariance procedures in the context of this radar imaging and target detection application.

Interference blanking probabilities for SLB in correlated Gaussian clutter plus noise

This work presents closed-form expressions of the probability P/sub FA/ of false alarm, the probability P/sub TB/ of blanking a target received in the main lobe, and the probability P/sub B/ of blanking a coherent repeater interference (CRI) via an SLB (sidelobe blanking) device operating in correlated Gaussian clutter with known Doppler spectrum plus white Gaussian thermal noise.

Design of SLB systems in the presence of correlated ground clutter

Impulsive interference might increase the number of false alarms in a surveillance radar. The sidelobe-blanking (SLB) device, used in connection with the radar system, reduces the number of false alarms when the interference impinges on the antenna sidelobes. The paper describes how to design an SLB system operating in correlated Gaussian clutter with known Doppler spectrum plus white Gaussian thermal noise and impulsive interference. Closed-form expressions of the probability of false alarm, the probability of blanking a target received in the main lobe, and the probability of blanking a coherent repeater interference (CRI) are also derived for two statistical models of target/CRI, namely: Swerling-0 (known amplitude and random phase), and Swerling-I (random amplitude and random phase).

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.

Clairvoyant and adaptive signal detection in non-Gaussian clutter: a data-dependent threshold interpretation

This paper addresses the problem of signal detection in correlated non-Gaussian clutter modeled as a spherically invariant random process. The optimum strategy to detect a constant signal, with either known or unknown complex amplitude, embedded in correlated Gaussian clutter is given by comparing the whitening-matched filter output with a fixed threshold. When the clutter is non-Gaussian, the performance of the matched filter sensibly degrades. The optimum strategy is the classical whitening-matched filter output compared with a data-dependent threshold. This interpretation provides a deeper insight into the structure of the optimum detector and allows us to single out a family of suboptimum detectors based on a polynomial approximation of the data-dependent threshold. They are easy to implement and have performance that is really close to the optimal. The adaptive implementation of the polynomial detectors is also investigated, and their performance is analyzed by means of Monte Carlo simulation for various clutter scenarios.

Structures for radar detection in compound Gaussian clutter

The problem of coherent radar target detection in a background of non-Gaussian clutter modeled by a compound Gaussian distribution is studied here. We show how the likelihood ratio may be recast into an estimator-correlator form that shows that an essential feature of the optimal detector is to compute an optimum estimate of the reciprocal of the unknown random local power level. We then proceed to show that the optimal detector may be recast into yet another form, namely a matched filter compared with a data-dependent threshold. With these reformulations of the optimal detector, the problem of obtaining suboptimal detectors may be systematically studied by either approximating the likelihood ratio directly, utilizing a suboptimal estimate in the estimator-correlator structure or utilizing a suboptimal function to model the data-dependent threshold in the matched filter interpretation. Each of these approaches is studied to obtain suboptimal detectors. The results indicate that for processing small numbers of pulses, a suboptimal detector that utilizes information about the nature of the non-Gaussian clutter can be implemented to obtain quasi-optimal performance. As the number of pulses to be processed increases, a suboptimal detector that does not require information about the specific nature of the non-Gaussian clutter may be implemented to obtain quasi-optimal performance.