Adaptive Matched Filter Research Articles

Parametric Adaptive Radar Detector with Enhanced Mismatched Signals Rejection Capabilities

We consider the problem of adaptive signal detection in the presence of Gaussian noise with unknown covariance matrix. We propose a parametric radar detector by introducing a design parameter to trade off the target sensitivity with sidelobes energy rejection. The resulting detector merges the statistics of Kelly's GLRT and of the Rao test and so covers Kelly's GLRT and the Rao test as special cases. Both invariance properties and constant false alarm rate (CFAR) behavior for this detector are studied. At the analysis stage, the performance of the new receiver is assessed and compared with several traditional adaptive detectors. The results highlight better rejection capabilities of this proposed detector for mismatched signals. Further, we develop two two-stage detectors, one of which consists of an adaptive matched filter (AMF) followed by the aforementioned detector, and the other is obtained by cascading a GLRT-based Subspace Detector (SD) and the proposed adaptive detector. We show that the former two-stage detector outperforms traditional two-stage detectors in terms of selectivity, and the latter yields more robustness.

Identification of Gender‐Related Normality Regions for T‐Wave Alternans

T-wave alternans (TWA), a harbinger of sudden cardiac death, associates to a broad variety of pathologies. In a previous study, we observed the presence of unstable and low-amplitude TWA also in healthy subjects, and considered it as "physiological TWA." The possible existence of different TWA characteristics between males and female is investigated in the present work. Resting ECG recordings from 142 control healthy subjects, 77 males and 65 females, were submitted to our adaptive match filter (AMF) based method for TWA detection and characterization in terms of duration, amplitude, and their product. The 99.5th percentile of these parameters distributions over the entire control population and over the male and female subgroups, were used to define thresholds which delimit a gender-independent and male- and female-related TWA normality regions, respectively, out of which abnormal TWA cases (TWA+) are expected to fall. Clinical usefulness of these regions was tested using a population of 151 coronary artery disease (CAD) patients, divided into 128 males and 23 females. In our control-female population, TWA duration was significantly longer than in control-male population (65 ± 13 beat vs 52 ± 14 beat; P < 10(-6) ). Our gender-related normality regions allowed identification of 36 (23.8%) TWA+ cases among the CAD patients, 17 more than those obtained from a gender-independent region. All these 17 patients were CAD males with over-threshold TWA duration. TWA is a gender-related phenomenon. Definition of gender-related TWA normality regions improves identification of patients at increased TWA stability (i.e., prolonged TWA duration) and, thus, at increased risk of arrhythmic events.

Impact of Sea Clutter Nonstationarity on Disturbance Covariance Matrix Estimation and CFAR Detector Performance

Adaptive detection of signals embedded in non-Gaussian clutter is an important challenge for radar engineers. We present an analysis of sea clutter nonstationarity with respect to clutter covariance matrix estimation and its impact on the constant false alarm rate (CFAR) property of the normalized adaptive matched filter (NAMF). Three covariance matrix estimators, e.g., the sample covariance matrix (SCM), the normalized sample covariance matrix (NSCM), and the approximate maximum likelihood (AML) estimators, have been investigated. The impact of nonstationarity, which emerges in the statistical analysis of the clutter data, is measured in terms of probability of false alarm and probability of detection. Performance analysis is presented using both simulated data and measured sea clutter data recorded by two different X-band radars, namely, the Fynmeet radar and the IPIX radar.

Adaptive multidimensional Wiener filtering for target detector improvement

In this paper, we consider the problem of hyperspectral image denoising. Current denoising is based on multichannel restoration filters assuming the separability of the signal covariance, which describes the between-channel and within-channel relationships. We propose a new algorithm for a spectral band restoration scheme, the adaptive multidimensional Wiener filter, based on a local signal model, without assuming spectral and spatial separability. The proposed filter can be applied as a preprocessing step for detection in hyperspectral imagery. We highlight the target detection improvement when the developed method is used before existing methods the well-known hyperspectral imagery detectors as: AMF (Adaptive Matched Filter), ACE (Adaptive coherence/cosine Estimator) and RX (Reed and Xiaoli algotithm). We demonstrate that integrating a multidimensional restoration leads to significant improvement of the detection probability. The performance of our method is exemplified using real-world HYDICE images.

A Bayesian Parametric Test for Multichannel Adaptive Signal Detection in Nonhomogeneous Environments

This paper considers the problem of knowledge-aided space-time adaptive processing (STAP) in nonhomogeneous environments, where the covariance matrices of the training and test signals are assumed random and different from each other. A Bayesian detector is proposed by incorporating some a priori knowledge of the disturbance covariance matrices, and exploring their inherent block-Toeplitz structure. Specifically, the block-Toeplitz structure of the covariance matrix allows us to model the training signals as a multichannel auto-regressive (AR) process. The resulting detector is referred to as the Bayesian parametric adaptive matched filter (B-PAMF) which, compared with nonparametric Bayesian detectors, entails a lower training requirement and alleviates the computational complexity. Numerical results show that the proposed B-PAMF detector outperforms the standard PAMF test in nonhomogeneous environments.

Sample-Deficient Adaptive Detection: Adaptive Scalar Thresholding versus CFAR Detector Performance

The well-known problem of adaptive signal detection in background interference is addressed for situations where only a small number of training data samples are available. Since all known constant false-alarm rate (CFAR) adaptive detectors such as the traditional generalized likelihood-ratio test (GLRT), adaptive matched filter (AMF), and adaptive coherence estimator (ACE) detectors use the generic maximum-likelihood (ML) sample covariance matrix estimate (CME), the sample support necessary for accurate detection must significantly exceed the adaptive system (e.g., antenna array) dimension M, and so is often impractically large. For scenarios with a limited number m of dominant covariance matrix eigenvalues, more efficient diagonally loaded CMEs are available, whose required sample support is comparable to m (rather than M) for efficient interference mitigation. Since detectors that adopt these and other CMEs that use some a~priori information are not strictly CFAR, here we consider a two-stage adaptive detection scheme that optimally partitions the total sample support T into two sets: T_CME data samples are used to design the adaptive filter (beamformer), and the remaining T_CFAR samples are used to calculate the adaptive scalar false-alarm threshold. We present a comparative analysis of the detection performance of one-stage CFAR and two-stage adaptive detectors.

Envelope-Law and Geometric-Mean STAP Detection

Two detectors for space-time adaptive processing (STAP) are proposed here. These are variants that use envelope-law and geometric-mean (GM) (or logarithmic) processing, both being well-known concepts from conventional constant false alarm rate (CFAR) square-law radar detection. The variants are based on normalized adaptive matched filter (NAMF) STAP processing, and their CFAR property is established. Threshold setting for the detectors for specified false alarm probability (FAP) is accomplished using fast simulation based on importance sampling. Performance analyses of these detectors reveal almost indistinguishable loss in detection probability in homogeneous Gaussian interference compared with conventional square-law STAP detector versions. In addition, they exhibit robust detection performance in the presence of interfering targets in the training data for both nonfluctuating as well as fluctuating target models. Comparisons are made with the corresponding envelope-law and GM variants of the adaptive matched filter (AMF) detector previously proposed in a recent paper.

Band-Inverse TVAR Covariance Matrix Estimation for Adaptive Detection

We characterize a sequence of M interference observations by a time-varying autoregressive model of order m (TVAR(m)). We recently demonstrated that the maximum-likelihood (ML) TVAR(m) covariance matrix estimate (CME) of Gaussian data is the Dym-Gohberg transformation of the sample (direct data) covariance matrix averaged over the T independent training samples (snapshots), provided that T > m. Here we investigate the efficiency of adaptive filters and adaptive detectors based on this CME which (for m ? M) permits a significant reduction in training sample support compared with the traditional sample matrix inversion (SMI) method that requires T ? M samples. We analyze truly TVAR(m) or AR(m) (autoregressive) interferences, focusing on the signal-to-noise-ratio (SNR) loss factors in these adaptive filters and adaptive detectors that are due to the finite-sample support T, and the accuracy of false-alarm threshold calculation. We compare the performance of diagonally loaded adaptive matched filter (LAMF) and TVAR(m) adaptive detectors, and find that, even for TVAR(m) interferences, the question of which detector is better strongly depends on the eigenspectrum of the interference covariance matrix. When properly applied, both detectors are significantly better than the adaptive matched filter (AMF) detector (that uses the conventional sample CME with more than M training samples).

Assessment of Physiological Amplitude, Duration, and Magnitude of ECG T‐Wave Alternans

An association between T-wave alternans (TWA) and malignant ventricular arrhythmias is generally recognized. Because relatively low levels of TWA have also been observed in healthy (H) subjects, the question arises as to whether these are ascribable to noise and artifacts, or can be given the relevance of a physiological phenomenon characterizing a preclinical condition. To answer this question, in the present study 20-minute not noisy, sinus ECG recordings, from 138 H-subjects and 148 coronary artery diseased (CAD) patients, were submitted to our adaptive match filter (AMF) procedure to identify and parameterize TWA in terms of duration (TWAD), amplitude (TWAA), and magnitude (TWAM, defined as the product of TWAD times TWAA). The 99.5th percentiles of mean values of TWAA, TWAD, and TWAM over 20-minute ECGs were used to define three threshold levels (THRD, THRA, and THRM), which allow discrimination of abnormal TWA levels. Nonstationary TWA was found in all our H-subjects and CAD-patients. TWAD, TWAA, and TWAM levels were classified as being physiological in 99% of H-subjects and 87% of CAD-patients. A linear correlation (r =-0.52, P < 0.001) was found between TWAA and RR interval in the H-population. Our results support the hypothesis of the existence of physiological TWA levels, which are to be considered in the effort to improve reliability of nonphysiological TWA levels discrimination.

Integrating Heterogeneous Classifier Ensembles for EMG Signal Decomposition Based on Classifier Agreement

In this paper, we present a design methodology for integrating heterogeneous classifier ensembles by employing a diversity-based hybrid classifier fusion approach, whose aggregator module consists of two classifier combiners, to achieve an improved classification performance for motor unit potential classification during electromyographic (EMG) signal decomposition. Following the so-called overproduce and choose strategy to classifier ensemble combination, the developed system allows the construction of a large set of base classifiers, and then automatically chooses subsets of classifiers to form candidate classifier ensembles for each combiner. The system exploits kappa statistic diversity measure to design classifier teams through estimating the level of agreement between base classifier outputs. The pool of base classifiers consists of different kinds of classifiers: the adaptive certainty-based, the adaptive fuzzy k -NN, and the adaptive matched template filter classifiers; and utilizes different types of features. Performance of the developed system was evaluated using real and simulated EMG signals, and was compared with the performance of the constituent base classifiers. Across the EMG signal datasets used, the developed system had better average classification performance overall, especially in terms of reducing classification errors. For simulated signals of varying intensity, the developed system had an average correct classification rate CCr of 93.8% and an error rate Er of 2.2% compared to 93.6% and 3.2%, respectively, for the best base classifier in the ensemble. For simulated signals with varying amounts of shape and/or firing pattern variability, the developed system had a CCr of 89.1% with an Er of 4.7% compared to 86.3% and 5.6%, respectively, for the best classifier. For real signals, the developed system had a CCr of 89.4% with an Er of 3.9% compared to 84.6% and 7.1%, respectively, for the best classifier.

Adaptive detectors with diagonal loading for airborne multi-input multi-output radar

The problem of adaptive target detection for airborne multi-input multi-output (MIMO) radars with space–time receivers in the presence of Gaussian interference (including clutter and noise) is studied. Previous work has assumed the interference covariance matrix to be known. The case with unknown covariance matrix is investigated here. By exploiting the low rank property of clutter subspace, generalised likelihood ratio test detector and adaptive matched filter detector with diagonal loading are suggested to improve the detection performance of MIMO radars in limited secondary data case. The closed-form detection probabilities and false alarm probabilities of the two proposed detectors are derived and numerically evaluated. Theoretical analysis and numerical results show the advantages of the proposed detectors.

Adaptive detection and diversity order in multistatic radar

We derive the generalized likelihood ratio test (GLRT) for multistatic space-time radar where each sensor platform has a coherent multi-channel array. A multistatic version of the adaptive matched filter (AMF) detector is also developed and its performance results compared with that of the GLRT. Results show that the multistatic GLRT outperforms the multistatic AMF and that the performance advantage increases with the number of radars in the system. The concepts of geometry gain and diversity gain for multistatic STAP are defined in terms of asymptotic properties of the system's probability of miss.

SIGNAL PROCESSING ALGORITHMS FOR STARING SINGLE PIXEL HYPERSPECTRAL SENSORS

Remote sensing of chemical warfare agents (CWA) with stand-off hyperspectral sensors has a wide range of civilian and military applications. These sensors exploit the spectral changes in the ambient photon flux produced thermal emission or absorption after passage through a region containing the CWA cloud. In this work we focus on (a) staring single-pixel sensors that sample their field of view at regular intervals of time to produce a time series of spectra and (b) scanning single or multiple pixel sensors that sample their FOV as they scan. The main objective of signal processing algorithms is to determine if and when a CWA enters the FOV of the sensor. We shall first develop and evaluate algorithms for staring sensors following two different approaches. First, we will assume that no threat information is available and we design an adaptive anomaly detection algorithm to detect a statistically-significant change in the observed spectrum. The algorithm processes the observed spectra sequentially-in-time, estimates adaptively the background, and checks whether the next spectrum differs significantly from the background based on the Mahalanobis distance or the distance from the background subspace. In the second approach, we will assume that we know the spectral signature of the CWA and develop sequential-in-time adaptive matched filter detectors. In both cases, we assume that the sensor starts its operation before the release of the CWA; otherwise, staring at a nearby CWA-free area is required for background estimation. Experimental evaluation and comparison of the proposed algorithms is accomplished using data from a long-wave infrared (LWIR) Fourier transform spectrometer.

Adaptive Match Filter Based Method for Time vs. Amplitude Characterization of Microvolt ECG T-Wave Alternans

To develop a new method for non-invasive identification of patients prone to ventricular tachyarrhythmia and sudden cardiac death, an adaptive match-filter (AMF) was applied to detect and characterize T-wave alternans (TWA) in 200 coronary artery diseased (CAD) patients compared with 176 healthy (H) subjects. TWA was characterized in terms of duration (TWAD), amplitude (TWAA), and magnitude (TWAM, defined as the product of TWAD times TWAA). A criterion derived from these parameters, estimated over the H-population, allowed discrimination between a risk (TWA+) and a normality (NO TWA) zone in the TWAD-TWAA plane. To gain further ability to discriminate among different risk levels, the TWA+ zone was divided into four sub-zones respectively characterized by low duration and low amplitude (LDLA), low duration and high amplitude (LDHA), high duration and low amplitude (HDLA), and high duration and high amplitude (HDHA). With our methodology, 21 CAD-patients (10.5%) were identified as TWA+, 9 falling in the LDLA zone, 4 in the HDLA, 7 in the LDHA, and 1 in the HDHA. These results are in agreement with clinical expectations and pave the way to further clinical follow-up studies finalized to analyze pathophysiological implications and risk factors associated to each TWA+ zone.

A Bayesian Approach to Adaptive Detection in Nonhomogeneous Environments

We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter.

Regularized Spectral Matched Filter for Target Recognition in Hyperspectral Imagery

This letter extends the idea of regularization to spectral matched filters. It incorporates a quadratic penalization term in the design of spectral matched filters in order to restrict the possible matched filters (models) to a subset which are more stable and have better performance than the non-regularized adaptive spectral matched filters. The effect of regularization depends on the form of the regularization term and the amount of regularization which is controlled by a parameter so-called the regularization coefficient. In this letter, the sum-of-squares of the filter coefficients is used as the regularization term, and different values for the regularization coefficient are tested. A Bayesian-based derivation of the regularized matched filter is also described which provides a procedure for choosing the regularization coefficient. Experimental results for detecting targets in hyperspectral imagery are presented for regularized and non-regularized spectral matched filters.

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.

Parametric GLRT for Multichannel Adaptive Signal Detection

This paper considers the problem of detecting a multichannel signal in the presence of spatially and temporally colored disturbance. A parametric generalized likelihood ratio test (GLRT) is developed by modeling the disturbance as a multichannel autoregressive (AR) process. Maximum likelihood (ML) parameter estimation underlying the parametric GLRT is examined. It is shown that the ML estimator for the alternative hypothesis is nonlinear and there exists no closed-form expression. To address this issue, an asymptotic ML (AML) estimator is presented, which yields asymptotically optimum parameter estimates at reduced complexity. The performance of the parametric GLRT is studied by considering challenging cases with limited or no training signals for parameter estimation. Such cases (especially when training is unavailable) are of great interest in detecting signals in heterogeneous, fast changing, or dense-target environments, but generally cannot be handled by most existing multichannel detectors which rely more heavily on training at an adequate level. Compared with the recently introduced parametric adaptive matched filter (PAMF) and parametric Rao detectors, the parametric GLRT achieves higher data efficiency, offering improved detection performance in general.

Optical Cluster Finding with an Adaptive Matched‐Filter Technique: Algorithm and Comparison with Simulations

We present a modified adaptive matched filter algorithm designed to identify clusters of galaxies in wide-field imaging surveys such as the Sloan Digital Sky Survey. The cluster-finding technique is fully adaptive to imaging surveys with spectroscopic coverage, multicolor photometric redshifts, no redshift information at all, and any combination of these within one survey. It works with high efficiency in multi-band imaging surveys where photometric redshifts can be estimated with well-understood error distributions. Tests of the algorithm on realistic mock SDSS catalogs suggest that the detected sample is {approx} 85% complete and over 90% pure for clusters with masses above 1.0 x 10{sup 14}h{sup -1} M and redshifts up to z = 0.45. The errors of estimated cluster redshifts from maximum likelihood method are shown to be small (typically less that 0.01) over the whole redshift range with photometric redshift errors typical of those found in the Sloan survey. Inside the spherical radius corresponding to a galaxy overdensity of {Delta} = 200, we find the derived cluster richness {Lambda}{sub 200} a roughly linear indicator of its virial mass M{sub 200}, which well recovers the relation between total luminosity and cluster mass of the input simulation.

Comparative evaluation of background characterization techniques for hyperspectral unstructured matched filter target detection

Algorithms exploiting hyperspectral imagery for target detection have continually evolved to provide improved detection results. Adaptive matched filters, which may be derived in many different fields, can be used to locate spectral targets by modeling the scene background as either structured (i.e., geometric, with endmembers or basis vectors) or unstructured (i.e., stochastic, with a mean and covariance matrix). In unstructured techniques, various methods of calculating the background covariance matrix have been developed, each involving either the removal of target signatures from the background model or the appropriate choice of a subset of the image to be used as training data based on spatial or spectral characteristics. The objective of these methods is to derive a background which matches the source of mixture interference for the detection of sub-pixel targets, or matches the source of false alarms in the scene for the detection of fully resolved targets. In addition, these techniques may increase the multivariate normality of the data from which the background is characterized, thus increasing adherence to the normality assumption inherent in the matched filter and ultimately improving target detection results. Such techniques for improved background characterization are widely practiced but not well understood or documented. This work describes in detail several methods for unstructured background characterization, both new methods and those taken from the literature. A comparison of methods across a common set of targets is presented. Training data are chosen either spatially, spectrally, or both prior to estimation of the background statistics. Evaluation of the methods indicates that consistent improvements over scene-wide statistics can be achieved through such spatial or spectral subsetting of the image data. However, results are not conclusive as to the overall best method for all targets in the test set.