Adaptive Generalized Likelihood Ratio Research Articles

Long-time adaptive coherent detection of small targets in sea clutter by fast inversion algorithm of block tridiagonal speckle covariance matrices

Low-velocity small target detection in maritime surveillance radars is always a challenging task. Low signal-to-clutter ratio requires long-time coherent integration to obtain enough gain of target returns. However, long-time coherent integration encounters insufficient secondary data due to the spatial inhomogeneity of sea clutter. In this paper, considering the decorrelation time of speckle component of sea clutter short up to a dozen of milliseconds, the spherical invariant random vector (SIRV) model with block tridiagonal speckle covariance matrix and the inverse Gamma distributed texture is proposed to model sea clutter sequences in several tenths of a second. In this model, a long-time adaptive generalized likelihood ratio test with linear threshold detector (GLRT-LTD) is constructed. Owing to the block tridiagonal structure of speckle covariance matrices, the adaptive detection requires much less reference cells for speckle covariance matrix estimation and much lower computational cost for its inversion. The proposed detector is verified by an X-band high-resolution island-based radar data with an unmanned aerial vehicle (UAV) as test target. The experimental result shows that it obtains competitive detection performance in comparison with the state-of-the-art detectors.

Combination of Sequential Sampling Technique with GLR Control Charts for Monitoring Linear Profiles Based on the Random Explanatory Variables

Control charts play a beneficial role in the manufacturing process by reduction of non-compatible products and improving the final quality. In line with these aims, several adaptive methods in which samples can be taken with variable sampling rates and intervals have been proposed in the area of statistical process control (SPC). In some SPC applications, it is important to monitor a relationship between the response and independent variables—this is called profile monitoring. This article proposes adaptive generalized likelihood ratio (GLR) control charts based on variable sampling interval (VSI) and sequential sampling (SS) techniques for monitoring simple linear profiles. Because in some real-life problems, it may be possible that the user cannot control the values of explanatory variables; thus, in this paper, we focus on such a scenario. The performance of the proposed method is compared under three different situations, i.e., the fixed sampling rate (FSR), VSI, and SS, based on average time to signal (ATS) criteria for phase II analysis. Since the SS approach uses a novel sampling procedure based on the statistic magnitude, it has a superior performance over other competing charts. Several simulation studies indicate the superiority as the SS approach yields lower ATS values when there are single-step changes in the intercept, slope, standard deviation of the error term, and explanatory variables. In addition, some other related sensitivity analysis indicates that other aspects of the proposed methods, such as computational time, comparison with other control charts, and consideration of fixed explanatory variables. Furthermore, the results are supported by a real-life illustrative example from the adhesive manufacturing industry.

SAR Image Segmentation by Efficient Fuzzy C-Means Framework with Adaptive Generalized Likelihood Ratio Nonlocal Spatial Information Embedded

The existence of multiplicative noise in synthetic aperture radar (SAR) images makes SAR segmentation by fuzzy c-means (FCM) a challenging task. To cope with speckle noise, we first propose an unsupervised FCM with embedding log-transformed Bayesian non-local spatial information (LBNL_FCM). This non-local information is measured by a modified Bayesian similarity metric which is derived by applying the log-transformed SAR distribution to Bayesian theory. After, we construct the similarity metric of patches as the continued product of corresponding pixel similarity measured by generalized likelihood ratio (GLR) to avoid the undesirable characteristics of log-transformed Bayesian similarity metric. An alternative unsupervised FCM framework named GLR_FCM is then proposed. In both frameworks, an adaptive factor based on the local intensity entropy is employed to balance the original and non-local spatial information. Additionally, the membership degree smoothing and the majority voting idea are integrated as supplementary local information to optimize segmentation. Concerning experiments on simulated SAR images, both frameworks can achieve segmentation accuracy of over 97%. On real SAR images, both unsupervised FCM segmentation frameworks work well on SAR homogeneous segmentation in terms of region consistency and edge preservation.

Bi-Phase Compound-Gaussian Mixture Model of Sea Clutter and Scene-Segmentation-Based Target Detection

In high-resolution maritime surveillance radars, sea clutter exhibits highly spatial heterogeneity due to modulation of long waves with wavelengths longer than the width of one range cell. Compound-Gaussian model (CGM) fails to characterize the heterogeneous high-resolution sea clutter in both amplitude distribution and Doppler spectrum. In this article, a bi-phase compound-Gaussian mixture model (BP-CGMM) is proposed to characterize the heterogeneous sea clutter. In the BP-CGMM, spatial resolution cells are grouped into two disjoint sets, and the sea clutter in each set is represented by one CGM with inverse Gamma-distributed texture. The spectral heterogeneity indicates that sea clutter vectors at spatially adjacent resolution cells in one set share the same speckle covariance matrix, while that at two adjacent spatial cells separated in the two sets often have different speckle covariance matrices. The BP-CGMM is validated by a mass of measured high-resolution sea clutter data. Moreover, under the BP-CGMM, a detection method based on batch test is given to detect sea-surface small targets, which is composed of scene segmentation, by the aid of Bayesian threshold and morphological filtering, and adaptive generalized likelihood ratio test linear-threshold detector (GLRT-LTD) separately in each set. The detection method is verified by measured data with small targets under test. The experimental results show that it attains better detection performance than the adaptive GLRT-LTD under the CGM of sea clutter.

Adaptive Generalized Likelihood Ratio Test for Change Detection in SAR Images

Generalized likelihood ratio test (GLRT) was widely used in the change detection of synthetic aperture radar (SAR) images and employed as a competitive method in many studies. GLRT is applied to the neighborhood areas corresponding to the same geographical area in multitemporal SAR images. Generally, the difference image is acquired by applying the GLRT on a moving window empirically determined by the user, which is clearly unreasonable because the different pixels in an image may have different optimal windows. To overcome this drawback, we propose an adaptive GLRT (AGLRT) method for change detection in SAR images. AGLRT adaptively selects the homogeneity window for each pixel and can decrease the uncertainty of change detection due to manual selection of the moving window. Experiments are conducted on two data sets to confirm the performance of the proposed method. Experimental results show that AGLRT can both suppress the influence of noise and preserve edge details and improve the accuracy of change detection.

Adaptive GLR-, Rao- and Wald-based CFAR detectors for a subspace signal embedded in structured Gaussian interference

The problem of detecting a subspace signal embedded in subspace Gaussian interference and thermal noise is studied in this paper. In this problem, both the signal-independent and signal-dependent interferences are assumed to be present, therefore the overall interference subspace covers the signal subspace. The approach of this paper extends previous works involving either of those two kinds of interferences. A set of secondary data containing only interference plus noise is employed to estimate the interference covariance matrix and the noise power. Three new detectors are designed via the generalized likelihood ratio (GLR), Rao and Wald tests, respectively. Their probabilities of false alarms (PFAs) and detections are analytically derived. The PFAs show that the new detectors have the constant false alarm rate (CFAR) property against the interference and noise. Numerical results show that the new detectors outperform their counterparts for the studied problem. Furthermore, the new detectors are less sensitive to the secondary data size and to the mismatched subspace signal than some other detectors, such as the GLR detector (GLRD), the adaptive matched filter (AMF), the adaptive subspace detector (ASD), etc.

Adaptive two-step Bayesian MIMO detectors in compound-Gaussian clutter

The problem of adaptive target detection in compound-Gaussian clutter with unknown covariance matrix for multiple-input multiple-output (MIMO) radar is addressed in this paper. A set of secondary data for each receiver is assumed to be available, and the primary data and the secondary data own the same covariance matrix structure but different power levels (textures). Firstly, a Bayesian approach is proposed, where the structure is modeled as a random matrix with an appropriate distribution. Then, two ways are adopted to model the texture: an unknown deterministic quantity or a random variable ruled by certain distribution. In this framework, three adaptive generalized likelihood ratio tests (GLRTs) are developed using the two-step design procedure. Finally, the capabilities of the proposed detectors and their superiority with respect to some existing techniques are evaluated via numerical simulations.

Automated Surface Defect Detection Using High-Density Data

State-of-the-art measurement technologies, such as 3D laser scanners, provide new opportunities for knowledge discovery and development of quality control (QC) strategies for complex manufacturing systems. These technologies can rapidly provide millions of data points to represent a manufactured part's surface. The resulting high-density (HD) datasets have a great potential to be used for inspecting parts for surface and feature abnormalities. The current use of these datasets for part inspection can be divided into two main categories: (1) extracting feature parameters, which does not complement the nature of these datasets as it wastes valuable data and (2) an ad hoc inspection process, where a visual representation of the data is manually analyzed, which tends to suffer from slow, inefficient, and inconsistent inspection results. To overcome these deficiencies, this paper proposes an adaptive generalized likelihood ratio (AGLR) technique to automate the surface defect inspection process using HD data. This paper presents the performance results of the proposed AGLR approach with respect to the probability of detecting varying size and magnitude defects in addition to the probability of false alarms. In addition, a formal approach for designing an optimal AGLR inspection system is proposed. Finally, simulation results are presented and analyzed to showcase the performance gains of the AGLR approach versus a more traditional generalized likelihood ratio (GLR) approach.

Shape-parameter-dependent coherent radar target detection in K-distributed clutter

In this paper, shape-parameter-dependent matched filter (MF) detectors are proposed for moving target detection in K-distributed clutter, which are specified by a single parameter α [0, 1], the α-MF detectors for short. The α-MF detectors include the MF and normalized matched filter (NMF) detectors as special examples with α = 0 and 1. The parameter α can be chosen to match clutter characteristics. An empirical formula is given that the optimal parameter α equals the number of integrated pulses divided by it plus the shape parameter of K-distributed clutter. It is proved that the α-MF detectors are constant false alarm rate (CFAR) with respect to the scale parameter, clutter covariance matrix, and Doppler steering vector. The properties of adaptive α-MF (α-AMF) detectors are discussed. For K-distributed clutter, the optimal α-MF detectors are superior to the MF and NMF detectors and are comparable with the optimal K-distributed detectors (OKDs) of high computational cost. Finally, real high-resolution sea clutter data are available to verify the proposed detectors. The optimal α-AMF detectors under K-distributed clutter model are competitive in performance with the adaptive generalized likelihood ratio test linear threshold detectors (GLRT-LTDs) that are optimal for the compound-Gaussian clutter with the inverse Gamma texture.

Adaptive Generalized Likelihood Ratio Control Charts for Detecting Unknown Patterned Mean Shifts

Traditional statistical control schemes have been mainly focused on detecting constant mean shifts. In many practical applications, however, the mean of the observed sequence can exhibit a time-varying behavior after the fault occurrence. Shewhart control charts supplemented with sensitizing run rules have been suggested for detecting nonrandom dynamic mean patterns. However, the choice of a particular set of run rules requires some prior knowledge of the possible expected patterns. In addition, the resulting schemes can have poor performance against small shifts. When the mean shift pattern is known in advance, generalized likelihood ratio (GLR), cumulative score (CUSCORE), and optimal general linear filter (OGLF) control charts have also been proposed for change-point detection. Further, some adaptive CUSCORE schemes have been recently developed for detecting an unknown patterned mean shift. However, these adaptive CUSCOREs assume the occurrence of one-sided mean shifts. Hence, their performance may be poor in the case of an oscillatory behavior of the process mean. To overcome these limitations, we propose estimating a possible pattern in the mean using an exponentially weighted moving average (EWMA), which is especially effective with one-sided shifts in the mean, combined with a wavelet smoother, which is effective in estimating oscillatory mean patterns. The two estimates then drive two separate conventional GLR tests for significance. A control chart is proposed for observations from normal distributions and then extended to a completely distribution-free setting. Extensive simulation results demonstrate the efficiency of the proposed charts with a wide variety of patterned mean shifts in both the independent and autocorrelated scenarios and with a wide variety of distributions. In addition, the proposed scheme provides post-signal diagnostic information that estimates the change-point location and the shift pattern of the mean. An R package is available online as supplementary material.

A mixed active and passive GLR test for a fault tolerant control system

A mixed active and passive GLR test for a fault tolerant control system This paper presents an adaptive Generalized Likelihood Ratio (GLR) test for multiple Faults Detection and Isolation (FDI) in stochastic linear dynamic systems. Based on the work of Willsky and Jones (1976), we propose a modified generalized likelihood ratio test, allowing detection, isolation and estimation of multiple sequential faults. Our contribution aims to maximise the good decision rate of fault detection using another updating strategy. This is based on a reference model updated on-line after each detection and isolation of one fault. To reduce the computational requirement, the passive GLR test will be derived from a state estimator designed on a fixed reference model directly sensitive to system changes. We will show that active and passive GLR tests will be mixed and give interesting results compared with the GLR of Willsky and Jones (1976), and that they can be easily integrated in a reconfigurable Fault-Tolerant Control System (FTCS) to asymptotically recover the nominal system performances of the jump-free system.

Distributed target detection with polarimetric MIMO radar in compound-Gaussian clutter

This paper mainly deals with distributed targets detection with a polarimetric MIMO radar against compound-Gaussian clutter dominated scenario with unknown covariance matrix. First, the general polarimetric detecting problem of the distributed targets is developed to the MIMO radar, and then, the fully adaptive Generalized Likelihood Ratio Test (GLRT) is devised according to the well known two-step design procedure. Three covariance matrix estimation strategies using the secondary data are introduced to make derived receiver fully adaptive. A thorough performance assessment is given, and via several numerical examples, the results highlight that the spatial and polarization diversities can be exploited to improve the detection performance of the distributed targets in compound-Gaussian background, and it outperforms the phased-array counterpart, the adaptive loss is completely acceptable in practical applications. Meanwhile, the fixed-point estimation strategy is more suitable to implement the adaptive detection algorithm.

Novel Adaptive Generalized Likelihood Ratio Detector with Application to Maneuvering Target Tracking

A novel adaptive jump-detection algorithm is introduced for scenarios involving abrupt changes in the inputs to linear systems, such as those that might occur in tracking maneuvering targets. Improving upon the standard generalized likelihood ratio (GLR) detector, presented over two decades ago, the new algorithm is characterized by increased robustness with respect to uncertainties in the system input, which frequently arise in the context of target tracking applications. The performance of the new algorithm is demonstrated in an endgame scenario involving an interceptor missile and a maneuerable tactical ballistic missile. An extensive Monte Carlo simulation study is used to demonstrate the superiority of the method over the conventional GLR method in terms of its much smaller observed false alarm probability, which actually agrees with the theoretical value. The new algorithm also facilitates a correct isolation of the abrupt change, is consistent in the usual statistical sense, and generally proves more reliable.

Subspace-based adaptive generalized likelihood ratio detection

Subspace-based adaptive detection performance is examined for the generalized likelihood ratio detector based on Wilks' /spl Lambda/ statistic. The problem considered here is detecting the presence of one or more signals of known shape embedded in Gaussian distributed noise with unknown covariance structure. The data is mapped into a subspace prior to detection. The probability of false alarm is independent of the subspace transformation and depends only on subspace dimension. The probability of detection depends on the subspace transformation through a nonadaptive signal-to-noise ratio (SNR) parameter. Subspace processing results in an SNR loss that tends to decrease performance and a gain in statistical stability that tends to increase performance. It is shown that the statistical stability effect dominates the SNR loss for short data records, and subspace detectors can require substantially less SNR than full space detectors for equivalent performance. A method for designing the subspace transformation to minimize the SNR loss is proposed and illustrated through simulations.