Generalized Likelihood Ratio Test Approach Research Articles

Generalized Likelihood Ratio Test for Adversarially Robust Hypothesis Testing

Machine learning models are known to be susceptible to adversarial attacks which can cause misclassification by introducing small but well designed perturbations. In this paper, we consider a classical hypothesis testing problem in order to develop fundamental insight into defending against such adversarial perturbations. We interpret an adversarial perturbation as a nuisance parameter, and propose a defense based on applying the generalized likelihood ratio test (GLRT) to the resulting composite hypothesis testing problem, jointly estimating the class of interest and the adversarial perturbation. While the GLRT approach is applicable to general multi-class hypothesis testing, we first evaluate it for binary hypothesis testing in white Gaussian noise under $\ell_{\infty}$ norm-bounded adversarial perturbations, for which a known minimax defense optimizing for the worst-case attack provides a benchmark. We derive the worst-case attack for the GLRT defense, and show that its asymptotic performance (as the dimension of the data increases) approaches that of the minimax defense. For non-asymptotic regimes, we show via simulations that the GLRT defense is competitive with the minimax approach under the worst-case attack, while yielding a better robustness-accuracy tradeoff under weaker attacks. We also illustrate the GLRT approach for a multi-class hypothesis testing problem, for which a minimax strategy is not known, evaluating its performance under both noise-agnostic and noise-aware adversarial settings, by providing a method to find optimal noise-aware attacks, and heuristics to find noise-agnostic attacks that are close to optimal in the high SNR regime.

Alternative classification rules for two normal populations with a common mean and ordered variances

The problem of classification into two normal populations with a common mean and ordered variances is revisited. So far in the literature, authors have proposed classification rules which are based on either the Graybill-Deal estimator or its improved version of the common mean under order restricted variances. Surprisingly, the maximum likelihood estimator (MLE) of the common mean has not been used for classification purposes. However, it is interesting to know that the MLE has better performance than the Graybill-Deal estimator in most of the parameter ranges. In this article, utilizing the MLE and its plug-in type restricted version of the common mean, two new classification rules have been proposed. Further, a classification rule based on the generalized likelihood ratio test approach has been obtained. Moreover, certain rules based on some of the improved existing estimators of the common mean under order restricted variances have been proposed. More importantly, a simulation study has been carried out to numerically compare the probabilities of misclassification for all the classification rules, including the existing ones. It has been observed that the classification rules which are based on the MLE and its restricted version perform quite satisfactorily (if not the best) compared to other rules.

Fault diagnosis of biological systems using improved machine learning technique

Fault detection and isolation (FDI) is considered as one of the most critical problems in biological processes. Therefore, in this paper, we consider a new FDI framework that aims to improve the monitoring of biological processes. To do that, a machine learning-based statistical hypothesis approach, which can identify the model, detect and isolate the faults, will be developed. In the developed approach, so-called partial Gaussian process regression (PGPR)-based generalized likelihood ratio test (GLRT), first, the GPR model that can accurately model biological processes is presented. Then, the fault detection phase is performed using the GLRT chart. Finally, the PGPR-based GLRT, which can effectively isolate the faults, is developed. The FDI performances of the developed PGPR-based GLRT approach are compared with partial support vector regression (SVR), extreme learning machines (ELM), Kernel ridge regression (KRR) and relevance vector machines (RVM)-based GLRT methods in terms of missed detection rate (MDR), false alarm rate (FAR), root mean square error (RMSE), execution time (ET) and isolation accuracy. The obtained results show that the proposed technique can reliably detect and isolate various faults using two examples: a synthetic data and a biological process representing a Cad System in E. coli (CSEC) model.

Reliable Fault Detection and Diagnosis of Large-Scale Nonlinear Uncertain Systems Using Interval Reduced Kernel PLS

Kernel partial least squares (KPLS) models are widely used as nonlinear data-driven methods for faults detection (FD) in industrial processes. However, KPLS models lead to irrelevant performance over long operation periods due to process parameters changes, errors and uncertainties associated with measurements. Therefore, in this paper, two different interval reduced KPLS (IRKPLS) models are developed for monitoring large scale nonlinear uncertain systems. The proposed IRKPLS models present an interval versions of the classical KPLS model. The two proposed IRKPLS models are based on the Euclidean distance between interval-valued observations as a dissimilarity metric to keep only the more relevant and informative samples. The first proposed IRKPLS technique uses the centers and ranges of intervals to estimate the interval model, while the second one is based on the upper and lower bounds of intervals for model identification. These obtained models are used to evaluate the monitored interval residuals. The aforementioned interval residuals are fed to the generalized likelihood ratio test (GLRT) chart to detect the faults. In addition to considering the uncertainties in the input-output systems, the new IRKPLS-based GLRT techniques aim to decrease the execution time when ensuring the fault detection performance. The developed IRKPLS-based GLRT approaches are evaluated across various faults of the well-known Tennessee Eastman (TE) process. The performance of the proposed IRKPLS-based GLRT methods is evaluated in terms of missed detection rate, false alarms rate, and execution time. The obtained results demonstrate the efficiency of the proposed approaches, compared with the classical interval KPLS.

Multi-Antenna Spectrum Sensing using Bootstrap on Cognitive Radio for Internet of Things Application

Cognitive Radio (CR) is a technology used for other developing technologies like Internet of Things (IoT), one part of CR is spectrum sensing which is useful as an empty spectrum searcher. The use of spectrum is now considered very minimal and raises the problem of scarcity of spectrum. But after testing the real problem is the spectrum in utilization. This problem can be overcome by using efficient utilization of CR technology using Spectrum Sensing. Sensing algorithms that are usually used such as: a suitable filter, energy detector and cyclostationary are not enough because there are many antennas to be detected. In the case of multi-antenna detection, research usually uses the Generalized likelihood ratio test (GLRT) approach. The GLRT Approach Detector also has three types of detectors, type-3 detectors do not determine statistical tests. However, if you use monte carlo or the literacy algorithm, you need a lot of data to get the detector performance. this research will combine algorithms using bootstrap to determine detector performance using small data because using Bootstrap basically only requires a small resampling. The research wants to show if a type-3 detector can help the detector produce good probabilities using little data. The expected result is that the GLRT approach can be combined with a bootstrap for type-3 detectors such as: arithmetic and geometric statistical tests (TAGM) and GLRT time code space code statistical tests (TSTBCGLRT) to help determine assumptions Pd assumptions. Then an experiment was carried out to determine the threshold, by comparing bootstrap with monte carlo, research is expected to show that bootstrap works without a known H0 distribution and set the same threshold at all times.

Machine learning-based statistical testing hypothesis for fault detection in photovoltaic systems

In this paper, we consider a machine learning approach merged with statistical testing hypothesis for enhanced fault detection performance in photovoltaic (PV) systems. The developed method makes use of a machine learning based Gaussian process regression (GPR) technique as a modeling framework, while a generalized likelihood ratio test (GLRT) chart is applied to detect PV system faults. The developed GPR-based GLRT approach is assessed using simulated and real PV data through monitoring the key PV system variables (current, voltage, and power). The computation time, missed detection rate (MDR), and false alarm rate (FAR) are computed to evaluate the fault detection performance of the proposed approach.

Fault detection of uncertain chemical processes using interval partial least squares-based generalized likelihood ratio test

Fault detection (FD) is essential for monitoring various chemical processes. Many chemical processes can be described by input-output models. Partial least squares (PLS) method is one of the most popular statistical approaches used for modeling and monitoring chemical processes. In many situations, measured process data can exhibit some level of uncertainty. In such cases, expressing the data in interval form can be useful. Therefore, this work addresses the problem of fault detection of uncertain chemical processes using interval input-output PLS-based generalized likelihood ratio test (GLRT). The proposed novel approach helps extend the applicability of GLRT to uncertain processes represented by interval-valued input-output data. In the developed approach, the modeling phase is performed using PLS and then the GLRT chart is applied to the interval residuals for fault detection. To evaluate the fault detection abilities of the proposed PLS-based interval valued GLRT approach, two examples are used: a simulated example and a distillation column example. The performance of the proposed technique is evaluated in terms of the missed detection and false alarms rates.

A Direct-Path Interference Resistant Passive Detector

Passive radar, which detects and tracks targets of interest by using noncooperative illuminators of opportunity (IOs), has become popular since qualified IO sources are widely accessible nowadays. This letter examines the target detection problem for a passive multistatic radar, where the receivers are contaminated by nonnegligible noise and direct-path interference (DPI). The signal transmitted from the IO is treated as a deterministic but unknown process. A generalized likelihood ratio test approach is proposed, where the $\mathcal {H}_1$ estimation problem is solved using an iterative method. A clairvoyant matched filtering detector, which assumes the knowledge of the IO waveform, is provided as well to benchmark performance. Simulation results are presented to show the effectiveness of the proposed detector in the presence of DPI.

A Multifamily GLRT for Oil Spill Detection

This paper deals with detection of oil spills from multipolarization synthetic aperture radar images. The problem is cast in terms of a composite hypothesis test aimed at discriminating between the polarimetric covariance matrix (PCM) equality (absence of oil spills in the tested region) and the situation where the region under test exhibits a PCM with at least an ordered eigenvalue smaller than that of a reference covariance. This last setup reflects the physical condition where the backscattering associated with the oil spills leads to a signal, in some eigendirections, weaker than the one gathered from a reference area where the absence of any oil slicks is a priori known. A multifamily generalized likelihood ratio test approach is pursued to come up with an adaptive detector ensuring the constant false alarm rate property. At the analysis stage, the behavior of the new architecture is investigated in comparison with a benchmark (but nonimplementable) structure and some other suboptimum adaptive detectors available in the open literature. This study, which is conducted in the presence of both simulated and real data, confirms the practical effectiveness of the new approach.

Adaptive Beacon Transmission in Cognitive-OFDM-Based Industrial Wireless Networks

Wireless interferences from heterogeneous networks in the crowded industrial scientific medical band set up technical barriers for reliable communication of industrial wireless network (IWN). In this letter, an adaptive beacon transmission strategy is proposed for dynamically scheduling the cognitive-OFDM IWN to avoid channel interferences without using a dedicated control channel. Preambles of beacons are specifically designed in the PHY layer to embed specific information. A generalized likelihood ratio test (GLRT)-based approach is applied to detect the beacon transmission and a maximum likelihood estimator is employed to estimate the beacon information embedded in the preamble. The performance of the GLRT approach to detect the adaptive beacon transmission is evaluated through simulations and practical experiments. The detection and decoding accuracies of the proposed adaptive beacon transmission are close to 100% with reasonable signal-to-noise ratio even under interference.

A New Detection Algorithm for Coherent Scatterers in SAR Data

In contrast to the random nature of synthetic aperture radar (SAR) data, it is also possible to identify bright targets whose scattering properties scarcely vary within imaging and time. These targets are commonly named point-like scatterers and can be found in both urban and natural environments. Permanent-scatterer interferometry techniques single out stable scatterers in a stack of SAR images, which preserve their backscattering stability along time. However, this methodology may not be optimum in natural scenarios, where the temporal stability of the scattering is rather reduced, or when the number of available SAR acquisitions is significantly small. Consequently, alternative methods have come out to detect stable scatters in a single SAR image, thus reducing all constraints related to their temporal behavior. Particularly, spectral diversity techniques are exploited to detect the so-called coherent scatterers. In this paper, a new detection scheme based on the generalized likelihood ratio test approach (GLRTA) is proposed, and its performance is extensively evaluated compared with three of the traditional methods, namely, the sublook coherence approach, the sublook entropy approach, and the phase variance approach. Remarkably, the GLRTA exploits both amplitude and phase information and does not need any further averaging (apart from sublooking processing with reduced signal bandwidth). The presented analysis is conducted both theoretically and with simulated data. For all scenarios, the new detector outperforms the other methods. The obtained results are validated also on real data. Finally, the proposed GLRTA is tested over different scattering scenarios, considering three TerraSAR-X acquisitions.

Extension of the Linear Chromodynamics Model for Spectral Change Detection in the Presence of Residual Spatial Misregistration

A generalized likelihood ratio test (GLRT) statistic for spectral change detection based on the linear chromodynamics model is extended to accommodate unknown residual misregistration between imagery described by a prior probability density function for the spatial misregistration. Using a normal prior distribution leads to a fourth-order polynomial that can be numerically minimized over the unknown misregistration parameters. A more computationally efficient closed-form solution is developed based on a quadratic approximation and provides comparable results to the numerical minimization for the investigated test cases while running 30 times faster. The results applying the method to hyperspectral imagery indicate up to an order of magnitude reduction in false alarms at the same detection rate relative to baseline change detection methods for synthetically misregistered test data particularly in image regions containing edges and fine spatial features. Sensitivity to model parameters is assessed, and the method is compared with a previously published misregistration compensation approach yielding comparable results. Although the GLRT approach appears to exhibit comparable change detection performance, it offers the possibility of tailoring the algorithm to a priori knowledge of expected misregistration errors or to compensate structured misregistration as would occur due to parallax errors due to perspective variations (e.g., image parallax).

Kronecker-Based Fusion Rule for Cooperative Spectrum Sensingwith Multi-Antenna Receivers

This paper considers a novel fusion rule for spectrum sensing scheme for a cognitive radio network with multi-antenna receivers. The proposed scheme exploits the fact that when any primary signal is present, measurements are spatially correlated due to presence of inter-antenna and inter-receiver spatial correlation. In order to exploit this spatial structure, the generalized likelihood ratio test (GLRT) operates with the determinant of the sample covariance matrix. Therefore, it depends on the sample size N and the dimensionality of the received data (i.e., the number of receivers K and antennas L). However, when the dimensionality fK; Lg is on the order, or larger than the sample size N, the GLRT degenerates due to the ill-conditioning of the sample covariance matrix. In order to circumvent this issue, we propose two techniques that exploit the inner spatial structure of the received observations by using single pair and multi-pairs Kronecker products. The performance of the proposed detectors is evaluated by means of numerical simulations, showing important advantages with respect to the traditional (i.e., unstructured) GLRT approach.

GLRT Approach for Performance Improvement in Practical Burst Packet Acquisition with AGC Amplifier

For code-aided burst packet acquisition, the extensively used square-law cross-correlation noncoherent (CCN) detector is generally studied under a fixed-gain (FG) amplifier model. However, in practical communication systems an automatic-gain-control (AGC) amplifier is usually employed. In such a case CCN will significantly deteriorate, because the amplification of noise in hypothesis $${\mathcal{H }_0}$$ H 0 is larger than that of noisy signals in hypothesis $${\mathcal{H }_1}$$ H 1 . To improve detection performance, the generalized likelihood ratio test (GLRT) approach is adopted. Closed-form expressions of false alarm probability (FAP) and detection probability (DP) are derived for CCN and GLRT in both FG and AGC cases. Based on these expressions, GLRT is compared with CCN in terms of both performance and implementation complexity. Results show that although GLRT reveals a slightly poorer performance than CCN in an ideal case that an FG amplifier is used, it achieves a significant and increasing performance superiority over CCN in a practical case that AGC is exploited with an affordable extra hardware cost.

GLRT Approach for Robust Burst Packet Acquisition in Wireless Communications

Rapid detection of the arrival of a packet is challenging in burst wireless communications, where many parameters are unknown, such as signal power, noise power and carrier phase offset. Due to the unknown noise power, it is hard to set appropriate thresholds for the existing common detectors under the Neyman-Pearson criterion, which results in vulnerable acquisition and poor performance. In order to solve this problem, we propose the generalized likelihood-ratio test (GLRT) approach for sequence-aided packet acquisition in this paper. GLRT detection is formulated under multipath channel. Moreover, false alarm probability and detection probability of GLRT are derived and confirmed via simulations. Comparisons are conducted between GLRT and the common detectors, as well as GLRT under different channels. Results show that GLRT basically reveals more competitive and robust performance than the common detectors in practice, with only a little extra hardware cost by using the provided recursive computation structure. Additionally, it is shown that fading results in significant deterioration for GLRT; whereas GLRT has ability to exploit multipath diversity to reduce fading effect and improve acquisition performance.

An Initial Ranging Scheme for the IEEE 802.16 OFDMA Uplink

The IEEE 802.16 family of standards for nomadic wireless metropolitan area networks adopts orthogonal frequency-division multiple-access as an air interface. In these systems, timing errors between the uplink signals and the base station time reference give rise to interchannel interference as well as multiple-access interference with an ensuing degradation of the error-rate performance. To mitigate this problem, users that intend to establish a communication link go through a synchronization procedure called Initial Ranging (IR) by which uplink signals can arrive at the base station synchronously and with approximately the same power level. In this work, a novel IR scheme compliant with the IEEE 802.16 specifications is presented. In contrast to existing methods, our solution operates on the basis of a generalized likelihood ratio test (GLRT) and provides improved timing and power estimates by properly taking into account the channel correlation across the signal bandwidth. In order to increase the resilience to multiple access interference, the GLRT approach is also exploited to derive a two-stage interference cancellation scheme. Numerical simulations and theoretical analysis are used to demonstrate the effectiveness of the proposed solutions and to make comparisons with existing alternatives.

On Multiple Antenna Spectrum Sensing Under Noise Variance Uncertainty and Flat Fading

We investigate a spectrum sensing method based on asymptotic analysis of the discrete Fourier transform of the received multiantenna signal, possibly non-Gaussian, for flat-fading primary user signals in white noise under noise variance uncertainty. The proposed approach is based on the generalized likelihood ratio test (GLRT) paradigm for a restricted version of the problem obtained by ignoring the spatial structure of the primary users' received signals, and it permits the noise variances to be different at different antennas without requiring knowledge of their values. Simulation examples show the efficacy of the proposed approach compared with the energy detector and some existing time-domain GLRT approaches. A performance analysis of the proposed detector is carried out and verified via simulations. It is also shown that the proposed test statistic is equivalent to an existing time-domain GLRT statistic except that the latter has been derived under the assumption that received signal is Gaussian whereas we make no such assumption.

Multi-antenna based spectrum sensing for cognitive radios: A GLRT approach

In this letter, we propose multi-antenna based spectrum sensing methods for cognitive radios (CRs) using the generalized likelihood ratio test (GLRT) paradigm. The proposed methods utilize the eigenvalues of the sample covariance matrix of the received signal vector from multiple antennas, taking advantage of the fact that in practice, the primary user signals to be detected will either occupy a subspace of dimension strictly smaller than the dimension of the observation space, or have a non-white spatial spectrum. These methods do not require prior knowledge of the primary user signals, or the channels from the primary users to the CR. By making different assumptions on the availability of the white noise power value at the CR receiver, we derive two algorithms that are shown to outperform the standard energy detector.

A differential receiver for uwb systems

We consider a UWB communication system operating in a typical indoor environment and we propose a novel differential receiver in which encoding is performed symbol-by-symbol rather than frame-by-frame, as is normally done. The detector structure is derived in a single-user scenario using a generalized likelihood ratio test approach. Its performance is assessed by simulation in the presence of multiple-access interference. The proposed receiver has a simple structure and outperforms other differential schemes of comparable complexity

Methods to detect objects in photon-limited images

We investigate the problem of detecting and localizing a known signal in a photon-limited image, where Poisson noise is the dominant source of image degradation. For this purpose we developed and evaluated three new algorithms. The first two are based on the impulse restoration (IR) principle and the third is based on the generalized likelihood ratio test (GLRT). In the IR approach, the problem is formulated as one of restoring a delta function at the location of the desired object. In the GLRT approach, which is a well-known variation on the optimal likelihood ratio test, the problem is formulated as a hypothesis testing problem, in which the unknown background intensity of the image and the intensity scale of the object are obtained by maximum-likelihood estimation. We used Monte Carlo simulations and localization receiver operating characteristic (LROC) curves to evaluate the proposed algorithms quantitatively. LROC curves demonstrate the ability of an algorithm to detect and locate objects in a scene correctly. Our simulations demonstrate that the GLRT approach is superior to all other tested algorithms.