Generalized Likelihood Ratio Approach Research Articles

Detection by Block- and Band-Permuted Data

Unlabeled detection is an important problem in large sensor networks faced with big-data applications. The focus of this paper is on decision problems in which the data vector received at the fusion center (FC), tasked to perform the final inference, undergoes an unknown permutation. Two representative permutation models are considered, whose structure is imposed by practical considerations. The first is the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -block permutation model, where the observations are split into different blocks of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> , and independent data permutations affect each block. The second is the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r$</tex-math></inline-formula> -banded permutation model, in which each sample of the vector received by the FC lies at most <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r$</tex-math></inline-formula> positions ahead or behind its original location. To solve these challenging detection tasks, three detectors for both permutation models are proposed. The first is inspired by the uniformly most powerful invariant principle; the second relies on a distribution-averaged strategy; and the third is designed according the generalized likelihood ratio approach. The performance of these detectors is investigated by computer experiments, and their relative merits are discussed.

New Approaches for Monitoring Image Data.

In this paper, we develop new techniques for monitoring image processes under a fairly general setting with spatially correlated pixels in the image. Monitoring and handling the pixels directly is infeasible due to an extremely high image resolution. To overcome this problem, we suggest control charts that are based on regions of interest. The regions of interest cover the original image which leads to a dimension reduction. Nevertheless, the data are still high-dimensional. We consider residual charts based on the generalized likelihood ratio approach. Existing control statistics typically depend on the inverse of the covariance matrix of the process, involving high computing times and frequently generating instable results in a high-dimensional setting. As a solution of this issue, we suggest two further control charts that can be regarded as modifications of the generalized likelihood ratio statistic. Within an extensive simulation study, we compare the newly proposed control charts using the median run length as a performance criterion.

Large-Scale Datastreams Surveillance via Pattern-Oriented-Sampling

Monitoring large-scale datastreams with limited resources has become increasingly important for real-time detection of abnormal activities in many applications. Despite the availability of large datasets, the challenges associated with designing an efficient change-detection when clustering or spatial pattern exists are not yet well addressed. In this article, a design-adaptive testing procedure is developed when only a limited number of streaming observations can be accessed at each time. We derive an optimal sampling strategy, the pattern-oriented-sampling, with which the proposed test possesses asymptotically and locally best power under alternatives. Then, a sequential change-detection procedure is proposed by integrating this test with generalized likelihood ratio approach. Benefiting from dynamically estimating the optimal sampling design, the proposed procedure is able to improve the sensitivity in detecting clustered changes compared with existing procedures. Its advantages are demonstrated in numerical simulations and a real data example. Ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of traditional detection procedures. Supplementary materials for this article are available online.

Robust multipixel matched subspace detection with signal-dependent background power

A modified matched subspace detector (MSD) has been recently proposed for detecting a barely discernible object in an additive Gaussian background clutter using a single pixel in a sequence of digital images. In contrast to this detector designed for the subpixel object, we developed a generalized likelihood ratio approach to the detection of a multipixel object of unknown shape, size, and position in an additive signal-dependent Gaussian background and noise. The proposed detector modifies the MSD by adding the additional term proportional to the square of the difference between the background variances under two statistical hypotheses. The performances of these detectors are evaluated for the example scenario of two multipixel floating objects on the agitated sea surface. The crucial characteristic of the proposed detector is that prior knowledge of the target size, shape, and position is not required. Computer simulation and experimental results have shown that the proposed detector outperforms the MSD, especially in the case of weak and poorly contrasted objects of unknown shape, size, and position.

Multi-wave-mode, multi-frequency detectors for guided wave interrogation of plate structures

The detection and localization of damage using an array of closely spaced transducers is investigated theoretically and experimentally using single- and multiple-mode guided wave active sensing models. Detectors are derived using a generalized likelihood ratio approach assuming that amplitude, absolute phase, and source location of a scattered wave are unknown, while frequency, group velocity, and phase velocity are known. Theoretical detection performance for processing with each detector is derived and related to the energy-to-noise ratio of a scattered mode as a metric of determining when processing with multiple modes provides increased performance over processing with a single mode. Experimentally, detectors are implemented to detect scattering from a small mass glued to the surface of an aluminum plate with a 7 × 7 array of transducers. Relative detection and localization performance is compared through receiver operating characteristic curves and histograms of distance from true damage location for 1000 no-damage and damaged measurements. A single-mode, multi-frequency detector is shown to have the best detection and localization performance for the tested damage scenarios.

On control charts for monitoring the variance of a time series

In this paper we derive control charts for the variance of a Gaussian process using the likelihood ratio approach, the generalized likelihood ratio approach, the sequential probability ratio method and a generalized sequential probability ratio procedure, the Shiryaev–Roberts procedure and a generalized modified Shiryaev–Roberts approach. Recursive presentations for the calculation of the control statistics are given for autoregressive processes of order 1. In an extensive simulation study these schemes are compared with existing control charts for the variance. In order to asses the performance of the schemes both the average run length and the average delay are used.

Multiantenna Spectrum Sensing Exploiting Spectral a priori Information

Dynamic Spectrum Access (DSA) is receiving considerable interest as a means to improve spectral usage in licensed bands. In order to avoid interference to licensed users, spectrum sensing has emerged as an enabling technology for DSA. The requirements for spectrum sensors are stringent, as licensed user detection must be performed reliably at low signal-to-noise ratios (SNR). Sensing performance can be improved by exploiting signal features not present in the background noise. These approaches result in tradeoffs among performance and robustness to departures from the signal model. We consider second-order signal features and develop detectors exploiting spatial (by using multiple antennas) as well as temporal signal correlation, taking advantage of the fact that the power spectrum of the primary signal at each antenna can be known up to a complex scalar representing the unknown propagation channel. A low-SNR Generalized Likelihood Ratio approach is adopted in order to overcome this uncertainty, resulting in different tests intimately related to familiar diversity combining techniques. The performance of the proposed detectors is analyzed and tested in different scenarios.

Change Detection in a Distillation Column Based on the Generalized Likelihood Ratio Approach

With increasing demands for efficiency, product quality, reliability and process safety, the field of fault detection (FD) plays an important role in chemical industries. This paper deals with a FD method based on the combination of Generalized Likelihood Ration Test (GLRT) and Artificial Neural Networks (ANNs). A reliable neural model in normal conditions, under all regimes (i.e. steady-state and dynamic conditions), is found by means of a NARX (Nonlinear Auto-Regressive with eXogenous input) model and by an experimental design. The efficiency of the combination of these two approaches used for detecting faults has been tested under real anomalous conditions on a real plant as a distillation column. From the experimental results, it is observed that the proposed FD is able to detect the process status effectively.

CUSUM charts for monitoring the mean of a multivariate Gaussian process

In this paper control charts for the mean of a multivariate Gaussian process are considered. Using the generalized likelihood ratio approach and the sequential probability ratio test under an additional constraint on the magnitude of the change various types of CUSUM control charts are derived. It is analyzed under which conditions these schemes are directionally invariant. These charts are compared with several other control schemes proposed in literature. The performance of the charts is studied based on the maximum average delay.

Identification of real sinusoids in noise, the global matched filter approach.

We consider the basic identification of real sinusoids in Gaussian noise problem. Since the maximum likelihood function is ill-conditioned and possesses numerous local maxima, we propose to somehow approximate it by a function that is convex and easy to optimize. The procedure amounts to apply the Global Matched Filter to the present problem using a complex redundant basis. It performs simultaneously the detection of the sinusoids and the identification of their characteristics. From a detection point of view, it is similar to a generalized likelihood ratio approach. The performances are close to the Cramer-Rao bounds for scenarios where few competing methods work. The approach can handle arbitrarily sampled data without further difficulties.

Variable-Structure Multiple-Model Approach to Fault Detection, Identification, and Estimation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A scheme is proposed to detect, identify, and estimate failures, including abrupt total, partial, and multiple failures, in a dynamic system. The new approach, named IM<formula formulatype="inline"><tex>$^{3}$</tex></formula>L, is developed based on variable-structure multiple-model estimation, which allows to improve performance by online adaptation. It uses an interacting multiple model estimator for fault detection and identification but the maximum likelihood estimator for estimating the extent of failure. It provides an effective and integrated framework for fault detection, identification, and state estimation. For two aircraft examples, the proposed approach is evaluated and compared with hierarchical multiple-model approaches and a widely used single-model residual-based generalized likelihood ratio approach in terms of detection and estimation performance. The results show that the IM<formula formulatype="inline"><tex>$^{3}$</tex></formula>L provides not only fast detection and proper identification, but also good estimation of the failure extent as well as robust state estimation. </para>

Soft-Decision Metrics for Coded Orthogonal Signaling in Symmetric Alpha-Stable Noise

This paper derives new soft-decision metrics for coded orthogonal signaling in impulsive noise, more specifically symmetric alpha-stable noise. For the case of a known channel amplitude and known noise dispersion, exact metrics are derived both for Cauchy and Gaussian noise. For the case that the channel amplitude or the dispersion is unknown, approximate metrics are obtained in closed-form based on a generalized-likelihood ratio approach. The performance of the new metrics is compared numerically for a turbo-coded system, and the sensitivity to side information of the optimum receiver for Cauchy noise is considered. The gain that can be achieved by using a properly chosen decoding metric is quantified, and it is shown that this gain is significant. The application of the results to frequency hopping ad hoc networks is also discussed.

Interrelationship of single-filter and multiple-model adaptive algorithms

An equivalent filter bank structure for multiple model adaptive estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filter and linear transforms to produce equivalent residuals of a complete Kalman filter bank. The linear transforms, which are a function of the differences between the system models used by the various Kalman filters, are developed for modeling differences in the system input matrix, the output matrix, and the state transition matrix. The computational cost of this new structure is compared with the cost of the standard Kalman filter bank (SKFB) for each of these modeling differences. This structure is quite similar to the generalized likelihood ratio (GLR) structure, where the linear transforms can be used to compute the matched filters used in the GLR approach. This approach produces the best matched filters in the sense that they truly represent the time history of the residuals caused by a physically motivated failure model.

Generalized likelihood ratio approach for fault detection in linear dynamic stochastic systems with unknown inputs

Abstract The generalized likelihood ratio (GLR) technique performs statistical tests on the innovations sequence of a Kalman filter state estimator. Using the results of these tests, sensor or actuator failures are detected and identified. In this paper, we generalize this strategy for linear dynamic stochastic systems with unknown inputs

Decentralized Fault Detection: A Generalized Likelihood Ratio Approach

The detection and diagnosis of faults occurring in local subsystems are considered as abrupt changes of unknown magnitudes at unknown times, using the local information alone. Because of limited information the application of the centralized fault detection methods in general is not straight forward to decentralized fault detection and requires a new approach. Here we show that, using a projection operator to suppress the information due to the unknown interactions of other subsystems on the residuals of the local systems, the application of the centralized generalized likelihood ratio test for fault detection is straight forward.

Urinary neopterin concentrations and T-cell subset data in HIV-1 infection

We investigated the ability of urinary neopterin concentrations and T-cell subset data, and their ratios to discriminate between anti-HIV-1 seronegatives, seropositives, and AIDS cases. Using receiver-operated-characteristics curves, neopterin levels were shown to provide the best discrimination. Of the ratios derived from the single variables, neopterin per CD4+ cell counts and neopterin per CD4+/CD8+ cell ratio were superior to the CD4+/CD8+ cell ratio. Multivariate analyses were performed using a generalized likelihood ratio approach as well as linear discriminant analysis. The combination of neopterin concentration and CD4+ T-cell count is well suited to discriminate between various stages of HIV-1 infection and, therefore, we recommend using more than one assay to evaluate disease progression.

A Generalized Likelihood Ratio Approach to Detecting and Identifying Failures in Pressurizer Instrumentation

The generalized likelihood ratio (GLR) technique performs statistical tests on the innovations sequence of a Kalman filter state estimator. Using the results of these tests, failures in the sensors of a pressurized water reactor pressurizer are detected and identified. A third-order, linear model of the pressurizer dynamics, which is required by both the GLR and Kalman filter formulations, is developed from first principles. Using actual pressurizer data, the GLR method is employed to identify a bias in one of three level sensors.

A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems

We consider a class of stochastic linear systems that are subject to jumps of unknown magnitudes in the state variables occurring at unknown times. This model can be used when considering such problems as estimation for systems subject to possible component failures and the tracking of vehicles capable of abrupt maneuvers. Using Kalman-Bucy filtering and generalized likelihood ratio techniques, we devise an adaptive filtering system for the detection and estimation of the jumps. An example that illustrates the dynamical properties of our filtering scheme is discusssed in detail.