Generalized Likelihood Ratio Detector Research Articles

Active GLR detector for resilient LQG controller in networked control systems

In computing science, resilience is the ability of system or network architecture to recover normal operation after a brutal crash. When malicious cyber act on control signals of a Networked Control System (NCS) is designed to remain undetectable from passive model-based Fault Detection and Isolation (FDI) schemes, we show that the unobservable consequence on the state variable of the plant becomes brutally observable after the disappearance of the damaging action. In order to quickly recover the nominal behavior of the Linear Quadratic Gaussian (LQG) controller, a resilient LQG controller is obtained from an active version of the Generalized Likelihood Ratio (GLR) test designed to detect the disappearance of the malicious act and to increase the tracking ability of the Kalman filter at detection time.

A CFAR Adaptive Subspace Detector Based on a Single Observation in System-Dependent Clutter Background

In this paper, the problem of detecting target in system-dependent clutter (SDC) background with a single observation from the test cell is researched. Classical detectors, such as the generalized likelihood ratio detectors (GLRDs) and the adaptive matched filters (AMFs), etc., usually deal with the clutter and the noise as a whole. The low rank detectors (LRDs) make use of the low rank property of the clutter to improve the detection performance. However, the performance of LRDs degrades when the signal is not orthogonal with respect to (w.r.t.) the clutter. In this paper, an adaptive subspace detector for SDC (SDC-ASD) background which deals with the clutter and the noise separately is proposed. The SDC-ASD designs the test statistic by replacing the signal and the clutter covariance matrix with their maximum likelihood estimations (MLEs). Its theoretical false alarm probability and detection probability are analytically deduced. Analytical results show that the test statistic has the form of non-central F distribution. Besides, it is shown that the SDC-ASD has constant false alarm rate (CFAR) performance w.r.t. the clutter and the noise. Numerical experiments are provided to validate the detection performance of the SDC-ASD in dealing with the target detection in SDC background.

Distributed Cooperative Spectrum Sensing in Mixture of Large and Small Scale Fading Channels

In this paper, we study distributed energy detectors for spectrum sensing in cognitive radio networks. We treat the primary signal as unknown and deterministic with a known power and the channels as random with a Nakagami-Lognormal mixture distribution. In other words, the channel gains are modeled as product of two terms corresponding to the small and large-scale fadings. The small-scale terms are all Nakagami and independent for all sensors. Whereas for large-scale fading, sensors in each cluster are assumed to have identical Lognormal terms. We also assume that different clusters have independent large-scale fading. Assuming that the total energies from clusters are received, we investigate four distributed detection strategies: 1) Equal Gain Combining detector (EGCD), 2) Neyman-Pearson detector (NPD) or Likelihood Ratio detector (LRD) for known channel gains, 3) Generalized Likelihood Ratio detector (GLRD) for unknown gains, and 4) Average Likelihood Ratio detector (ALRD) given a priori distribution of channel gains. The simulation results show that the effects of both small and large-scale fadings on sensing performance should be considered simultaneously and confirm that a priori statistical information about large and small-scale fading used in ALRD result in performance improvement compared to EGCD and GLRD.

Cooperative Spectrum Sensing over Mixture-Nakagami Channels

We propose novel detectors for cooperative spectrum sensing in mixture-Nakagami fading channels, namely 1) the Neyman-Pearson Detector (NPD), 2) a Locally Optimum Detector for weak signals that exploit the correlation between the observations and transmitted signals, 3) a weak signal detector for unknown parameters and 4) two Generalized-Likelihood-Ratio detectors (GLRDs) that exploit the received energies. They significantly outperform energy and cyclostationary detectors in practical scenarios. We also analyze the performance of the NPD and GLRD for unknown transmitted signal over Rayleigh channels, where they reduce to a linear weighted-correlator and a weighted-energy detector respectively.

TARGET DETECTION IN PULSE-TRAIN MIMO RADARS APPLYING ICA ALGORITHMS

In this paper, the problem of target detection in co- located \multi-input multi-output (MIMO) radars is considered. A pulse-train signaling is assumed to be used in this system. As the doppler efiect should be considered for the pulse-train signaling, we are confronted by a compound hypothesis testing problem, so in this paper a Generalized Likelihood Ratio (GLR) detector is derived. The high complexity of this detector makes us derive a new detector based on the theory of Independent Component Analysis (ICA). It is shown that the computational load of the ICA-based detector is much less than the GLR detector. It is also shown that the sensitivity of the ICA-based detector to the doppler efiect is very low. According to this approach, an appropriate signal design method is presented, based on the separation performance of the ICA algorithms. It is shown that independent random sequences are proper signals in the sense of detection performance.

Invariant detection of orthogonal frequency division multiplexing signals with unknown parameters for cognitive radio applications

The authors propose a computationally efficient spectrum sensing solution for an orthogonal frequency division multiplexing (OFDM) signal in a frequency-selective fading channel with additive white Gaussian noise (AWGN). The authors’ assumption is that the data symbols, channel coefficients and the noise variance are all unknown. The nature of the problem leads them to find an invariant detector. The optimum one is uniformly most powerful invariant (UMPI); their effort shows that this test does not exist, as the final decision statistic depends on some unknown parameters; although, they derive the most powerful invariant (MPI) detector, implanting these parameters, to provide an upper bound for invariant detectors. Instead, the authors develop the generalised likelihood ratio test (GLRT), substituting the unknown parameters by their maximum likelihood (ML) estimates in the Neyman–Pearson likelihood ratio. Furthermore, they propose a computationally efficient implementation of the resulting detector. Simulation results show a slight decrease in efficiency against gaining so much computational complexity (CC) improvement. For more comparisons they also derive the conventional energy detector, namely, generalised energy detector (GED) for a binary phase shift keying (BPSK) signal, to show the adequacy of the GLR detector performance which would be demonstrated by simulation results.

Malicious Data Attacks on the Smart Grid

Malicious attacks against power systems are investigated, in which an adversary controls a set of meters and is able to alter the measurements from those meters. Two regimes of attacks are considered. The strong attack regime is where the adversary attacks a sufficient number of meters so that the network state becomes unobservable by the control center. For attacks in this regime, the smallest set of attacked meters capable of causing network unobservability is characterized using a graph theoretic approach. By casting the problem as one of minimizing a supermodular graph functional, the problem of identifying the smallest set of vulnerable meters is shown to have polynomial complexity. For the weak attack regime where the adversary controls only a small number of meters, the problem is examined from a decision theoretic perspective for both the control center and the adversary. For the control center, a generalized likelihood ratio detector is proposed that incorporates historical data. For the adversary, the trade-off between maximizing estimation error at the control center and minimizing detection probability of the launched attack is examined. An optimal attack based on minimum energy leakage is proposed.

Adaptive Detection of a Partly Known Signal Corrupted by Strong Interference

In this letter, we consider adaptive detection of a partly known signal corrupted by additive noise and strong interference with support that is only partly known. Assuming a homogeneous environment where the covariance matrix of the additive noise is the same for the primary and secondary data sets, although with the secondary data set also being affected by the interference, we allow for conic uncertainty models for both the signal and interference subspaces, developing a generalized likelihood ratio detector for the signal of interest. Numerical examples indicate that the proposed method offers a notable performance gain as compared to other recent related methods.

On High Performance MIMO Communications with Imperfect Channel Knowledge

This paper compares the performance of a MIMO system applying a Mismatched Maximum Likelihood Detector (MMLD) with that applying a Generalized Likelihood Ratio Detector (GLRD) in the presence of channel estimation errors. Two sources of error are considered: errors due to noise and errors due to time variations induced by Doppler effects. The MMLD relies on the available channel estimate whereas the GLRD combines the channel estimate with a block of received data and uses a joint channel-symbol estimation approach to solve for the transmitted symbols. The GLRD is shown to outperform the MMLD whenever errors in channel estimation are incurred and the performance gap depends on the amount of error. Furthermore, the GLRD provides a unified receiver structure which can also be applied to differentially encoded MIMO systems and to situation where no channel estimate is available as in blind MIMO. The improved performance of the GLRD comes with increased computational complexity. This problem is addressed through search efficient algorithms based on the branch-estimate-bound optimization framework. We analyze the performance of the GLRD and provide a tight upper bound on the BER of the system at high SNR. Simulation results are shown for a 2 × 2 MIMO system.

Generalised likelihood ratio test-based multiple-target detection for fluctuating targets with unknown parameters

In this paper, we address the radar adaptive detection problem in the case of multiple fluctuating targets with unknown parameters. The unknown parameters are: the number and location of targets, the amplitude and phase of received signals, the Doppler frequency of targets in slowly fluctuating case the target signal vectors in rapid-fluctuating case and the statistical characteristics of noise and clutter. We extract the generalised likelihood ratio test (GLRT) in Gaussian interference with unknown covariance matrix. Owing to high computational complexity of these detectors when the number of probable targets is large, we design a simple detector relying on the GLRT procedure, namely simplified GLR detector for implementation. This detector achieves satisfactory performance under several situations of practical interest and is simpler to implement than the designed GLR detector. Also in slowly fluctuation case, based on adaptive-matched filter (AMF), Kelly's detector (KD) and adaptive coherence estimator (ACE) that are used for single-target detection, some detectors are presented for multiple-target detection called generalised AMF, generalised KD and generalised ACE. Furthermore, in rapid fluctuation case in Gaussian interference with unknown covariance matrix, we propose an intuitive inexpensive detector with low computational complexity, which we will refer to as the generalised energy detector. Simulation results illustrate and compare the performance and the efficiency of the proposed detectors.

AR-model-based adaptive detection of range-spread targets in compound Gaussian clutter

In this paper, we consider the problem of adaptive detection for range-spread targets with known Doppler and unknown complex amplitude in compound Gaussian clutter. The speckle component of the clutter is modeled as an autoregressive (AR) process. By using the generalized likelihood ratio test (GLRT) approach, we will first estimate the AR parameters and the unknown complex amplitude, and then propose an adaptive AR-based GLR detector. The performance assessments are presented too. The computer simulations show that the proposed detector, without a priori information of the covariance matrix, has the same asymptotical performances as the two-step GLR-based detector with known covariance matrix.

Multiple antenna spectrum sensing in cognitive radios

In this paper, we consider the problem of spectrum sensing by using multiple antenna in cognitive radios when the noise and the primary user signal are assumed as independent complex zero-mean Gaussian random signals. The optimal multiple antenna spectrum sensing detector needs to know the channel gains, noise variance, and primary user signal variance. In practice some or all of these parameters may be unknown, so we derive the generalized likelihood ratio (GLR) detectors under these circumstances. The proposed GLR detector, in which all the parameters are unknown, is a blind and invariant detector with a low computational complexity. We also analytically compute the missed detection and false alarm probabilities for the proposed GLR detectors. The simulation results provide the available traded-off in using multiple antenna techniques for spectrum sensing and illustrates the robustness of the proposed GLR detectors compared to the traditional energy detector when there is some uncertainty in the given noise variance.

Count data regression charts for the monitoring of surveillance time series

Control charts based on the Poisson and negative binomial distribution for monitoring time series of counts typically arising in the surveillance of infectious diseases are presented. The in-control mean is assumed to be time-varying and linear on the log-scale with intercept and seasonal components. If a shift in the intercept occurs the system goes out-of-control. Using the generalized likelihood ratio (GLR) statistic a monitoring scheme is formulated to detect on-line whether a shift in the intercept occurred. In the case of Poisson the necessary quantities of the GLR detector can be efficiently computed by recursive formulas. Extensions to more general alternatives e.g. containing an auto-regressive epidemic component are discussed. Using Monte Carlo simulations run-length properties of the proposed schemes are investigated and the Poisson scheme is compared to existing methods. The practicability of the charts is demonstrated by applying them to the observed number of salmonella hadar cases in Germany 2001–2006.

On the Probability Density Function of the Test Statistic for One Nonlinear GLR Detector Arising from fMRI

Recently an important and interesting nonlinear generalized likelihood ratio (GLR) detector emerged in functional magnetic resonance imaging (fMRI) data processing. However, the study of that detector is incomplete: the probability density function (pdf) of the test statistic was draw from numerical simulations without much theoretical support and is therefore, not firmly grounded. This correspondence presents more accurate (asymptotic) closed form of the pdf by resorting to a non-central Wishart matrix and by asymptotic expansion of some integrals. It is then confirmed theoretically that the detector does possess constant false alarm rate (CFAR) property under some practical regimes of signal to noise ratio (SNR) for finite samples and the correct threshold selection method is given, which is very important for real fMRI data processing.

On the invariance property of one nonlinear GLR detector arising from fMRI

Recently an important and interesting nonlinear generalized likelihood ratio (GLR) detector emerged in functional magnetic resonance imaging (fMRI) data processing [F. Nan, R.D. Nowak, Generalized likelihood ratio detection for fMRI using complex data, IEEE Trans. Med. Imag. 18 (4) (1999) 320-329]. However, [F. Nan, R.D. Nowak, Generalized likelihood ratio detection for fMRI using complex data, IEEE Trans. Med. Imag. 18 (4) (1999) 320-329] is defective in the invariant study of the hypothesis testing problem: the invariant transformation group provided in Appendix II is not the largest and rigorous proof is not furnished either. This paper provides remedy to these deficiencies: the largest invariant transformation group is constructed rigorously and algebraically by matrix equation and method of undetermined coefficients. The group turns out to be larger than prescribed in [F. Nan, R.D. Nowak, Generalized likelihood ratio detection for fMRI using complex data, IEEE Trans. Med. Imag. 18 (4) (1999) 320-329]. Maximal invariants under both the original and the induced transformation groups are provided as well. The invariance property's utilities in exploring the dependence of the pdf on unknown parameters is strictly established. As a by-product of this paper, we point out that the geometrical method is defective in finding the largest invariant transformation group.

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.

Estimates of error probability for complex Gaussian channels with generalized likelihood ratio detection

We derive approximate expressions for the probability of error in a two-class hypothesis testing problem in which the two hypotheses are characterized by zero-mean complex Gaussian distributions. These error expressions are given in terms of the moments of the test statistic employed and we derive these moments for both the likelihood ratio test, appropriate when class densities are known, and the generalized likelihood ratio test, appropriate when class densities must be estimated from training data. These moments are functions of class distribution parameters which are generally unknown so we develop unbiased moment estimators in terms of the training data. With these, accurate estimates of probability of error can be calculated quickly for both the optimal and plug-in rules from available training data. We present a detailed example of the behavior of these estimators and demonstrate their application to common pattern recognition problems, which include quantifying the incremental value of larger training data collections, evaluating relative geometry in data fusion from multiple sensors, and selecting a good subset of available features.

Optimum Noncoherent Multiuser Decision Feedback Detection

A theory of noncoherent decision feedback multiuser detection for nonorthogonal binary modulation is developed that parallels that of coherent decision feedback multiuser detection for single-pulse modulation. In particular, an optimum noncoherent decision feedback detector is obtained that maximizes symmetric energy over a newly defined class of decision feedback detectors. Unlike the usual per-user performance metrics such as asymptotic efficiency or near-far resistance, the symmetric energy measure captures, with a single number, the asymptotic (high signal-to-noise ratio (SNR)) bit-error performance of all users at once. Several properties of the optimum decision feedback detector are established, one of which is that it outperforms the decision feedback generalized-likelihood ratio (GLR) detector in symmetric energy. It is also shown that, regardless of the order in which users are detected, the optimum noncoherent decision feedback detector outperforms its non-decision feedback counterpart in symmetric energy. Furthermore, two simple rules are obtained for determining the order in which users must be detected to guarantee that the optimum decision feedback detector outperforms its non-decision feedback counterpart (which in turn, is superior to the decorrelative GLR detector presented earlier) in terms of asymptotic effective energy for every user. In fact, one of the two (greedy) ordering rules also maximizes symmetric energy among all possible orderings. Such ordering rules are not available for the noncoherent decision feedback GLR detector in earlier work of the authors. Feasible sets of received energies are characterized in which it is possible, with power control, to achieve quality-of-service objectives for each user. None of the results in this paper make simplifying assumptions about the effects of error propagation. The term "noncoherent" in this work is used to denote that the receiver has no knowledge of the carrier phases and received signal energies of any of the users.

A New Generalized Likelihood Ratio Test for Sequential Jumps Detection

For sequential jumps detection, isolation and estimation in discrete-time stochastic linear systems, Willsky and Jones (1976) have developed the Generalized Likelihood Ratio (GLR) test. For the treatment of sequential jumps, the jump-free Kalman filter is updated on-line after each detection of one jump by a direct state estimate and covariance incrementation using the informations produced by the GLR detector. This paper proposes another updating strategy based on a reference model updated on-line by the states of jumps declared to be occurred during the sequential processing. The augmented state Kalman filter designed on this updated reference model will be optimaly initialized at each detection time from information given by the GLR detector.

A FDI Procedure Based on Linearized Bilinear Mass and Heat Conservation Models

Fault detection and isolation (FDI) for processes involving linear mass or energy conservation constraints is straightforward using standard statistical tools like GLR (generalized likelihood ratio). Non-linear relationships involving processes combining heat and material flows complicate FDI procedures. This paper proposes a method based on stationary bilinear mass and energy conservation models for the diagnosis of both sensor and process faults, making use of linear FDI tools. By locally linearizing the model equations, GLR detection and isolation tests can be applied to the residuals of parity relations. The method is illustrated for a simulated iron oxide pellet sintering furnace and its robustness is assessed with respect to the evaluation of the local operating level. Copyright ©2004 IFAC.