Scalable multichannel joint sequential change detection and isolation

It is supposed that there is a multisensor system in which each sensor performs sequential detection of a target. Then the binary decisions on target presence and absence are transmitted to a fusion center, which combines them to improve the performance of the system. We assume that sensors represent multichannel systems with possibly each one having different number of channels. Sequential detection of a target in each sensor is done by implementing a generalized Wald's sequential probability ratio test which is based on the maximum likelihood ratio statistic and allows one to fix the false alarm rate and the mis-detection rate at specified levels. We first show that this sequential detection procedure is asymptotically optimal for general statistical models in the sense of minimizing the expected sample size when the probabilities of errors vanish. We then construct the optimal non-sequential fusion rule that waits until all the local decisions in all sensors are made and then fuses them. It is optimal in the sense of maximizing the probability of target detection for a fixed probability of a false alarm or minimizing the maximal probability of error (minimax criterion). An analysis shows that the final decision can be made substantially more reliable even for a small number of sensors (3-5). The performance of the system is illustrated by the example of detecting a deterministic signal in correlated (color) Gaussian noise. In this example, we provide both the results of theoretical analysis and the results of Monte Carlo experiment. These results allow us to conclude that the use of the sequential detection algorithm substantially reduces the required resources of the system compared to the best non-sequential algorithm.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Sequential analysis has been used in many cases when the decision is supposed to be taken quickly such as for signal detection in statistical signal processing, namely sequential detector. For identical error probabilities, a sequential detector needs a smaller average sample number (ASN) than its counterpart of a fixed sample number quadrature detector based on Neyman-Pearson criteria. The optimum sequential detector was derived based on the assumption that the observations are uncorrelated (independent). However, in realistic scenario, such as in radar, the assumption is commonly violated. Using a sequential detector under correlated observations is sub-optimal and it poses a problem. It demands a high computational complexity, since it needs to recalculate the inverse and the determinant of the signal covariance matrix for each new sample taken. This paper presents a technique for reducing the computational complexity, which involves using recursive matrix inverse to subsequently calculate conditional probability density functions (pdf). This eliminates the need to recalculate the inverse and determinant, leading to a more reasonable solution in real-world scenario. We evaluate the performance of the proposed (recursive) sequential detector by using Monte-Carlo simulations and we use the conventional and non-recursive sequential detectors for comparisons. The results show that the recursive sequential detector has equal probabilities of false alarm and miss-detection with the conventional sequential detector and performs better than the non-recursive sequential detector. In terms of ASN, it maintains comparable results to the two conventional detectors. The recursive approach has reduced the computational complexity for matrix multiplication to from and it also has rendered the calculation of matrix determinant to be unnecessary. Therefore, by having better probabilities of error and reduced computational complexities under correlated observations, the proposed recursive sequential detector may become a viable alternative to obtain a more agile detection system as required in future applications, such as in radar and cognitive radio.

Nous proposons une methode « operationnelle » pour le probleme de tests d’hypotheses composites convexes lorsque les distributions sous-jacentes possedent des queues lourdes. Elle s’appuie sur la separation euclidienne des ensembles convexes et peut etre vue comme une extension de la methode developpee dans (Electron. J. Stat. 9 (2015) 1645–1712 ; Electron. J. Stat. 10 (2016) 2204–2242) pour l’etude des tests d’hypotheses reposant sur des techniques d’optimisation convexe. En particulier, nous montrons comment construire des tests quasi-optimaux pour des familles de distributions qui sont majorees, dans un sens precis, par une distribution symetrique quasi-spherique et etudions la relation entre les tests bases sur la separation euclidienne et les tests utilisant des potentiels. Nous appliquons la methodologie proposee au probleme de la detection sequentielle et decrivons sa mise en oeuvre pour la detection sequentielle de ruptures dans l’entree d’un systeme dynamique.

The problem of sequential detection of spontaneous changes in equations for unobserved state variables and observations of linear and nonlinear multivariate state-space models is considered. We consider the case of new additive terms and the case of changing coefficients of these equations. The proposed nonparametric method uses the idea of the “moving window” of observations. In Theorem 4.1 the exponential rate of convergence to zero for type 1 error probability (a wrong decision about a change) is proved. In Theorem 4.2 we consider type 2 error probability and the normalized (by the volume N of the moving window) delay time in change-point detection. Asymptotic optimality of the proposed method is proved in Theorem 5.1. Experimental study includes Monte Carlo examples of sequentially detected changes in coefficients of linear and nonlinear state-space models.

This paper formulates and solves a sequential detection problem that involves the mutual information (stochastic observability) of a Gaussian process observed in noise with missing measurements. The main result is that the optimal decision is characterized by a monotone policy on the partially ordered set of positive definite covariance matrices. This monotone structure implies that numerically efficient algorithms can be designed to estimate and implement monotone parametrized decision policies.The sequential detection problem is motivated by applications in radar scheduling where the aim is to maintain the mutual information of all targets within a specified bound. We illustrate the problem formulation and performance of monotone parametrized policies via numerical examples in fly-by and persistent-surveillance applications involving a GMTI (Ground Moving Target Indicator) radar.

This paper considers a statistical signal processing problem involving agent-based models of financial markets, which at a microlevel are driven by socially aware and risk-averse agents. These agents trade (buy or sell) stocks at each trading instant by using the decisions of all previous agents (social learning) in addition to a private (noisy) signal they receive on the value of the stock. We are interested in the following: 1) modelling the dynamics of these risk averse agents and 2) sequential detection of a market shock based on the behaviour of these agents. Structural results that characterize social learning under a risk measure, conditional value-at-risk (CVaR), are presented and formulation of the Bayesian change point detection problem is provided. The structural results exhibit two interesting properties: 1) risk averse agents herd more often than risk neutral agents and 2) the stopping set in the sequential detection problem is nonconvex. The framework is validated on data from the Yahoo! Tech Buzz game dataset and it is revealed that 1) the model identifies the value changes based on agent’s trading decisions. 2) Reasonable quickest detection performance is achieved when the agents are risk-averse.

Objective.Neuroprosthetic devices require multichannel stimulator systems with an increasing number of channels. However, there are inherent power losses in typical multichannel stimulation circuits caused by mismatches between the power supply voltage and the voltage required at each electrode to successfully stimulate tissue. This imposes a bottleneck towards high-channel-count devices, which is particularly severe in wirelessly-powered devices. Hence, advances in the power efficiency of stimulation systems are critical. To support these advances, this paper presents a methodology to identify and quantify power losses associated with different power supply scaling strategies in multichannel stimulation systems.Approach.The methodology uses distributions of stimulation amplitudes and electrode impedances to calculate power losses in multichannel systems. Experimental data from prior studies spanning various stimulation applications were analyzed to evaluate the performance of fixed, global, and stepped supply scaling methods, focusing on their impact on power dissipation and efficiency.Main Results.Variability in output conditions results in low power efficiency in multichannel stimulation systems across all applications. Stepped voltage scaling demonstrates substantial efficiency improvements, achieving an increase of 43% to 100%, particularly in high-channel-count applications with significant variability in tissue impedance. In contrast, global scaling proved effective only in systems with fewer channels and minimal inter-channel variation.Significance.The findings highlight the importance of tailoring power management strategies to specific applications to optimize efficiency while minimizing system complexity. The proposed methodology provides a framework for evaluating trade-offs between efficiency and system complexity, facilitating the design of more scalable and power-efficient neurostimulation systems.

The problem of sequentially detecting a moving anomaly is studied, in which the anomaly affects different parts of a sensor network over time. Each network sensor is characterized by a pre- and post-change distribution. Initially, the observations of each sensor are generated according to the corresponding pre-change distribution. After some unknown but deterministic time instant, a moving anomaly emerges, affecting different sets of sensors as time progresses. Our goal is to design a stopping procedure to detect the emergence of the anomaly as quickly as possible, subject to false alarms constraints. The problem is studied in a quickest change detection framework where it is assumed that the evolution of the anomaly is unknown but deterministic. A modification of Lorden's detection delay is proposed to account for the trajectory of the anomaly that maximizes the detection delay of a detection procedure. It is established that a Cumulative Sum-type test solves the resulting sequential detection problem exactly when the sensors are homogeneous. For the case of heterogeneous sensors, the proposed detection scheme can be modified to provide a first-order asymptotically optimal algorithm.

Recommender systems are widely used in electronic commerce, social media and online streaming services to provide personalized recommendations to the users by exploiting past ratings and interactions. This paper considers the security aspect with quick and accurate detection of attacks by observing the newly created profiles sequentially to prevent the damage which may be incurred by the injection of new profiles with dishonest ratings. The proposed framework consists of a latent variable model, which is trained by a variational EM algorithm, followed by a sequential detection algorithm. The latent variable model generates homogeneous representations of the users given their rating history and mixed data-type attributes such as age and gender. The representations are then exploited to generate univariate statistics to be efficiently used in a CUSUM-like sequential detection algorithm that can quickly detect persistent attacks while maintaining low false alarm rates. We apply our proposed framework to three different real-world datasets and exhibit superior performance in comparison to the existing baseline algorithms for both attack profile and sequential detection. Furthermore, we demonstrate robustness to different attack strategies and configurations.

In this study, a novel framework using multiple novelty detection filters is developed to learn a model of the normality of a robot’s visual perception, which is called multichannel novelty detection. Subsequently, the acquired model was used to highlight dissimilar perceptions when the robot explored an environment. The main purpose of fusing multiple novelty filters is that each novelty filter performs well in detecting specific types of novelties; therefore, a new framework is proposed that demonstrates a new way to combine multiple different purposed novelty detection filters together in order to yield an overall more robust novelty status on the visual features. To develop a multichannel novelty detection system, expectation- and appearance-based novelty detection models were used in this study. To become experts in detecting different types of novelty using these models, different features from the input image were extracted as inputs for the models. The expectation-based novelty detection model uses the MobileNetV2 deep network to extract the deep features of the input image, which is subsequently used to learn a sequential and temporal model of normality to detect novelty. By contrast, the appearance-based novelty detection model uses speeded up robust features (SURF), which provide more region-focused features within the input image, to identify whether a specific region of the image is novel. The proposed multichannel novelty detection system is a completely online and real-time approach that is very important for mobile robotics applications. The proposed framework was tested in three novel environments, and it was reported that the proposed multichannel novelty detection system performs better than expectation-based and appearance-based novelty filters separately. Statistically, in the three novel environments, the Matthews correlation coefficients are reported to be 0.94, 0.97, and 0.93, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> scores are reported to be 0.95, 0.97, and 0.93, respectively, which proves that and can be concluded as almost perfect statistically.

The analysis of remote sensing data enables us to detect changes and monitor land surface temperature (LST). However, analysis of times series data poses some challenges, including weather conditions, seasonality and noise, that limit the effectiveness of change detection algorithms. While existing algorithms perform relatively well for detecting abrupt transitions, reliable detection of gradual changes is more difficult. In this paper, we formulate the problem of spatiotemporal LST detection as a statistical sequential change detection problem. LST images are modeled as stochastic processes, with temperature changes reflected as changes in the parameters (i.e., mean) of the process. A generalized likelihood ratio test is used to detect these changes and estimate the exact time/space where they occur. To minimize processing time and memory requirements, we represent LST images by their reduced dimensionality using direct cosine transformation followed by principal component analysis. Statistical sequential analysis is used to provide a unified mathematical framework for the detection of both abrupt and gradual changes in LST observations of Bridgeton Missouri landfill over 17 years.

We sequentially observe independent observations $X_1, X_2,\ldots$ such that initially they have distribution $G_0$; at some unknown time $\nu$ they become stochastically larger, having distribution $G_1$. Neither $G_0$ nor $G_1$ is fully specified. We wish to detect that a change has taken place as soon as possible after its occurrence, subject to a constraint on the rate of false alarms. We derive a family of nonparametric sequential procedures based on ranks, with noncontiguous alternatives in mind. Large-sample approximations to the operating characteristics are obtained analytically. The proposed procedures all possess robustness of validity, because they are based on ranks. Near-optimal sensitivity can be obtained for specific alternatives by choosing an appropriate procedure. For example, when observations are normally distributed with one standard deviation shift in mean postchange, an appropriate nonparametric surveillance scheme yields 97% asymptotic relative efficiency, as compared to the optimal procedure when all distributional parameters are known. Our procedures are computationally feasible. Monte Carlo experiments confirm the applicability of the asymptotic calculations, including high levels of efficiency, for sample sizes met in practice.

The problem of sequential change diagnosis is considered, where a sequence of independent random elements is accessed sequentially, there is an abrupt change in its distribution at some unknown time, and there are two main operational goals: to quickly detect the change and to accurately identify the post-change distribution among a finite set of alternatives. A standard algorithm is considered, which does not explicitly address the isolation task and raises an alarm as soon as the CuSum statistic that corresponds to one of the post-change alternatives exceeds a certain threshold. It is shown that in certain cases, such as the so-called multichannel problem, this algorithm controls the worst-case conditional probability of false isolation and minimizes Lorden’s criterion, for every possible post-change distribution, to a first-order asymptotic approximation as the false alarm rate goes to zero sufficiently faster than the worst-case conditional probability of false isolation. These theoretical results are also illustrated with a numerical study.

The problem of quickly detecting the occurrence of an unusual event that happens on one of multiple independent data streams is considered. In the considered problem, all data streams at the initial are under normal state and are generated by probability distribution P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> . At some unknown time, an unusual event happens and the distribution of one data stream is modified to P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> while the distributions of the rest remain unchange. The observer can only observe one data stream at one time. With his sequential observations, the observer wants to design an online stopping rule and a data stream switching rule to minimize the detection delay, namely the time difference between the occurrence of the unusual event and the time of raising an alarm, while keeping the false alarm rate under control. We model the problem under non-Bayesian quickest detection framework, and propose a detection procedure based on the CUSUM statistic. We show that this proposed detection procedure is asymptotically optimal.

In this work we extend the setting of communication without power constraint, proposed by Poltyrev, to a t × r multiple-input multiple-output (MIMO) fast fading channels with channel state information (radio ) at the receiver. The optimal codewords density, or actually the optimal normalized log density (NLD), is considered. Poltyrev's capacity for this channel is the highest achievable NLD, at possibly large number of channel uses, that guarantees a vanishing error probability. For a given finite number of channel uses n and a fixed error probability e, there is a gap between the highest achievable NLD and Poltyrev's capacity. As in other channels, this gap asymptotically vanishes as the square root of V over n, multiplied by the inverse Q-function of the allowed error probability ϵ, where V is the channel dispersion. Currently our results are valid for t ≤ r.