Quickest changepoint detection in distributed multisensor systems under unknown parameters (original) (raw)
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Bayesian Methods for Multiple Change-Point Detection With Reduced Communication
IEEE Trans. Signal Process., 2020
In many modern applications, large-scale sensor networks are used to perform statistical inference tasks. In this article, we propose Bayesian methods for multiple change-point detection using a sensor network in which a fusion center (FC) can receive a data stream from each sensor. Due to communication limitations, the FC monitors only a subset of the sensors at each time slot. Since the number of change points can be high, we adopt the false discovery rate (FDR) criterion for controlling the rate of false alarms, while aiming to minimize the average detection delay (ADD) and the average number of observations (ANO) communicated until discovery. We propose two Bayesian detection procedures that handle the communication limitations by monitoring the subset of the sensors with the highest posterior probabilities of change points having occurred. This monitoring policy aims to minimize the delay between the occurrence of each change point and its declaration using the corresponding posterior probabilities. One of the proposed procedures is more conservative than the second one in terms of having lower FDR at the expense of higher ADD. It is analytically shown that both procedures control the FDR under a specified tolerated level and are also scalable in the sense that they attain ADD and ANO that do not increase asymptotically with the number of sensors. In addition, it is demonstrated that the proposed detection procedures are useful for trading off between reduced ADD and reduced ANO. Numerical simulations are conducted for validating the analytical results and for demonstrating the properties of the proposed procedures. Index Terms-Bayesian multiple change-point detection, false discovery rate, communication limitations, average detection delay, average number of observations.
2008 11th International Conference on Information Fusion, 2008
The decentralized quickest change detection problem is studied in sensor networks, where a set of sensors receive observations from a hidden Markov model X and send sensor messages to a central processor, called the fusion center, which makes a final decision when observations are stopped. It is assumed that the parameter thetas in the hidden Markov model for X changes from thetas0 to thetas1 at some unknown time. The problem is to determine the policies at the sensor and fusion center levels to jointly optimize the detection delay subject to the average run length (ARL) to false alarm constraint. In this article, a CUSUM-type fusion rule with stationary binary sensor messages is studied and a simple method for choosing the optimal local sensor thresholds is introduced. Further research is also given.
Change Detection for Large Distributed Sensor Networks With Multitriggered Local Sensors
IEEE Access
The emergence of large sensor networks and the Internet of Things has reinvigorated interest into distributed quickest change detection. Important shortcomings of existing approaches are ease of design, flexibility in communication, and applicability to larger networks. The new approach proposed in this work features local sensors that can be triggered multiple times, i.e., can reset and continue monitoring after transmitting their decisions. With larger sensor networks as a focus, the system allows for multiple simultaneous transmissions to a fusion center within bandwidth limitations. The proposed system uses the cumulative-sum procedure at local sensors to binarize local decisions, which are then transmitted to the fusion center that also employs cumulative-sum quickest detection. Test overdesign due to sequential test overshoot is avoided, and global and local thresholds are chosen to meet a desired false alarm rate constraint using numerical computation of expected delay performance. The system compares favourably to several existing methods while offering greater flexibility in the amount of fusion center communication. INDEX TERMS Sequential change detection, distributed detection, sequential probability ratio test, CUSUM, sensor networks, decision fusion.
Asymptotically optimum tests for decentralized change detection
We propose an asymptotically optimum test for the problem of decentralized sequential hypothesis testing in continuous time, in the case where the sensors have full local memory and no feedback from the fusion center. According to our scheme, the sensors perform locally repeated SPRTs and communicate, asynchronously, their one-bit decisions to the fusion center. The fusion center in turn uses the received information to perform a centralized SPRT in order to make the final decision. The expected time for a decision of the proposed scheme differs from the optimum continuous-time centralized SPRT only by a constant. This fact suggests order-2 asymptotic optimality of our test as compared to existing schemes that are optimal of order-1. Moreover, simulation experiments reveal that the performance of our scheme is significantly better than that of the discrete-time centralized SPRT.
One shot schemes for decentralized quickest change detection
Computing Research Repository, 2008
This work considers the problem of quickest detection with N distributed sensors that receive continuous sequential observations from the environment. These sensors employ cumulative sum (CUSUM) strategies and communicate to a central fusion center by one shot schemes. One shot schemes are schemes in which the sensors communicate with the fusion center only once, after which they must signal a detection. The communication is clearly asynchronous and the case is considered in which the fusion center employs a minimal strategy, which means that it declares an alarm when the first communication takes place. It is assumed that the observations received at the sensors are independent and that the time points at which the appearance of a signal can take place are different. It is shown that there is no loss of performance of one shot schemes as compared to the centralized case in an extended Lorden minmax sense, since the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound.
Quickest Change Detection in Hidden Markov Models for Sensor Networks
2009
The decentralized quickest change detection problem is stu died in sensor networks, where a set of sensors receive observations from a hidden Markov model (HMM) X and send sensor messages to a central processor, called the f usion center, which makes a final decision when observations are stopped. I t is assumed that the parameter θ in the hidden Markov model for X changes fromθ0 to θ1 at some unknown time. The primary goal of this paper is to inve stigate how to choose the best stationary quantizers in the context of quickest change det ction in sensor networks. A closely related goal of this pap er is to report the distribution of the run length to false alarm for H MM in some scenarios.
A hybrid fusion system applied to off-line detection and change-points estimation
Information Fusion, 2010
In this paper we investigate the problem of off-line detection and estimation of change-point instants on data provided by two sensors. In this context sensors synchronization, that provides simultaneous change-point instants on the data, is in practice a constraint hard to maintain. The contribution of this work is the proposition of a hybrid fusion system that performs as well as the centralized fusion detector respectively optimal for simultaneous and not simultaneous change. The system we propose is composed of two GLR tests (Generalized Likelihood Ratio) defined as centralized fusion detectors for the two configurations of change-point (simultaneous and not simultaneous). Decisions of these fusion detectors are combined in a fusion operator. The system is hybrid (centralized and distributed) because the distributed decisions supplied by the centralized fusion systems are combined in a global fusion operator. The contribution of our method is shown on synthetic data. The application to the treatment of a real multi-carrier GPS signal shows the feasibility of the method.
Precision of sequential change point detection
Applicationes Mathematicae, 2017
A random sequence having two segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each process are known and a priori distribution of the disorder moment is given. The decision maker aim is to detect the moment of the transition probabilities change. The detection of the disorder rarely is precise. The decision maker accepts some deviation in estimation of the disorder moment. In the considered model the aim is to indicate the change point with fixed, bounded error with maximal probability. The case with various precision for over and under estimation of this point is analyzed. The case when the disorder does not appears with positive probability is also included. The results insignificantly extends range of application, explain the structure of optimal detector in various circumstances and shows new details of the solution construction. The motivation for this investigation is the modelling of the attacks in the node of networks. The objectives is to detect one of the attack immediately or in very short time before or after it appearance with highest probability. The problem is reformulated to optimal stopping of the observed sequences. The detailed analysis of the problem is presented to show the form of optimal decision function.
Decentralized sequential detection with a fusion center performing the sequential test
IEEE Transactions on Information Theory, 1993
A decentralized sequential detection problem is considered in which each one of a set of sensors receives a sequence of observations about the hypothesis. Each sensor sends a sequence of summary messages to the fusion center where a sequential test is carried out to determine the true hypothesis. A Bayesian framework for this problem is introduced, and for the case when the information structure in the system is quasi-classical, it is shown that the problem is tractable. A detailed analysis of this case is presented along with some numerical results.
Consensus based distributed change detection using Generalized Likelihood Ratio Methodology
2011
In this paper a novel distributed algorithm derived from the Generalized Likelihood Ratio is proposed for real time change detection using sensor networks. The algorithm is based on a combination of recursively generated local statistics and a global consensus strategy, and does not require any fusion center. The problem of detection of an unknown change in the mean of an observed random process is discussed and the performance of the algorithm is analyzed in the sense of a measure of the error with respect to the corresponding centralized algorithm. The analysis encompasses asymmetric constant and randomly time varying matrices describing communications in the network, as well as constant and time varying forgetting factors in the underlying recursions. An analogous algorithm for detection of an unknown change in the variance is also proposed. Simulation results illustrate characteristic properties of the algorithms including detection performance in terms of detection delay and false alarm rate. They also show that the theoretical analysis connected to the problem of detecting change in the mean can be extended to the problem of detecting change in the variance.