Quickest Change Detection of a Markov Process Across a Sensor Array

Recent attention in quickest change detection in the multi-sensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general scenario is considered where the change propagates across the sensors, and its propagation can be modeled as a Markov process. A centralized, Bayesian version of this problem, with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process, is considered. The problem of minimizing the average detection delay subject to false alarm constraints is formulated as a partially observable Markov decision process (POMDP). Insights into the structure of the optimal stopping rule are presented. In the limiting case of rare disruptions, we show that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened. We establish the asymptotic optimality (in the vanishing false alarm probability regime) of this threshold test under a certain condition on the Kullback-Leibler (K-L) divergence between the post- and the pre-change densities. In the special case of near-instantaneous change propagation across the sensors, this condition reduces to the mild condition that the K-L divergence be positive. Numerical studies show that this low complexity threshold test results in a substantial improvement in performance over naive tests such as a single-sensor test or a test that wrongly assumes that the change propagates instantaneously.Comment: 40 pages, 5 figures, Submitted to IEEE Trans. Inform. Theor

Distributed Detection over Fading MACs with Multiple Antennas at the Fusion Center

A distributed detection problem over fading Gaussian multiple-access channels is considered. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify and forward scheme. The fusion center has multiple antennas with different channel models considered between the sensors and the fusion center, and different cases of channel state information are assumed at the sensors. The performance is evaluated in terms of the error exponent for each of these cases, where the effect of multiple antennas at the fusion center is studied. It is shown that for zero-mean channels between the sensors and the fusion center when there is no channel information at the sensors, arbitrarily large gains in the error exponent can be obtained with sufficient increase in the number of antennas at the fusion center. In stark contrast, when there is channel information at the sensors, the gain in error exponent due to having multiple antennas at the fusion center is shown to be no more than a factor of (8/pi) for Rayleigh fading channels between the sensors and the fusion center, independent of the number of antennas at the fusion center, or correlation among noise samples across sensors. Scaling laws for such gains are also provided when both sensors and antennas are increased simultaneously. Simple practical schemes and a numerical method using semidefinite relaxation techniques are presented that utilize the limited possible gains available. Simulations are used to establish the accuracy of the results.Comment: 21 pages, 9 figures, submitted to the IEEE Transactions on Signal Processin

Distributed M-ary hypothesis testing for decision fusion in multiple-input multiple output wireless sensor networks

In this study, the authors study binary decision fusion over a shared Rayleigh fading channel with multiple antennas at the decision fusion centre (DFC) in wireless sensor networks. Three fusion rules are derived for the DFC in the case of distributed M-ary hypothesis testing, where M is the number of hypothesis to be classified. Namely, the optimum maximum a posteriori (MAP) rule, the augmented quadratic discriminant analysis (A-QDA) rule and MAP observation bound. A comparative simulation study is carried out between the proposed fusion rules in-terms of detection performance and receiver operating characteristic (ROC) curves, where several parameters are taken into account such as the number of antennas, number of local detectors, number of hypothesis and signal-to-noise ratio. Simulation results show that the optimum (MAP) rule has better detection performance than A-QDA rule. In addition, increasing the number of antennas will improve the detection performance up to a saturation level, while increasing the number of the hypothesis will deteriorate the detection performance

One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. The proposed scheme achieves the order-optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review format), 4 figures. Submitted to IEEE Transactions on Signal Processing. Current version is updated for journal submission: revised author list, modified formulation and framework. Previous version appeared in Proceedings of Allerton Conference On Communication, Control, and Computing 200

Distributed detection, localization, and estimation in time-critical wireless sensor networks

In this thesis the problem of distributed detection, localization, and estimation (DDLE) of a stationary target in a fusion center (FC) based wireless sensor network (WSN) is considered. The communication process is subject to time-critical operation, restricted power and bandwidth (BW) resources operating over a shared communication channel Buffering from Rayleigh fading and phase noise. A novel algorithm is proposed to solve the DDLE problem consisting of two dependent stages: distributed detection and distributed estimation. The WSN performs distributed detection first and based on the global detection decision the distributed estimation stage is performed. The communication between the SNs and the FC occurs over a shared channel via a slotted Aloha MAC protocol to conserve BW. In distributed detection, hard decision fusion is adopted, using the counting rule (CR), and sensor censoring in order to save power and BW. The effect of Rayleigh fading on distributed detection is also considered and accounted for by using distributed diversity combining techniques where the diversity combining is among the sensor nodes (SNs) in lieu of having the processing done at the FC. Two distributed techniques are proposed: the distributed maximum ratio combining (dMRC) and the distributed Equal Gain Combining (dEGC). Both techniques show superior detection performance when compared to conventional diversity combining procedures that take place at the FC. In distributed estimation, the segmented distributed localization and estimation (SDLE) framework is proposed. The SDLE enables efficient power and BW processing. The SOLE hinges on the idea of introducing intermediate parameters that are estimated locally by the SNs and transmitted to the FC instead of the actual measurements. This concept decouples the main problem into a simpler set of local estimation problems solved at the SNs and a global estimation problem solved at the FC. Two algorithms are proposed for solving the local problem: a nonlinear least squares (NLS) algorithm using the variable projection (VP) method and a simpler gird search (GS) method. Also, Four algorithms are proposed to solve the global problem: NLS, GS, hyperspherical intersection method (HSI), and robust hyperspherical intersection (RHSI) method. Thus, the SDLE can be solved through local and global algorithm combinations. Five combinations are tied: NLS2 (NLS-NLS), NLS-HSI, NLS-RHSI, GS2, and GS-N LS. It turns out that the last algorithm combination delivers the best localization and estimation performance. In fact , the target can be localized with less than one meter error. The SNs send their local estimates to the FC over a shared channel using the slotted-Aloha MAC protocol, which suits WSNs since it requires only one channel. However, Aloha is known for its relatively high medium access or contention delay given the medium access probability is poorly chosen. This fact significantly hinders the time-critical operation of the system. Hence, multi-packet reception (MPR) is used with slotted Aloha protocol, in which several channels are used for contention. The contention delay is analyzed for slotted Aloha with and without MPR. More specifically, the mean and variance have been analytically computed and the contention delay distribution is approximated. Having theoretical expressions for the contention delay statistics enables optimizing both the medium access probability and the number of MPR channels in order to strike a trade-off between delay performance and complexity

Distributed M-ary hypothesis testing for decision fusion in multiple-input multipleoutput wireless sensor networks

In this study, the authors study binary decision fusion over a shared Rayleigh fading channel with multiple antennas at the decision fusion centre (DFC) in wireless sensor networks. Three fusion rules are derived for the DFC in the case of distributed M-ary hypothesis testing, where M is the number of hypothesis to be classified. Namely, the optimum maximum a posteriori (MAP) rule, the augmented quadratic discriminant analysis (A-QDA) rule and MAP observation bound. A comparative simulation study is carried out between the proposed fusion rules in-terms of detection performance and receiver operating characteristic (ROC) curves, where several parameters are taken into account such as the number of antennas, number of local detectors, number of hypothesis and signal-to-noise ratio. Simulation results show that the optimum (MAP) rule has better detection performance than A-QDA rule. In addition, increasing the number of antennas will improve the detection performance up to a saturation level, while increasing the number of the hypothesis will deteriorate the detection performance