Optimal Inference for Distributed Detection

In distributed detection, there does not exist an automatic way of generating optimal decision strategies for non-affine decision functions. Consequently, in a detection problem based on a non-affine decision function, establishing optimality of a given decision strategy, such as a generalized likelihood ratio test, is often difficult or even impossible. In this thesis we develop a novel detection network optimization technique that can be used to determine necessary and sufficient conditions for optimality in distributed detection for which the underlying objective function is monotonic and convex in probabilistic decision strategies. Our developed approach leverages on basic concepts of optimization and statistical inference which are provided in appendices in sufficient detail. These basic concepts are combined to form the basis of an optimal inference technique for signal detection. We prove a central theorem that characterizes optimality in a variety of distributed detection architectures. We discuss three applications of this result in distributed signal detection. These applications include interactive distributed detection, optimal tandem fusion architecture, and distributed detection by acyclic graph networks. In the conclusion we indicate several future research directions, which include possible generalizations of our optimization method and new research problems arising from each of the three applications considered

Distributed Detection With Multiple Sensors: Part I—Fundamentals

In this paper, basic results on distributed detection are reviewed. In particular, we consider the parallel and the serial architectures in some detail and discuss the decision rules obtained from their optimization based on the Neyman–Pearson (NP) criterion and the Bayes formulation. For conditionally independent sensor observations, the optimality of the likelihood ratio test (LRT) at the sensors is established. General comments on several important issues are made including the computational complexity of obtaining the optimal solutions, the design of detection networks with more general topologies, and applications to different areas

Decentralized Narrowband and Wideband Spectrum Sensing with Correlated Observations

This dissertation evaluates the utility of several approaches to the design of good distributed sensing systems for both narrowband and wideband spectrum sensing problems with correlated sensor observations

On Distributed and Acoustic Sensing for Situational Awareness

Recent advances in electronics enable the development of small-sized, low-cost, low-power, multi-functional sensor nodes that possess local processing capability as well as to work collaboratively through communications. They are able to sense, collect, and process data from the surrounding environment locally. Collaboration among the nodes are enabled due to their integrated communication capability. Such a system, generally referred to as sensor networks are widely used in various of areas, such as environmental monitoring, asset tracking, indoor navigation, etc. This thesis consists of two separate applications of such mobile sensors. In this first part, we study decentralized inference problems with dependent observations in wireless sensor networks. Two separate problems are addressed in this part: one pertaining to collaborative spectrum sensing while the other on distributed parameter estimation with correlated additive Gaussian noise. In the second part, we employ a single acoustic sensor with co-located microphone and loudspeaker to reconstruct a 2-D convex polygonal room shape. For spectrum sensing, we study the optimality of energy detection that has been widely used in the literature. This thesis studies the potential optimality (or sub-optimality) of the energy detector in spectrum sensing. With a single sensing node, we show that the energy detector is provably optimal for most cases and for the case when it is not theoretically optimal, its performance is nearly indistinguishable from the true optimal detector. For cooperative spectrum sensing where multiple nodes are employed, we use a recently proposed framework for distributed detection with dependent observations to establish the optimality of energy detector for several cooperative spectrum sensing systems and point out difficulties for the remaining cases. The second problem in decentralized inference studied in this thesis is to investigate the impact of noise correlation on decentralized estimation performance. For a tandem network with correlated additive Gaussian noises, we establish that threshold quantizer on local observations is optimal in the sense of maximizing Fisher information at the fusion center; this is true despite the fact that subsequent estimators may differ at the fusion center, depending on the statistical distribution of the parameter to be estimated. In addition, it is always beneficial to have the better sensor (i.e. the one with higher signal-to-noise ratio) serve as the fusion center in a tandem network for all correlation regimes. Finally, we identify different correlation regimes in terms of their impact on the estimation performance. These include the well known case where negatively correlated noises benefit estimation performance as it facilitates noise cancellation, as well as two distinct regimes with positively correlated noises compared with that of the independent case. In the second part of this thesis, a practical problem of room shape reconstruction using first-order acoustic echoes is explored. Specifically, a single mobile node, with co-located loudspeaker, microphone and internal motion sensors, is deployed and times of arrival of the first-order echoes are measured and used to recover room shape. Two separate cases are studied: the first assumes no knowledge about the sensor trajectory, and the second one assumes partial knowledge on the sensor movement. For either case, the uniqueness of the mapping between the first-order echoes and the room geometry is discussed. Without any trajectory information, we show that first-order echoes are sufficient to recover 2-D room shapes for all convex polygons with the exception of parallelograms. Algorithmic procedure is developed to eliminate the higher-order echoes among the collected echoes in order to retrieve the room geometry. In the second case, the mapping is proved for any convex polygonal shapes when partial trajectory information from internal motion sensors is available.. A practical algorithm for room reconstruction in the presence of noise and higher order echoes is proposed

Adaptive quantization in wireless sensor networks with encryption

We consider the estimation of a deterministic unknown parameter in an encrypted wireless sensor networks. Adaptive quantization is used on the sensor\u27s observation and the outputs of the sensors are then encrypted using a probabilistic cipher. In a conventional fixed quantization scheme, estimation error grows exponentially with the difference between the threshold and the unknown parameter to be estimated. Hence, to avoid this, we used and adaptive quantization scheme where each sensor adaptively adjusts its quantization threshold. We find the Cramer-Rao Lower Bound for the Ally Fusion Center (AFC) and then find the optimal estimate of the unknown parameter for the AFC. To find this, we first prove that the sequence of thresholds used for the quantization process forms a markov chain and that this chain is recurrent non-null and thus has a stationary distribution. This distribution is then obtained analytically in closed form as well as through numerical methods. The optimal estimate of the unknown parameter for the AFC is obtained asymptotically in the number of sensors. The performance of the Third Party Fusion Center (TPFC) is only computed through simulation and compared to that of AFC