We consider a joint sensor and controller design problem for linear Gaussian stochastic systems in which a weighted sum of quadratic control cost and the amount of information acquired by the sensor is minimized. This problem formulation is motivated by situations where a control law must be designed in the presence of sensing, communication, and privacy constraints. We show that the optimal joint sensor-controller design is relatively easy when the sensing policy is restricted to be linear. Namely, an explicit form of the optimal linear sensor equation, the Kalman filter, and the certainty equivalence controller that jointly solves the problem can be efficiently found by semidefinite programming (SDP). Whether the linearity assumption in our design is restrictive or not is currently an open problem.
However, the majority of the existing work in this context assume sensor models and or channel models , and are different from ). A few exceptions include @cite_13 and @cite_26 , where sensor-controller joint design problems are considered. However, these works are concerned with sensor power constraints rather than information constraints, and are different from ). Our problem formulation ) falls into a general class of sensor optimization problems considered in @cite_17 , where several results are derived regarding the convexity of the problem and the existence of an optimal solution under different choices of topologies in the space of sensors. However, no structural results on specific problems appear there.
@cite_26 @cite_13 @cite_17
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In this paper, we address the problem of optimizing the detection performance of sensor networks under communication constraints on the common access channel. Our work helps understanding tradeoffs between sensor network para-meters like number of sensors, degree of quantization at each local sensor, and SNR. Traditionally, this problem is tack-led using asymptotic assumptions on the number of sensors, an approach that leads to the abstraction of important details such as the structure of the fusion center. We adopt a non-asymptotic approach and optimize both, the sensing and the fusion sides with respect to the probability of detection error. We show that the optimal fusion rule has an interesting structure similar to themajority-voting rule. In addition, we study the convergence with respect to the number of sensors of the performance of the fusion rule. We show that convergence is SNR dependent and that, in low-SNR environments, asymptotics may require a large number of sensors. This paper addresses the coverage breach problem in wireless sensor networks with limited bandwidths. In wireless sensor networks, sensor nodes are powered by batteries. To make efficient use of battery energy is critical to sensor network lifetimes. When targets are redundantly covered by multiple sensors, especially in stochastically deployed sensor networks, it is possible to save battery energy by organizing sensors into mutually exclusive subsets and alternatively activating only one subset at any time. Active nodes are responsible for sensing, computing and communicating. While the coverage of each subset is an important metric for sensor organization, the size of each subset also plays an important role in sensor network performance because when active sensors periodically send data to base stations, contention for channel access must be considered. The number of available channels imposes a limit on the cardinality of each subset. Coverage breach happens when a subset of sensors cannot completely cover all the targets. To make efficient use of both energy and bandwidth with a minimum coverage breach is the goal of sensor network design. This paper presents the minimum breach problem using a mathematical model, studies the computational complexity of the problem, and provides two approximate heuristics. Effects of increasing the number of channels and increasing the number of sensors on sensor network coverage are studied through numerical simulations. Overall, the simulation results reveal that when the number of sensors increases, network lifetimes can be improved without loss of network coverage if there is no bandwidth constraint; with bandwidth constraints, network lifetimes may be improved further at the cost of coverage breach. This brief introduces a class of problems and models for the prediction of the scalar field of interest from noisy observations collected by mobile sensor networks. It also introduces the problem of optimal coordination of robotic sensors to maximize the prediction quality subject to communication and mobility constraints either in a centralized or distributed manner. To solve such problems, fully Bayesian approaches are adopted, allowing various sources of uncertainties to be integrated into an inferential framework effectively capturing all aspects of variability involved. The fully Bayesian approach also allows the most appropriate values for additional model parameters to be selected automatically by data, and the optimal inference and prediction for the underlying scalar field to be achieved. In particular, spatio-temporal Gaussian process regression is formulated for robotic sensors to fuse multifactorial effects of observations, measurement noise, and prior distributions for obtaining the predictive distribution of a scalar environmental field of interest. New techniques are introduced to avoid computationally prohibitive Markov chain Monte Carlo methods for resource-constrained mobile sensors. Bayesian Prediction and Adaptive Sampling Algorithms for Mobile Sensor Networks starts with a simple spatio-temporal model and increases the level of model flexibility and uncertainty step by step, simultaneously solving increasingly complicated problems and coping with increasing complexity, until it ends with fully Bayesian approaches that take into account a broad spectrum of uncertainties in observations, model parameters, and constraints in mobile sensor networks. The book is timely, being very useful for many researchers in control, robotics, computer science and statistics trying to tackle a variety of tasks such as environmental monitoring and adaptive sampling, surveillance, exploration, and plume tracking which are of increasing currency. Problems are solved creatively by seamless combination of theories and concepts from Bayesian statistics, mobile sensor networks, optimal experiment design, and distributed computation. We consider the problem of decentralized detection under constraints on the number of bits that can be transmitted by each sensor. In contrast to most previous work, in which the joint distribution of sensor observations is assumed to be known, we address the problem when only a set of empirical samples is available. We propose a novel algorithm using the framework of empirical risk minimization and marginalized kernels, and analyze its computational and statistical properties both theoretically and empirically. We provide an efficient implementation of the algorithm, and demonstrate its performance on both simulated and real data sets. In a sensor network, in practice, the communication among sensors is subject to: 1) errors that can cause failures of links among sensors at random times; 2) costs; and 3) constraints, such as power, data rate, or communication, since sensors and networks operate under scarce resources. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. We model the network as a Bernoulli random topology and establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail. In particular, a necessary and sufficient condition is for the algebraic connectivity of the mean graph topology to be strictly positive. With these results, we show that the topology design with random link failures, link communication costs, and a communication cost constraint is a constrained convex optimization problem that can be efficiently solved for large networks by semidefinite programming techniques. Simulations demonstrate that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the performance of a non-random network at a fraction of the communication cost. We address the problem of placing a sensor network so as to minimize the uncertainty in estimating the position of targets. The novelty of our formulation is in the sensing model: we focus on stereo sensors where the measurements from two sensors must be combined for an estimation. We study two versions of this problem. In the first version, which we call the placement problem, we are given a workspace and an error threshold. The objective is to place a minimum number of cameras so that no matter where the target is located in the workspace, the uncertainty in localizing it is less than the threshold. For this problem, we present an approximation algorithm and prove that the deviation of its performance from the optimal value is bounded by a constant. In the second version, called the deployment problem, we study the problem of relocating a mobile sensor team to minimize the uncertainty in localizing possibly moving targets. We present a distributed, discrete-time algorithm which explicit addresses communication and motion constraints and show how to compute the optimal move within the time-step for a given target sensor-pair assignment. The utility of the algorithm is demonstrated with simulations This paper considers the problem of blindly calibrating sensor response using routine sensor network measurements. We show that as long as the sensors slightly oversample the signals of interest, then unknown sensor gains can be perfectly recovered. Remarkably, neither a controlled stimulus nor a dense deployment is required. We also characterize necessary and sufficient conditions for the identification of unknown sensor offsets. Our results exploit incoherence conditions between the basis for the signals and the canonical or natural basis for the sensor measurements. Practical algorithms for gain and offset identification are proposed based on the singular value decomposition and standard least squares techniques. We investigate the robustness of the proposed algorithms to model mismatch and noise on both simulated data and on data from current sensor network deployments. When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. There are several common strategies to address this task, for example, geometry or disk models, placing sensors at the points of highest entropy (variance) in the GP model, and A-, D-, or E-optimal design. In this paper, we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected. We prove that the problem of finding the configuration that maximizes mutual information is NP-complete. To address this issue, we describe a polynomial-time approximation that is within (1-1 e) of the optimum by exploiting the submodularity of mutual information. We also show how submodularity can be used to obtain online bounds, and design branch and bound search procedures. We then extend our algorithm to exploit lazy evaluations and local structure in the GP, yielding significant speedups. We also extend our approach to find placements which are robust against node failures and uncertainties in the model. These extensions are again associated with rigorous theoretical approximation guarantees, exploiting the submodularity of the objective function. We demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real-world data sets. Distributed processing through ad hoc and sensor networks is having a major impact on scale and applications of computing. The creation of new cyber-physical services based on wireless sensor devices relies heavily on how well communication protocols can be adapted and optimized to meet quality constraints under limited energy resources. The IEEE 802.15.4 medium access control protocol for wireless sensor networks can support energy efficient, reliable, and timely packet transmission by a parallel and distributed tuning of the medium access control parameters. Such a tuning is difficult, because simple and accurate models of the influence of these parameters on the probability of successful packet transmission, packet delay, and energy consumption are not available. Moreover, it is not clear how to adapt the parameters to the changes of the network and traffic regimes by algorithms that can run on resource-constrained devices. In this paper, a Markov chain is proposed to model these relations by simple expressions without giving up the accuracy. In contrast to previous work, the presence of limited number of retransmissions, acknowledgments, unsaturated traffic, packet size, and packet copying delay due to hardware limitations is accounted for. The model is then used to derive a distributed adaptive algorithm for minimizing the power consumption while guaranteeing a given successful packet reception probability and delay constraints in the packet transmission. The algorithm does not require any modification of the IEEE 802.15.4 medium access control and can be easily implemented on network devices. The algorithm has been experimentally implemented and evaluated on a testbed with off-the-shelf wireless sensor devices. Experimental results show that the analysis is accurate, that the proposed algorithm satisfies reliability and delay constraints, and that the approach reduces the energy consumption of the network under both stationary and transient conditions. Specifically, even if the number of devices and traffic configuration change sharply, the proposed parallel and distributed algorithm allows the system to operate close to its optimal state by estimating the busy channel and channel access probabilities. Furthermore, results indicate that the protocol reacts promptly to errors in the estimation of the number of devices and in the traffic load that can appear due to device mobility. It is also shown that the effect of imperfect channel and carrier sensing on system performance heavily depends on the traffic load and limited range of the protocol parameters. We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 sub-problems with different conditions on the gains, specifially i) gains with different amplitude and the same phase, ii) gains with the same amplitude and different phase and iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided. Processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions. The general problem considers sensors with arbitrary locations and arbitrary directional characteristics (gain phase polarization) in a noise interference environment of arbitrary covariance matrix. This report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution. A description is given of the multiple signal classification (MUSIC) algorithm, which provides asymptotically unbiased estimates of 1) number of incident wavefronts present; 2) directions of arrival (DOA) (or emitter locations); 3) strengths and cross correlations among the incident waveforms; 4) noise interference strength. Examples and comparisons with methods based on maximum likelihood (ML) and maximum entropy (ME), as well as conventional beamforming are included. An example of its use as a multiple frequency estimator operating on time series is included. One of the research issues in wireless sensor networks (WSNs) is how to efficiently deploy sensors to cover an area. In this paper, we solve the k-coverage sensor deployment problem to achieve multi-level coverage of an area I. We consider two sub-problems: k-coverage placement and distributed dispatch problems. The placement problem asks how to determine the minimum number of sensors required and their locations in I to guarantee that I is k-covered and the network is connected; the dispatch problem asks how to schedule mobile sensors to move to the designated locations according to the result computed by the placement strategy such that the energy consumption due to movement is minimized. Our solutions to the placement problem consider both the binary and probabilistic sensing models, and allow an arbitrary relationship between the communication distance and sensing distance of sensors. For the dispatch problem, we propose a competition-based and a pattern-based schemes. The former allows mobile sensors to bid for their closest locations, while the latter allows sensors to derive the target locations on their own. Our proposed schemes are efficient in terms of the number of sensors required and are distributed in nature. Simulation results are presented to verify their effectiveness. In this paper we develop a framework for a sequential decision making under budget constraints for multi-class classification. In many classification systems, such as medical diagnosis and homeland security, sequential decisions are often warranted. For each instance, a sensor is first chosen for acquiring measurements and then based on the available information one decides (rejects) to seek more measurements from a new sensor modality or to terminate by classifying the example based on the available information. Different sensors have varying costs for acquisition, and these costs account for delay, throughput or monetary value. Consequently, we seek methods for maximizing performance of the system subject to budget constraints. We formulate a multi-stage multi-class empirical risk objective and learn sequential decision functions from training data. We show that reject decision at each stage can be posed as supervised binary classification. We derive bounds for the VC dimension of the multi-stage system to quantify the generalization error. We compare our approach to alternative strategies on several multi-class real world datasets. Sensor networks not only have the potential to change the way we use, interact with, and view computers, but also the way we use, interact with, and view the world around us. In order to maximize the effectiveness of sensor networks, one has to identify, examine, understand, and provide solutions for the fundamental problems related to wireless embedded sensor networks. We believe that one of such problems is to determine how well the sensor network monitors the instrumented area. These problems are usually classified as coverage problems. There already exist several methods that have been proposed to evaluate a sensor network's coverage.We start from one of such method and provide a new approach to complement it. The method of using the minimal exposure path to quantify coverage has been optimally solved using a numerical approximation approach. The minimal exposure path can be thought of as the worst-case coverage of a sensor network. Our first goal is to develop an efficient localized algorithm that enables a sensor network to determine its minimal exposure path. The theoretical highlight of this paper is the closed-form solution for minimal exposure in the presence of a single sensor. This solution is the basis for the new and significantly faster localized approximation algorithm that reduces the theoretical complexity of the previous algorithm. On the other hand, we introduce a new coverage problem - the maximal exposure path - which is in a sense the best-case coverage path for a sensor network. We prove that the maximal exposure path problem is NP-hard, and thus, we provide heuristics to generate approximate solutions.In addition, we demonstrate the effectiveness of our algorithms through several simulations. In the case of the minimal single-source minimal exposure path, we use variational calculus to determine exact solutions. For the case of maximal exposure, we use networks with varying numbers of sensors and exposure models. We consider the problem of scheduling a set of sensors to observe the state of a discrete-time linear system subject to a limited energy budget. Our goal is to devise a sensor schedule that minimizes the mean squared error (MSE) of an optimal estimator (i.e., the Kalman Filter). Both the minimum-MSE and the minimum-cardinality optimal sensor scheduling problems are inherently combinatorial, and computationally intractable. We remedy the combinatorial complexity by using a greedy heuristic; the greedy heuristic is guaranteed to return near-optimal solutions when minimizing supermodular objectives. While it is known that the MSE is not supermodular (with counterexamples available in literature), we provide conditions on the prior information matrix and on the observation matrix under which supermodularity holds. More specifically, we require the prior information matrix to be a strictly-diagonally-dominant M-matrix (plus an extra technical requirement on its inverse). Empirical results confirm that random M-matrices lead to supermodular problems, while this is not the case for generic prior information matrices. M-matrices naturally arise in estimation problems over networks and we provide a practical application of our findings to an energy-constrained multi robot localization problem. A key problem in sensor networks is to decide which sensors to query when, in order to obtain the most useful information (e.g., for performing accurate prediction), subject to constraints (e.g., on power and bandwidth). In many applications the utility function is not known a priori, must be learned from data, and can even change over time. Furthermore for large sensor networks solving a centralized optimization problem to select sensors is not feasible, and thus we seek a fully distributed solution. In this paper, we present Distributed Online Greedy (DOG), an efficient, distributed algorithm for repeatedly selecting sensors online, only receiving feedback about the utility of the selected sensors. We prove very strong theoretical no-regret guarantees that apply whenever the (unknown) utility function satisfies a natural diminishing returns property called submodularity. Our algorithm has extremely low communication requirements, and scales well to large sensor deployments. We extend DOG to allow observation-dependent sensor selection. We empirically demonstrate the effectiveness of our algorithm on several real-world sensing tasks. The sensor network localization (SNL) problem in embedding dimension @math consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the sensors (called anchors). Current solution techniques relax this problem to a weighted, nearest, (positive) semidefinite programming (SDP) completion problem by using the linear mapping between Euclidean distance matrices (EDM) and semidefinite matrices. The resulting SDP is solved using primal-dual interior point solvers, yielding an expensive and inexact solution. This relaxation is highly degenerate in the sense that the feasible set is restricted to a low dimensional face of the SDP cone, implying that the Slater constraint qualification fails. Cliques in the graph of the SNL problem give rise to this degeneracy in the SDP relaxation. In this paper, we take advantage of the absence of the Slater constraint qualification and derive a technique for the SNL problem, with exact data, that explicitly solves the corresponding rank restricted SDP problem. No SDP solvers are used. For randomly generated instances, we are able to efficiently solve many huge instances of this NP-hard problem to high accuracy by finding a representation of the minimal face of the SDP cone that contains the SDP matrix representation of the EDM. The main work of our algorithm consists in repeatedly finding the intersection of subspaces that represent the faces of the SDP cone that correspond to cliques of the SNL problem. The problem of deploying sensors in a large water distribution network is considered, in order to detect the malicious introduction of contaminants. It is shown that a large class of realistic objective functions—such as reduction of detection time and the population protected from consuming contaminated water—exhibits an important diminishing returns effect called submodularity. The submodularity of these objectives is exploited in order to design efficient placement algorithms with provable performance guarantees. The algorithms presented in this paper do not rely on mixed integer programming, and scale well to networks of arbitrary size. The problem instances considered in the approach presented in this paper are orders of magnitude (a factor of 72) larger than the largest problems solved in the literature. It is shown how the method presented here can be extended to multicriteria optimization, selecting placements robust to sensor failures and optimizing minimax criteria. Extensive empirical evidence ... In this article, we design techniques that exploit data correlations in sensor data to minimize communication costs (and hence, energy costs) incurred during data gathering in a sensor network. Our proposed approach is to select a small subset of sensor nodes that may be sufficient to reconstruct data for the entire sensor network. Then, during data gathering only the selected sensors need to be involved in communication. The selected set of sensors must also be connected, since they need to relay data to the data-gathering node. We define the problem of selecting such a set of sensors as the connected correlation-dominating set problem, and formulate it in terms of an appropriately defined correlation structure that captures general data correlations in a sensor network. We develop a set of energy-efficient distributed algorithms and competitive centralized heuristics to select a connected correlation-dominating set of small size. The designed distributed algorithms can be implemented in an asynchronous communication model, and can tolerate message losses. We also design an exponential (but nonexhaustive) centralized approximation algorithm that returns a solution within O(log n) of the optimal size. Based on the approximation algorithm, we design a class of centralized heuristics that are empirically shown to return near-optimal solutions. Simulation results over randomly generated sensor networks with both artificially and naturally generated data sets demonstrate the efficiency of the designed algorithms and the viability of our technique—even in dynamic conditions. Wireless sensor networks are susceptible to interference that can disrupt sensor communication. In order to cope with this disruption, we explore channel surfing, whereby the sensor nodes adapt their channel assignments to restore network connectivity in the presence of interference. We explore two different approaches to channel surfing: coordinated channel switching, where the entire sensor network adjusts its channel; and spectral multiplexing, where nodes in a jammed region switch channels while nodes on the boundary of a jammed region act as radio relays between different spectral zones. For spectral multiplexing, we have devised both synchronous and asynchronous strategies to facilitate the spectral scheduling needed to improve network fidelity when sensor nodes operate on multiple channels. In designing these algorithms, we have taken a system-oriented approach that has focused on exploring actual implementation issues under realistic network settings. We have implemented these proposed methods on a testbed of 30 Mica2 sensor nodes, and the experimental results show that these strategies can each repair network connectivity in the presence of interference without introducing significant overhead.