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12
Sparsitypromoting adaptive sensor selection for nonlinear filtering
 in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP
, 2014
"... Sensor selection is an important design task in sensor networks. We consider the problem of adaptive sensor selection for applications in which the observations follow a nonlinear model, e.g., target/bearing tracking. In adaptive sensor selection, based on the dynamical state model and the state e ..."
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Sensor selection is an important design task in sensor networks. We consider the problem of adaptive sensor selection for applications in which the observations follow a nonlinear model, e.g., target/bearing tracking. In adaptive sensor selection, based on the dynamical state model and the state estimate from the previous time step, the most informative sensors are selected to acquire the measurements for the next time step. This is done via the design of a sparse selection vector. Additionally, we model the evolution of the selection vector over time to ensure a smooth transition between the selected sensors of subsequent time steps. The original nonconvex optimization problem is relaxed to a semidefinite programming problem that can be solved efficiently in polynomial time. Index Terms — Sensor networks, adaptive sensor selection, sensor placement, nonlinear measurement model, nonlinear filtering, convex optimization, sparsity. 1.
SPARSE SENSING FOR DISTRIBUTED GAUSSIAN DETECTION
"... An offline sampling design problem for Gaussian detection is considered in this paper. The sensing operation is modeled through a vector, whose sparsity order is determined by the prescribed global error probability. Since the numerical optimization of the error probability is difficult, equivalent ..."
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An offline sampling design problem for Gaussian detection is considered in this paper. The sensing operation is modeled through a vector, whose sparsity order is determined by the prescribed global error probability. Since the numerical optimization of the error probability is difficult, equivalent simpler costs, viz., the KullbackLiebler distance and Bhattacharyya distance are optimized. The sensing problem is formulated and solved suboptimally using convex optimization techniques. Furthermore, it is shown that the sensing problem can be solved optimally for conditionally independent Gaussian observations. Finally, we show that for equicorrelated nonidentical sensor observations, the number of sensors required to achieve a certain detection performance decreases as the correlation increases. Index Terms — Sensor networks, sparse sensing, sensor selection, sensor placement, detection, convex optimization, sparsity. 1.
Sparse sensing for distributed detection
 IEEE Trans. on Sig. Process
, 2015
"... Abstract—An offline sampling design problem for distributed detection is considered in this paper. To reduce the sensing, storage, transmission, and processing costs, the natural choice for the sampler is the sparsest one that results in a desired global error probability. Since the numerical optimi ..."
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Abstract—An offline sampling design problem for distributed detection is considered in this paper. To reduce the sensing, storage, transmission, and processing costs, the natural choice for the sampler is the sparsest one that results in a desired global error probability. Since the numerical optimization of the error probabilities is difficult, we adopt simpler costs related to distance measures between the conditional distributions of the sensor observations. We design sparse samplers for the Bayesian as well as the NeymanPearson setting. The developed theory can be applied to sensor placement/selection, sample selection, and fullydecentralized data compression. For conditionally independent observations, we give an explicit solution, which is optimal in terms of the error exponents. More specifically, the best subset of sensors is the one with the smallest local average rootlikelihood ratio and largest local average loglikelihood ratio in the Bayesian and NeymanPearson setting, respectively. We supplement the proposed framework with a thorough analysis for Gaussian observations, including the case when the sensors are conditionally dependent, and also provide examples for other observation distributions. One of the results shows that, for nonidentical Gaussian sensor observations with uncommon means and common covariances under both hypotheses, the number of sensors required to achieve a desired detection performance reduces significantly as the sensors become more coherent. Index Terms—Sparse sensing, sensor selection, sensor placement, Bhattacharyya distance, KullbackLeibler distance, Jdivergence, convex optimization, energyefficiency, distributed detection. I.
Continuous Sensor Placement
"... Abstract—Existing solutions to the sensor placement problem are based on sensor selection, in which the best subset of available sampling locations is chosen such that a desired estimation accuracy is achieved. However, the achievable estimation accuracy of sensor placement via sensor selection is ..."
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Abstract—Existing solutions to the sensor placement problem are based on sensor selection, in which the best subset of available sampling locations is chosen such that a desired estimation accuracy is achieved. However, the achievable estimation accuracy of sensor placement via sensor selection is limited to the initial set of sampling locations, which are typically obtained by gridding the continuous sampling domain. To circumvent this issue, we propose a framework of continuous sensor placement. A continuous variable is augmented to the gridbased model, which allows for offthegrid sensor placement. The proposed offline design problem can be solved using readily available convex optimization solvers. Index Terms—Convex optimization, joint sparsity, sensor placement, sensor selection, sparse sensing, sparsity. I. PROBLEM STATEMENT
ROBUST CENSORING FOR LINEAR INVERSE PROBLEMS
"... Existing methods for smart data reduction are typically sensitive to outlier data that do not follow postulated data models. We propose robust censoring as a joint approach unifying the concepts of robust learning and data censoring. We focus on linear inverse problems and formulate robust censor ..."
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Existing methods for smart data reduction are typically sensitive to outlier data that do not follow postulated data models. We propose robust censoring as a joint approach unifying the concepts of robust learning and data censoring. We focus on linear inverse problems and formulate robust censoring through a sparse sensing operator, which is a nonconvex bilinear problem. We propose two solvers, one using alternating descent and the other using MetropolisHastings sampling. Although the latter is based on the concept of Bayesian sampling, we avoid confining the outliers to a specific model. Numerical results show that the proposed MetropolisHastings sampler outperforms stateoftheart robust estimators. Index Terms — Robustness, censoring, sparse sensing, big data.
CORRELATIONAWARE SPARSITYENFORCING SENSOR PLACEMENT FOR SPATIOTEMPORAL FIELD ESTIMATION
"... In this work, we propose a generalized framework for designing optimal sensor constellations for spatiotemporally correlated field estimation using wireless sensor networks. The accuracy of the field intensity estimate in every point of a given service area strongly depends upon the number and t ..."
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In this work, we propose a generalized framework for designing optimal sensor constellations for spatiotemporally correlated field estimation using wireless sensor networks. The accuracy of the field intensity estimate in every point of a given service area strongly depends upon the number and the constellation of the sensors along with the spatiotemporal statistics of the field. We formulate and solve a sparsityenforcing optimization problem to select the best sensor locations that achieve some desired estimation performance. The sparsityenforcing iterative selection algorithm is aware of the nonseparable spacetime covariance structure of the field. Index Terms — Wireless sensor network, field estimation, Bayesian framework, convex optimization, sparsity. 1.
Sensor Selection for Estimation, Filtering, and Detection
"... Abstract—Sensor selection is a crucial aspect in sensor network design. Due to the limitations on the hardware costs, availability of storage or physical space, and to minimize the processing and communication burden, the limited number of available sensors has to be smartly deployed. The node deplo ..."
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Abstract—Sensor selection is a crucial aspect in sensor network design. Due to the limitations on the hardware costs, availability of storage or physical space, and to minimize the processing and communication burden, the limited number of available sensors has to be smartly deployed. The node deployment should be such that a certain performance is ensured. Optimizing the sensors ’ spatial constellation or their temporal sampling patterns can be casted as a sensor selection problem. Sensor selection is essentially a combinatorial problem involving a performance evaluation over all possible choices, and it is intractable even for problems of modest scale. Nevertheless, using convex relaxation techniques, the sensor selection problem can be solved efficiently. In this paper, we present a brief overview and recent advances on the sensor selection problem from a statistical signal processing perspective. In particular, we focus on some of the important statistical inference problems like estimation, tracking, and detection. Index Terms—Sensor placement, sensor selection, sparsity, convex optimization, sensor networks, statistical inference. I.
Compression Schemes for TimeVarying Sparse Signals
"... Abstract—In this paper, we will investigate an adaptive compression scheme for tracking timevarying sparse signals with possibly varying sparsity patterns and/or order. In particular, we will focus on sparse sensing, which enables a completely distributed compression and simplifies the sampling ar ..."
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Abstract—In this paper, we will investigate an adaptive compression scheme for tracking timevarying sparse signals with possibly varying sparsity patterns and/or order. In particular, we will focus on sparse sensing, which enables a completely distributed compression and simplifies the sampling architecture. The sensing matrix is designed at each time step based on the entire history of measurements and known dynamics such that the information gain is maximized. We illustrate the developed theory with a target tracking example. Finally, we provide a few extensions of the proposed framework to include a richer class of sparse signals, e.g., structured sparsity and smoothness. Index Terms—Structured sensing, sensor selection, sparsityaware Kalman filter, sparse sensing, adaptive compressed sensing, distributed compression, big data. I.
Big Data Sketching with Model Mismatch
"... Abstract—Data reduction for largescale linear regression is one of the most important tasks in this era of data deluge. Exact model information is however not often available for big data analytics. Therefore, we propose a framework for big data sketching (i.e., a data reduction tool) that is robus ..."
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Abstract—Data reduction for largescale linear regression is one of the most important tasks in this era of data deluge. Exact model information is however not often available for big data analytics. Therefore, we propose a framework for big data sketching (i.e., a data reduction tool) that is robust to possible model mismatch. Such a sketching task is cast as a Boolean minmax optimization problem, and then equivalently reduced to a Boolean minimization program. Capitalizing on the block coordinate descent algorithm, a scalable solver is developed to yield an efficient sampler and a good estimate of the unknown regression coefficient. Index Terms—Big data, model mismatch, data reduction, linear regression, sketching. I.
Sparse Sensing for Estimation with Correlated Observations
"... Abstract—We focus on discrete sparse sensing for nonlinear parameter estimation with colored Gaussian observations. In particular, we design offline sparse samplers to reduce the sensing cost as well as to reduce the storage and communications requirements, yet achieving a desired estimation accura ..."
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Abstract—We focus on discrete sparse sensing for nonlinear parameter estimation with colored Gaussian observations. In particular, we design offline sparse samplers to reduce the sensing cost as well as to reduce the storage and communications requirements, yet achieving a desired estimation accuracy. We optimize scalar functions of the CramérRao boundmatrix, which we use as the inference performance metric to design the sparse samplers of interest via a convex program. The sampler design does not require the actual measurements, however it needs the model parameters to be perfectly known. The proposed approach is illustrated with a sensor placement example. Index Terms—Sparse sensing, sensor selection, sensor placement, dependent observations, nonlinear least squares. I.