Sensor Selection via Convex Optimization

Joshi, Sameer; Boyd, Stephen

doi:10.1109/tsp.2008.2007095

Cited by 1,138 publications

(1,082 citation statements)

References 48 publications

Supporting

Mentioning

1,059

Contrasting

Unclassified

Order By: Relevance

“…It is easy to show that the log det of CRLB is a lower bound for the log det of the covariance matrix of any unbiased estimator. The D-criterion, due to the reasons mentioned above, is a popular choice and has been frequently used as the design criterion in many design problems in robotics, including sensor selection [14] and active SLAM [15]. In this section we define a connectivity metric based on the number of spanning trees, and reveal its impact on the D-criterion.…”

Section: Remark 1 the Following Statements Hold Regarding I(x)mentioning

confidence: 99%

Tree-connectivity: Evaluating the graphical structure of SLAM

Khosoussi

Huang

Dissanayake

2016

2016 IEEE International Conference on Robotics and Automation (ICRA)

View full text Add to dashboard Cite

Abstract-Simultaneous localization and mapping (SLAM) in robotics, and a number of related problems that arise in sensor networks are instances of estimation problems over weighted graphs. This paper studies the relation between the graphical representation of such problems and estimationtheoretic concepts such as the Cramér-Rao lower bound (CRLB) and D-optimality. We prove that the weighted number of spanning trees, as a graph connectivity metric, is closely related to the determinant of CRLB. This metric can be efficiently computed for large graphs by exploiting the sparse structure of underlying estimation problems. Our analysis is validated using experiments with publicly available pose-graph SLAM datasets.

show abstract

Section: Remark 1 the Following Statements Hold Regarding I(x)mentioning

confidence: 99%

Tree-connectivity: Evaluating the graphical structure of SLAM

Khosoussi

Huang

Dissanayake

2016

2016 IEEE International Conference on Robotics and Automation (ICRA)

View full text Add to dashboard Cite

show abstract

“…We now use some standard convex relaxation techniques to simplify (8) and solve it sub-optimally. The -(quasi) norm is relaxed with its best convex approximation, i.e., an -mixed norm defined as .…”

Section: Optimization Problemmentioning

confidence: 99%

Continuous Sensor Placement

Chepuri

Leus

2015

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

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 grid-based model, which allows for off-the-grid 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 SENSOR networks are widely used in a variety of applications like environmental monitoring, security and safety, to list a few. Sensors are devices capable of sensing a certain physical phenomenon, processing data, and communicating information to a central unit. Sensors are geographically deployed, and the data acquired by such distributed sensors are often used to solve statistical inference problems like field (e.g., heat, sound) estimation, target localization, and so on.The number of sensors available are often limited due to various factors like availability of physical or data storage space, economical constraints, or due to energy-efficiency reasons. Such a restriction on the number of sensors naturally limits the estimation accuracy. Moreover, selecting different sampling locations for the sensors generally leads to different values of the mean-squared-error. In this article, we are interested in finding the best placement of the sensors such that a desired estimation accuracy is ensured and the number of sensors are as low as possible. In other words, the focus will be on designing a sparse sensing technique to capture only informative data, thereby reducing the costs associated with sensing, data storage, and communication overheads.Let denote the observation signal with a continuousdomain argument, where without loss of generality (w.l.o.g.) denotes the sampling domain. We will restrict ourselves to the one-dimensional spatial domain, but the ideas presented can be applied directly to higher dimensions and even to temporal or spatio-temporal domains 1 . Assume that represents the measured physical field over a continuous one-dimensional space , and it satisfies the linear model (1) where collects the parameters to be estimated, is the known linear model representing the mapping between the parameters and the measurements, and is the noise. For example, in field estimation, might contain the source location and its field intensity. Furthermore, we assume for and . In other words, is completely described by its variation in the interval where we can place the sensors.The fundamental question of interest is-where to place the sensors such that the estimation error is as lo...

show abstract

“…For example, let us consider the MSE (A-optimality) criterion. Writing the relaxed sensor selection (3) in the epigraph form, we obtain [12] arg min…”

Section: A Sensor Selection For Estimationmentioning

confidence: 99%

“…The purpose of this partly tutorial paper is to describe the sensor selection problem from a statistical signal processing perspective, and to provide a brief overview with a specific emphasis on some recent advances based on results from [12]- [15].…”

Section: Introductionmentioning

confidence: 99%

Sensor selection for estimation, filtering, and detection

Chepuri

Leus

2014

2014 International Conference on Signal Processing and Communications (SPCOM)

View full text Add to dashboard Cite

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.

show abstract

Sensor Selection via Convex Optimization

Cited by 1,138 publications

References 48 publications

Tree-connectivity: Evaluating the graphical structure of SLAM

Tree-connectivity: Evaluating the graphical structure of SLAM

Continuous Sensor Placement

Sensor selection for estimation, filtering, and detection

Contact Info

Product

Resources

About