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## Sparsity-promoting sensor selection for nonlinear measurement models (2013)

Venue: | IEEE Trans. Signal Process. (Submitted |

Citations: | 12 - 9 self |

### Citations

12231 |
Elements of Information Theory,
- Cover, Thomas
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Citation Context ... the accuracy required and are assumed to be known. A higher accuracy level is obtained by reducing and/or increasing . This metric is used in several occasions as an accuracy measure (e.g., see [4], =-=[28]-=-, [29]). We next discuss two popular performance measures that satisfy the above requirement. 1) Trace Constraint: A sufficient condition to satisfy the accuracy requirement in (11) is (see Appendix A... |

7239 | Convex Optimization.
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Citation Context ... will simply be an affine function . The optimization problem in (15) is a standard SDP problem in the inequality form, which can be efficiently solved in polynomial time using interior-point methods =-=[11]-=-. An implementation of the interior-point method for solving SDP problems in the inequality form is typically based onNewton’smethod using an approximating barrier function. A brief description of the... |

1553 |
[Fundamentals of Statistical Signal Processing : Estimation Theory ],
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Citation Context ... vector . We make the following assumptions: a1. Regularity conditions: The log-likelihood of the measurements satisfies the regularity condition . This is a well-known condition for the CRB to exist =-=[26]-=-. a2. Independent observations: The measurements for , are a sequence of independent random variables. The proposed framework for sensor selection is valid as long as the above two assumptions hold. A... |

1317 | Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software:
- Sturm
- 1999
(Show Context)
Citation Context ... complexity per iteration of the projected Newton’s algorithm is then . Implementations of the interior-point methods are easily available in the form of well-known toolboxes like Yalmip [33], SeDuMi =-=[34]-=-, and CVX [35]. B. Projected Subgradient Algorithm The second-order Newton’s method (cf. Appendix C) is typically intractable when the number of candidate sensors is very CHEPURI AND LEUS: SPARSITY-PR... |

1150 |
Nonlinear programming. Athena Scientific,
- Bertsekas
- 1999
(Show Context)
Citation Context ...thod which is attractive for large-scale problems as each iteration is much cheaper to process. The subgradient method is typically used for optimizations involving non-differentiable functions [35], =-=[36]-=-. The subgradient method is a generalization of the gradient method for non-smooth and non-differentiable functions, such as, the ℓ1norm and the minimum eigenvalue constraint functions. We next derive... |

1040 |
CVX: Matlab software for disciplined convex programming, version 1.22,” http://cvxr.com/cvx,
- Grant, Boyd
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(Show Context)
Citation Context ...ration of the projected Newton’s algorithm is then O(M3). Implementations of the interior-point methods are easily available in the form of well-known toolboxes like Yalmip [32], SeDuMi [33], and CVX =-=[34]-=-. B. Projected subgradient algorithm The second-order Newton’s method (cf. Appendix C) is typically intractable when the number of sensors is very large (M ≫ 1000 for example). To circumvent this prob... |

552 | For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution,”
- Donoho
- 2006
(Show Context)
Citation Context ...ex constraints especially when the solution is sparse [31]. Such relaxations are well-studied for problems with linear constraints in the context of compressed sensing (CS) and sparse signal recovery =-=[32]-=-. The non-convex Boolean constraint in (13c) is further relaxed to the convex box constraint . The relaxed optimization problem is given as the following SDP problem (15a) (15b) (15c) where denotes th... |

427 |
Yalmip: A toolbox for modelling and optimization in
- Löfberg
- 2004
(Show Context)
Citation Context ...computational complexity per iteration of the projected Newton’s algorithm is then . Implementations of the interior-point methods are easily available in the form of well-known toolboxes like Yalmip =-=[33]-=-, SeDuMi [34], and CVX [35]. B. Projected Subgradient Algorithm The second-order Newton’s method (cf. Appendix C) is typically intractable when the number of candidate sensors is very CHEPURI AND LEUS... |

422 | Fast linear iterations for distributed averaging,”
- Xiao, Boyd
- 2004
(Show Context)
Citation Context ...h is much lower than the complexity of the projected Newton’s method. A distributed implementation of the projected subgradient algorithm is very easy. A simple distributed averaging algorithm (e.g., =-=[39]-=-) can be used to compute the sum of matrices . The minimum eigenvalue and the corresponding eigenvector can then be computed using power iterations at each node independently. The update step (18), th... |

361 |
Optimal Design of Experiments.
- Pukelsheim
- 1993
(Show Context)
Citation Context ...n sensor selection [9, and references therein]. The sensor selection problem is often formulated as an optimization problem based on some well-known performance measures from experimental design [9], =-=[10]-=-, [11, p. 384]. The sensor selection problem is expressed as the following optimization problem: (1) where is a selection vector of length , and is a scalar cost function related to the error covarian... |

329 | Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies.
- Krause, Singh, et al.
- 2008
(Show Context)
Citation Context ...desired performance. The above selection problem is applied to sensor placement for power grid monitoring in [12]. Alternative greedy approaches exploiting the submodularity of the objective function =-=[13]-=-–[17] are also proposed to solve the sensor selection problem. Sensor selection for dynamical systems often referred to as sensor polling or scheduling, is studied in [18]–[20]. In [21], the sensor pl... |

296 | Locating the nodes: cooperative localization in wireless sensor networks,”
- Patwari, Ash, et al.
- 2005
(Show Context)
Citation Context ...is pertinent to various diverse fields, especially to applications dealing with large-scale networks like network monitoring [2], [3], locationaware services like target localization and tracking [4]–=-=[6]-=-, field (e.g., heat, sound, precipitation) estimation [7], [8], and environmental monitoring in general. The fundamental questions of interest are: q1. Where to deploy the limited sensors available? q... |

190 | Localization via ultra-wideband radios: a look at positioning aspects for future sensor networks. - Gezici, Tian, et al. - 2005 |

147 |
Identification in Parametric Models,
- Rothenberg
- 1971
(Show Context)
Citation Context ...es to any specific estimator, however, we use the CRB as a performancemeasure. Themotivation behind using the CRB is as follows: 1) The CRB is a measure for the (local) identifiability of the problem =-=[27]-=-. More specifically, a non-singular FIM implies (local) solvability and a unique estimate of , however, the converse is not necessarily true. The sensor selection problem presented in this paper seeks... |

144 | Enhancing sparsity by reweighted ℓ1 minimization
- Candes, Wakin, et al.
- 2008
(Show Context)
Citation Context ...blem which also results in fewer selected sensors. Instead of relaxing the ℓ0-(quasi) norm with the ℓ1-norm, using a nonconvex surrogate 7function can yield a better approximation. It is motivated in =-=[39]-=- that the logarithm of the geometric mean of its elements can be used as an alternative surrogate function for linear inverse problems in CS. Adapting this to our sensor selection problem, we arrive a... |

93 |
Mobile positioning using wireless networks: possibil‐ ities and fundamental limitations based on available wireless network measurements.
- Gustafsson, Gunnarsson
- 2005
(Show Context)
Citation Context ...ion is pertinent to various diverse fields, especially to applications dealing with large-scale networks like network monitoring [2], [3], locationaware services like target localization and tracking =-=[4]-=-–[6], field (e.g., heat, sound, precipitation) estimation [7], [8], and environmental monitoring in general. The fundamental questions of interest are: q1. Where to deploy the limited sensors availabl... |

91 | Sensor selection via convex optimization,”
- Joshi, Boyd
- 2009
(Show Context)
Citation Context ...sts on sensor selection [9, and references therein]. The sensor selection problem is often formulated as an optimization problem based on some well-known performance measures from experimental design =-=[9]-=-, [10], [11, p. 384]. The sensor selection problem is expressed as the following optimization problem: (1) where is a selection vector of length , and is a scalar cost function related to the error co... |

88 | Near-optimal observation selection using submodular functions. - Krause, Guestrin - 2007 |

45 |
Recent advances it! nonlinear experimental design
- Ford, Kitsos, et al.
- 1989
(Show Context)
Citation Context ...in general) deals with measurements that are related to additive Gaussian linear models. Experimental design for non-linear models within the Bayesian and sequential design frameworks is discussed in =-=[22]-=-. In [18], sensor selection for target tracking based on extended Kalman filtering has been proposed, in which the selection is performed by designing a sparse gain matrix. Moreover [18] is limited to... |

44 | Robust submodular observation selection.
- Krause, McMahon, et al.
- 2008
(Show Context)
Citation Context ... desired performance. The above selection problem is applied to sensor placement for power grid monitoring in [12]. Alternative approaches exploiting the submodularity of the objective function [13]– =-=[15]-=-, heuristics based on genetic algorithms [16], and greedy algorithms [17] are also proposed to solve the sensor selection problem. Sensor selection for dynamical systems often referred to as sensor po... |

32 |
Performance analysis of bearing-only target location algorithms
- Gavish, Weiss
- 1992
(Show Context)
Citation Context ... FIM related to the th measurement is then given by C. Bearing Measurements Another popular target localization technique is based on bearing measurements from a set of direction finding (DF) sensors =-=[41]-=-. The bearing measurement of the th DF sensor is given by where , , and is the noise. Defining a 2 2 permutation matrix we can then compute the FIM contribution from the th DF sensor as D. Field Estim... |

32 |
Cover and Joy A Thomas. Elements of information theory
- Thomas
- 2012
(Show Context)
Citation Context ...accuracy required and are assumed to be known. A higher accuracy level is obtained by reducing Re and/or increasing Pe. This metric is used in several occasions as an accuracy measure (e.g., see [4], =-=[28]-=-, [29]). We next discuss two popular performance measures that satisfy the above requirement. 1) Trace constraint: A sufficient condition to satisfy the accuracy requirement in (10) is (see Appendix A... |

28 |
Enhancing sparsity by reweighted minimization
- Candes, Wakin, et al.
- 2008
(Show Context)
Citation Context ...n problem which also results in fewer selected sensors. Instead of relaxing the -(quasi) norm with the -norm, using a nonconvex surrogate function can yield a better approximation. It is motivated in =-=[40]-=- that the logarithm of the geometric mean of its elements can be used as an alternative surrogate function for linear inverse problems in CS. Adapting this to our sensor selection problem, we arrive a... |

20 | Giannakis, “From sparse signals to sparse residuals for robust sensing
- Kekatos, B
- 2011
(Show Context)
Citation Context ...the (noisy) past state estimate. This paper, on the other hand, deals with general non-linear models, without an explicit linearization. Sensor selection for detection problems is studied in [23]. In =-=[24]-=-, reliable sensor selection based on the actual measurements to identify the outliers is presented. A different problem, yet related to sensor selection, is the problem of identifying source-informati... |

18 |
Greedy sensor selection: Leveraging submodularity.
- Shamaiah, Banerjee, et al.
- 2010
(Show Context)
Citation Context ...acement for power grid monitoring in [12]. Alternative approaches exploiting the submodularity of the objective function [13]– [15], heuristics based on genetic algorithms [16], and greedy algorithms =-=[17]-=- are also proposed to solve the sensor selection problem. Sensor selection for dynamical systems often referred to as sensor polling or scheduling, is studied in [18]–[20]. In [21], the sensor placeme... |

18 |
Identification in Parametric Models." Econometrica
- Rothenberg
(Show Context)
Citation Context ... to any specific estimator, however, we use the CRB as a performance measure. The motivation behind using the CRB is as follows: 1. The CRB is a measure for the (local) identifiability of the problem =-=[27]-=-. More specifically, a non-singular FIM implies (local) solvability and a unique estimate of θ, however, the converse is not necessarily true. The sensor selection problem presented in this paper seek... |

17 |
Sensor placement for on-orbit modal identification via a genetic algorithm,”
- Yao, Sethares, et al.
- 1993
(Show Context)
Citation Context ...ed performance. The above selection problem is applied to sensor placement for power grid monitoring in [12]. Alternative greedy approaches exploiting the submodularity of the objective function [13]–=-=[17]-=- are also proposed to solve the sensor selection problem. Sensor selection for dynamical systems often referred to as sensor polling or scheduling, is studied in [18]–[20]. In [21], the sensor placeme... |

16 | Monitoring and optimization for power grids: A signal processing perspective
- Giannakis, Kekatos, et al.
- 2013
(Show Context)
Citation Context ...lected subject to a specific performance constraint. Sensor selection is pertinent to various diverse fields, especially to applications dealing with large-scale networks like network monitoring [2], =-=[3]-=-, locationaware services like target localization and tracking [4]–[6], field (e.g., heat, sound, precipitation) estimation [7], [8], and environmental monitoring in general. The fundamental questions... |

14 |
Sensor selection for event detection in wireless sensor networks
- Bajovic, Sinopoli, et al.
- 2011
(Show Context)
Citation Context ...d around the (noisy) past state estimate. This paper, on the other hand, deals with general non-linear models, without an explicit linearization. Sensor selection for detection problems is studied in =-=[23]-=-. In [24], reliable sensor selection based on the actual measurements to identify the outliers is presented. A different problem, yet related to sensor selection, is the problem of identifying source-... |

12 | Optimal placement of phasor measurement units via convex relaxation
- Kekatos, Giannakis, et al.
- 2012
(Show Context)
Citation Context ...s to select might not be known. Nevertheless, this number can always be tuned to achieve a desired performance. The above selection problem is applied to sensor placement for power grid monitoring in =-=[12]-=-. Alternative greedy approaches exploiting the submodularity of the objective function [13]–[17] are also proposed to solve the sensor selection problem. Sensor selection for dynamical systems often r... |

12 | Ranging energy optimization for robust sensor positioning based on semidefinite programming
- Wang, Leus, et al.
- 2009
(Show Context)
Citation Context ...ccuracy required and are assumed to be known. A higher accuracy level is obtained by reducing and/or increasing . This metric is used in several occasions as an accuracy measure (e.g., see [4], [28], =-=[29]-=-). We next discuss two popular performance measures that satisfy the above requirement. 1) Trace Constraint: A sufficient condition to satisfy the accuracy requirement in (11) is (see Appendix A) 1The... |

12 |
Yalmip : A toolbox for modeling and optimization
- Lfberg
- 2004
(Show Context)
Citation Context ...tational complexity per iteration of the projected Newton’s algorithm is then O(M3). Implementations of the interior-point methods are easily available in the form of well-known toolboxes like Yalmip =-=[32]-=-, SeDuMi [33], and CVX [34]. B. Projected subgradient algorithm The second-order Newton’s method (cf. Appendix C) is typically intractable when the number of sensors is very large (M ≫ 1000 for exampl... |

11 | Dynamic field estimation using wireless sensor networks: Tradeoffs between estimation error and communication cost
- Zhang, Moura, et al.
- 2009
(Show Context)
Citation Context ...rse fields, especially to applications dealing with large-scale networks like network monitoring [2], [3], location-aware services like target localization and tracking [4]–[6], field estimation [7], =-=[8]-=-, and environment monitoring in general. The fundamental questions of interest are: q1. Where to deploy the limited sensors available? q2. Do we need to process all the acquired measurements? To this ... |

9 | Sparsityexploiting anchor placement for localization in sensor networks
- Chepuri, Leus, et al.
- 2013
(Show Context)
Citation Context ...t by NWO-STW under the VICI program ( 10382). A conference precursor of this manuscript has been published in the Proceedings of the Twenty-First European Signal Processing Conference, September 2013 =-=[1]-=-. The authors are with the Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft 2628CD, The Netherlands (e-mail: s.p.chepuri@tudelft.nl; g.j.t.leu... |

8 | Static field estimation using a wireless sensor network based on the finite element method
- Waterschoot, Leus
(Show Context)
Citation Context ...lications dealing with large-scale networks like network monitoring [2], [3], locationaware services like target localization and tracking [4]–[6], field (e.g., heat, sound, precipitation) estimation =-=[7]-=-, [8], and environmental monitoring in general. The fundamental questions of interest are: q1. Where to deploy the limited sensors available? q2. Do we need to process all the acquired measurements? T... |

8 |
Sparsity-promoting extended Kalman filtering for target tracking in wireless sensor networks,”
- Masazade, Fardad, et al.
- 2012
(Show Context)
Citation Context ...ty of the objective function [13]–[17] are also proposed to solve the sensor selection problem. Sensor selection for dynamical systems often referred to as sensor polling or scheduling, is studied in =-=[18]-=-–[20]. In [21], the sensor placement problem for linear models is addressed as the design of a sensing matrix that optimizes a measure related to the orthogonality of its rows. All the above literatur... |

8 | Near-optimal sensor placement for linear inverse problems
- Ranieri, Chebira, et al.
- 2014
(Show Context)
Citation Context ...ctive function [13]–[17] are also proposed to solve the sensor selection problem. Sensor selection for dynamical systems often referred to as sensor polling or scheduling, is studied in [18]–[20]. In =-=[21]-=-, the sensor placement problem for linear models is addressed as the design of a sensing matrix that optimizes a measure related to the orthogonality of its rows. All the above literature (in general)... |

6 |
Distributed informative-sensor identification via sparsityaware matrix decomposition
- Schizas
- 2013
(Show Context)
Citation Context ...d on the actual measurements to identify the outliers is presented. A different problem, yet related to sensor selection, is the problem of identifying source-informative sensors, which is studied in =-=[25]-=-. B. Contributions We consider general scenarios where themeasurements of the unknown parameter follow a non-linear model (unlike [9] for instance). Non-linear measurement models are frequently encoun... |

4 | Sensor scheduling via compressed sensing,” - Carmi - 2010 |

4 |
Subgradient methods,” http://www. stanford.edu/class/ee364b/notes/subgrad method notes.pdf
- Boyd, Xiao, et al.
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Citation Context ...der method which is attractive for large-scale problems as each iteration is much cheaper to process. The subgradient method is typically used for optimizations involving non-differentiable functions =-=[35]-=-, [36]. The subgradient method is a generalization of the gradient method for non-smooth and non-differentiable functions, such as, the ℓ1norm and the minimum eigenvalue constraint functions. We next ... |

3 |
Distributed sensor allocation for multi-target tracking in wireless sensor networks
- Fu, Ling, et al.
- 2012
(Show Context)
Citation Context ... the objective function [13]–[17] are also proposed to solve the sensor selection problem. Sensor selection for dynamical systems often referred to as sensor polling or scheduling, is studied in [18]–=-=[20]-=-. In [21], the sensor placement problem for linear models is addressed as the design of a sensing matrix that optimizes a measure related to the orthogonality of its rows. All the above literature (in... |

3 |
An lmi approach to structured sparse feedback design in linear control systems
- Polyak, Khlebnikov, et al.
- 2013
(Show Context)
Citation Context ...the -(quasi) norm, namely the -norm heuristic. The -norm is known to represent an efficient heuristic for the -(quasi) norm optimization with convex constraints especially when the solution is sparse =-=[31]-=-. Such relaxations are well-studied for problems with linear constraints in the context of compressed sensing (CS) and sparse signal recovery [32]. The non-convex Boolean constraint in (13c) is furthe... |

1 |
Dynamic network cartography: Advances in network health monitoring
- Mateos, Rajawat
- 2013
(Show Context)
Citation Context ...re selected subject to a specific performance constraint. Sensor selection is pertinent to various diverse fields, especially to applications dealing with large-scale networks like network monitoring =-=[2]-=-, [3], locationaware services like target localization and tracking [4]–[6], field (e.g., heat, sound, precipitation) estimation [7], [8], and environmental monitoring in general. The fundamental ques... |

1 |
Dynamic field estimation usingwireless sensor networks: Tradeoffs between estimation error and communication cost
- Zhang, Moura, et al.
- 2009
(Show Context)
Citation Context ...ions dealing with large-scale networks like network monitoring [2], [3], locationaware services like target localization and tracking [4]–[6], field (e.g., heat, sound, precipitation) estimation [7], =-=[8]-=-, and environmental monitoring in general. The fundamental questions of interest are: q1. Where to deploy the limited sensors available? q2. Do we need to process all the acquired measurements? To thi... |

1 |
Trees, Detection, Estimation, Modulation Theory, Optimum Array Processing
- Van
- 2004
(Show Context)
Citation Context ...prior information of the unknown parameter is available, this additional knowledge can be incorporated in the CRB. The related information matrix is often called the Bayesian information matrix (BIM) =-=[30]-=-, and it is independent of the unknown parameter (hence, gridding is not needed). The BIM is given by , where is the prior information matrix with the (log) prior , and the expectation is under the pd... |

1 |
Nonlinear Programming, ser. Athena Scientific Optimization and Computation Series
- Bertsekas
- 1999
(Show Context)
Citation Context ...ethod which is attractive for largescale problems as each iteration is much cheaper to process. The subgradient method is typically used for optimizations involving non-differentiable functions [36], =-=[37]-=-. The subgradient method is a generalization of the gradient method for nonsmooth and non-differentiable functions, such as, the -norm and the minimum eigenvalue constraint functions. We next derive t... |