Further Relaxations of the Semidefinite Programming Approach to Sensor Network Localization

Wang, Zizhuo; Zheng, Shuang; Ye, Yinyu; Boyd, Stephen

doi:10.1137/060669395

Cited by 167 publications

(208 citation statements)

References 34 publications

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“…It is worthy to point out that [6] solves (10) in an iterative manner as W is a function of and (11) is exploited implicitly in its second step. Our major difference is that we try to solve (10)−(11) in a more explicit manner and to further increase the estimation accuracy with the use of (12). Note that it is impractical to tackle (10)−(12) using the Lagrange multipliers because numerous variables will be introduced in the solving procedure.…”

Section: Algorithm Developmentmentioning

confidence: 99%

Accurate time delay estimation based passive localization

Lui

Chan

2009

Signal Processing

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A conventional approach for source localization is to utilize time delay measurements of the emitted signal received at an array of sensors. The time delay information is then employed to construct a set of hyperbolic equations from which the target position can be determined. In this paper, we utilize semidefinite programming (SDP) technique to derive a passive source localization algorithm which can integrate the available knowledge such as admissible target range and other cues. It is shown that the SDP method is superior to the well-known two-step weighted least squares method at lower signal-to-noise ratio conditions.

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Section: Algorithm Developmentmentioning

confidence: 99%

Accurate time delay estimation based passive localization

Lui

Chan

2009

Signal Processing

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“…In the next section, we will show that problem (18) in the first step of the above algorithm can be efficiently solved by an alternating minimization method.…”

Section: : End Ifmentioning

confidence: 99%

“…For example, techniques of regularization and refinement have been employed in [17]. Edgebased SDP (ESDP) and node-based SDP (NSDP) relaxations of the full SDP (FSDP) [15] are studied in [18]. A sparse version of FSDP has been implemented as SFSDP by Kim et al in [19] and it requires much less computational time than most of the SDP relaxation methods.…”

Section: Introductionmentioning

confidence: 99%

Tackling the flip ambiguity in wireless sensor network localization and beyond

Bai

2016

Digital Signal Processing

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There have been significant advances in range-based numerical methods for sensor network localizations over the past decade. However, there remain a few challenges to be resolved to satisfaction. Those issues include, for example, the flip ambiguity, high level of noises in distance measurements, and irregular topology of the concerning network. Each or a combination of them often severely degrades the otherwise good performance of existing methods. Integrating the connectivity constraints is an effective way to deal with those issues. However, there are too many of such constraints, especially in a large and sparse network. This presents a challenging computational problem to existing methods. In this paper, we propose a convex optimization model based on the Euclidean Distance Matrix (EDM). In our model, the connectivity constraints can be simply represented as lower and upper bounds on the elements of EDM, resulting in a standard 3-block quadratic conic programming, which can be efficiently solved by a recently proposed 3-block alternating direction method of multipliers. Numerical experiments show that the EDM model effectively eliminates the flip ambiguity and retains robustness in terms of being resistance to irregular wireless sensor network topology and high noise levels.

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“…Another engineering example that leads to a conic feasibility problem is sensor network localization (see e.g. [50] and references therein). Efficiently solving conic feasibility can also have applications in conic programming itself, for example, for finding starting points or, following [28], for solving linear conic programming problems as conic feasibility problems after formulation of the optimality conditions.…”

Section: Conic and Semidefinite Feasibility Problemsmentioning

confidence: 99%

Projection methods for conic feasibility problems: applications to polynomial sum-of-squares decompositions

Henrion

Malick

2011

Optimization Methods and Software

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This paper presents a projection-based approach for solving conic feasibility problems. To find a point in the intersection of a cone and an affine subspace, we simply project a point onto this intersection. This projection is computed by dual algorithms operating a sequence of projections onto the cone and generalizing the alternating projection method. We release an easy-to-use Matlab package implementing an elementary dual-projection algorithm. Numerical experiments show that, for solving some semidefinite feasibility problems, the package is competitive with sophisticated conic programming software. We also provide a particular treatment for semidefinite feasibility problems modelling polynomial sum-of-squares decomposition problems.

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Further Relaxations of the Semidefinite Programming Approach to Sensor Network Localization

Cited by 167 publications

References 34 publications

Accurate time delay estimation based passive localization

Accurate time delay estimation based passive localization

Tackling the flip ambiguity in wireless sensor network localization and beyond

Projection methods for conic feasibility problems: applications to polynomial sum-of-squares decompositions

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