Semi-Definite Programming Algorithms for Sensor Network Node Localization With Uncertainties in Anchor Positions and/or Propagation Speed

Lui, Kenneth W. K.; Ma, Wing-Kin; So, Hing-Cheung; Chan, Frankie K. W.

doi:10.1109/tsp.2008.2007916

Cited by 161 publications

(116 citation statements)

References 51 publications

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“…The findings are similar to those of Figure 4. Figure 6 shows the results for the colored noise case and it is seen that the proposed algorithm outperforms [14]. Finally, the first test is repeated with receiver position uncertainty and the MSE performance is plotted in Figure 7.…”

Section: Draft V Simulation Resultsmentioning

confidence: 97%

“…Second, TOA-based localization is addressed and we first compare the proposed scheme with the standard SDR algorithm [14] and CRLB in the uncorrelated noise scenarios. For ease of presentation but without loss of generality, we use…”

Section: Draft V Simulation Resultsmentioning

confidence: 99%

“…In Sections III and IV, we apply this new SDR formulation technique to TOA and TDOA measurements, respectively. In particular, we prove that in the uncorrelated noise scenario, our TOA-based position estimator is equivalent to a standard formulation [14]. Numerical examples for evaluating the performance of the proposed approach are included in Section V. Finally, conclusions are drawn in Section VI.…”

Section: Introductionmentioning

confidence: 94%

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A flexible semi-definite programming approach for source localization problems

Chan

et al. 2013

Digital Signal Processing

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In this paper, a new semi-definite programming approach is devised for approximating nonlinear estimation problems. The main idea is to include the noise components as parameters of interests, which increases the flexibility in the convex optimization formulation. Using the source localization as an illustration, we develop semi-definite relaxation (SDR) positioning algorithms using angle-of-arrival, time-of-arrival and time-difference-of-arrival measurements. Numerical examples are included to show the effectiveness of the proposed SDR approach.

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Section: Draft V Simulation Resultsmentioning

confidence: 97%

Section: Draft V Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

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A flexible semi-definite programming approach for source localization problems

Chan

et al. 2013

Digital Signal Processing

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“…The first algorithms to focus on improving the computational feasibility of this problem via convex relaxations were based mainly on semi-definite programming (SDP), as in [16][17][18][19][20], and second-order cone programming (SOCP) [21]. Further SDP-based relaxations, e.g., the so-called edge-SDP relaxation, have also been derived to reduce the computational burden [22]. Furthermore, a computationally efficient multi-dimensional scaling (MDS) algorithm [23] and a matrix-completion-based approach [24] have been proposed.…”

Section: Related Workmentioning

confidence: 99%

Localization of ambiguously identifiable wireless agents: complexity analysis and efficient algorithms

Schlupkothen

Ascheid

2018

EURASIP J. Adv. Signal Process.

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In the localization of wireless agents, ambiguous measurements have significant implications regarding the complexity and quality of the agents' positioning. Ambiguous measurements occur, for example, in multiple source localization (MSL), in which the goal is to localize the sources of signals, although the signals themselves cannot be used to differentiate among their sources. The indifferentiability of the sources results in a combinatorial optimization problem that must be solved before a localization result can be obtained. Similar effects arise, for example, in the localization of highly resource-limited wireless agents that are subject to severe size and energy constraints, meaning that neither unique identification sequences (CDMA) nor unique frequency or time resources (FDMA, TMDA) can be used. This application scenario constitutes a more general and complex joint problem of localization and ambiguity resolution that also encompasses MSL. In this work, we focus on this more general problem and its corresponding application case while maintaining applicability to the MSL problem. More precisely, we prove the N P-hardness of the joint localization and ambiguity resolution problem and derive a solution framework that facilitates a comprehensive and concise formulation thereof. Thereby, we derive a minimum mean square error (MMSE)-optimal algorithm based on mixed-integer nonlinear programming and propose a relaxation of the problem with the aim of reducing the computational complexity. Additionally, simplifications are derived for the case in which bidirectional measurements are available or enforced, e.g., by the applied communication or ranging protocol.

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“…We will consider the following 3 scenarios to evaluate the performance of the SDP relaxation method. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 F o r P e e r R e v i e w 13 In this scenario, we fix the number of the anchors and the level of NLOS errors to show the performance of the SDP relaxation method when the measurement noise level is varying. The first 8 anchors listed above are used (i.e., the anchors at the boundary) and the mean of the NLOS error δ i,j is λ = 4 m in (4).…”

Section: A Known Nlos Status and Distribution Parametersmentioning

confidence: 99%

IEEE Transactions on Wireless Communications

2017

IEEE Trans. Wireless Commun.

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An unknown-position sensor can be localized if there are three or more anchors making time-ofarrival (TOA) measurements of a signal from it. However, the location errors can be very large due to the fact that some of the measurements are from non-line-of-sight (NLOS) paths. In this paper, a semi-definite programming (SDP) based node localization algorithm in NLOS environments is proposed for ultra-wideband (UWB) wireless sensor networks. The positions of sensors can be estimated using the distance estimates from location-aware anchors as well as other sensors. However, in the absence of line-of-sight (LOS) paths, e.g., in indoor networks, the NLOS range estimates can be significantly biased. As a result, the NLOS error can remarkably decrease the location accuracy, and it is not easy to accurately distinguish LOS from NLOS measurements. According to the information known about the prior probabilities and distributions of the NLOS errors, three different cases are introduced and the related localization problems are addressed respectively. Simulation results demonstrate that this algorithm achieves high location accuracy even for the case in which NLOS and LOS measurements are not identifiable. Index TermsWireless sensor networks, non-line-of-sight (NLOS), time-of-arrival (TOA), semi-definite programming (SDP).

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Semi-Definite Programming Algorithms for Sensor Network Node Localization With Uncertainties in Anchor Positions and/or Propagation Speed

Cited by 161 publications

References 51 publications

A flexible semi-definite programming approach for source localization problems

A flexible semi-definite programming approach for source localization problems

Localization of ambiguously identifiable wireless agents: complexity analysis and efficient algorithms

IEEE Transactions on Wireless Communications

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