On the Maximum Likelihood Approach for Source and Network Localization

Destino, Giuseppe; Abreu, Giuseppe

doi:10.1109/tsp.2011.2161302

Cited by 43 publications

(33 citation statements)

References 58 publications

(126 reference statements)

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“…Practical complexity of algorithms vs. ambient space dimension and number of anchors: Several authors have examined the theoretical (worst-case) complexity of localization algorithms, e.g., [11], [27], [28]. The emphasis here is on demonstrating the practical feasibility of our algorithms in centralized scenarios with moderate computational power, so we focus on actual running times, knowing that many technological factors related to hardware and software architectures may influence it 4 .…”

Section: Performance Analysis and Numerical Resultsmentioning

confidence: 99%

“…The positive semidefinite matrix W will replace U as an optimization variable, retaining the constraints along the diagonal blocks in (27), namely, tr(W ii ) = 1. Finally, we obtain the convex relaxation of (22) by combining all the above elements and dropping the rank-1 constraint for W that is implied by (27) minimize W,β,t…”

Section: A Localization Under Gaussian Noise: Slnnmentioning

confidence: 99%

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An Angular Approach for Range-Based Approximate Maximum Likelihood Source Localization Through Convex Relaxation

Oğuz-Ekim

Gomes

Stošić

et al. 2014

IEEE Trans. Wireless Commun.

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Abstract-This work considers the problem of locating a single source from noisy range measurements to a set of nodes in a wireless sensor network. We propose two new techniques that we designate as Source Localization with Nuclear Norm (SLNN) and Source Localization with 1 -norm (SL-1 ), which extend to arbitrary real dimensions our prior work on 2D source localization formulated in the complex plane. Our approach is based on formulating a Maximum-Likelihood (ML) estimation problem, and then using convex relaxation techniques to obtain a semidefinite program (SDP) that can be globally and efficiently solved. SLNN directly approximates the Gaussian ML solution, and the relaxation is shown to be tighter than in other methods in the same class. We present an analysis of the convexity properties of the constraint set for the 2D complex version of SLNN (SLCP) to justify the observed tightness of the relaxation. We propose the SL-1 algorithm to address the Laplacian noise case, which models the presence of outliers in range measurements. We overcome the nondifferentiability of the Laplacian likelihood function by rewriting the ML problem as an exact weighted version of the Gaussian case. In terms of accuracy of localization, the proposed algorithms globally outperform state-of-the-art optimization-based methods in different noise scenarios, while exhibiting moderate computational complexity.Index Terms-Centralized method, convex hull, convex relaxation, range-based source localization, semidefinite programming.

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Section: Performance Analysis and Numerical Resultsmentioning

confidence: 99%

Section: A Localization Under Gaussian Noise: Slnnmentioning

confidence: 99%

An Angular Approach for Range-Based Approximate Maximum Likelihood Source Localization Through Convex Relaxation

Oğuz-Ekim

Gomes

Stošić

et al. 2014

IEEE Trans. Wireless Commun.

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“…The matrix F pi is the Fisher information matrix (FIM) [13], [14] and which (k, l)-th element is defined as [15] …”

Section: B Fisher Uncertainty Ellipsesmentioning

confidence: 99%

Sensor localization with algebraic confidence

Saloranta

Severi

Macagnano

et al. 2012

2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)

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In this paper we introduce the concept of algebraic confidence, defined as the measure of belief provided by an algebraic algorithm without a priori information of ranging statistics. This is obtained by employing the Circular-based Interval SMACOF (CIS) algorithm which outputs an algebraic confidence level on targets' estimates, without relying on the propagation of location distributions. We illustrate the validity of our confidence by comparing it to the Fisher error ellipses derived from the Cramér-Rao lower bound (CRLB), corroborating the concept. To exploit the proposed confidence measures during the optimization process, we modify the cost function used in the Circular-based Interval SMACOF (CIS) algorithm and describe how to solve the corresponding optimization problem by means of majorization techniques. The resulting CIS+ algorithm is shown to outperform the CIS algorithm both in terms of accuracy as well as in terms of computational complexity.

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“…Given the limited number of pages, we omit all proofs which can be found in Destino & Abreu (2010); More & Wu (1997). …”

Section: Fundamentals Of the L-gdcmentioning

confidence: 99%