Tackling the flip ambiguity in wireless sensor network localization and beyond

Abstract

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.

On the equivalence of inexact proximal ALM and ADMM for a class of convex composite programming

“…A crucial implication of this result is that the (inexact) block sGS decomposition based multi-block majorized ADMM is equivalent to an inexact majorized proximal ALM. Consequently, we are able to prove the convergence of the whole sequence generated by the former even when the step-length is in the range (0,2).…”

Kinetic Euclidean Distance Matrices

“…Finally, we note that the KEDM formulation in (12) is a generalization of the static EDM formulation in (4). To see the equivalence, note that static points are modeled by a polynomial of degree zero, P = 0, in which case the Gramian becomes G(t) = G 0 since w 0 (t) = 1.…”

“…T He famous distance geometry problem (DGP) [1] asks to reconstruct the geometry of a point set from a subset of interpoint distances. It models a wide gamut of practical problems, from sensor network localization [2], [3], [4] and microphone positioning [5], [6], [7], [8] to clock synchronization [9], [10], to molecular geometry reconstruction from NMR data [11], [12]. Among the most successful vehicles for the design of DGP algorithms are the Euclidean distance matrices (EDM) [13].…”

A Fast Matrix Majorization-Projection Method for Penalized Stress Minimization With Box Constraints

“…In literature (e.g., [41]), this type of perturbation in δ ij is known to be multiplicative and follows the unit-ball rule in defining N x and N a (see [42,Sect. 3.1] for more detail).…”

“…Example 4.2: (EDM word network) This problem has a nonregular topology and is first used in [42] to challenge existing localization methods. In this example, n points are randomly generated in a region whose shape is similar to the letters "E", "D" and "M".…”