Distributed weighted-multidimensional scaling for node localization in sensor networks

Abstract

Accurate, distributed localization algorithms are needed for a wide variety of wireless sensor network applications. This article introduces a scalable, distributed weighted-multidimensional scaling (dwMDS) algorithm that adaptively emphasizes the most accurate range measurements and naturally accounts for communication constraints within the sensor network. Each node adaptively chooses a neighborhood of sensors, updates its position estimate by minimizing a local cost function and then passes this update to neighboring sensors. Derived bounds on communication requirements provide insight on the energy efficiency of the proposed distributed method versus a centralized approach. For received signal-strength (RSS) based range measurements, we demonstrate via simulation that location estimates are nearly unbiased with variance close to the Cramér-Rao lower bound. Further, RSS and time-of-arrival (TOA) channel measurements are used to demonstrate performance as good as the centralized maximum-likelihood estimator (MLE) in a real-world sensor network.

Algorithmic Aspects of Sensor Localization

“…Another iterative technique is shown in dwMDS [42]. It not only formulates the MDS problem with a novel optimization objective (the weighted cost function over multiple range measurements of pairwise distances) but also adopts an iterative algorithm starting from an initial estimation on the locations.…”

“…Since locations of nodes are of importance to the applications' tasks, the security of the location needs to be guaranteed. Although some researches on security of localization schemes are presented [70,71], the types of attacks and the related countermeasures are restricted to a few typi- [42] 2.48m for RSS; 1.12 for TOA O(nL) 4 anchors at corners Ecolocation (outdoor) [66] 20%D N/A 11 nodes with full connectivity Ecolocation (indoor) [66] 35%D N/A 12 anchors, 5 non-anchors Robust Quad [34] 5.18cm for ultrasound ranging N/A dg=12, total 40 nodes Multilateration [21,45] 10.67m N/A range data from 1 mobile beacon Mobile Beacon [45] 1.4m N/A 12 non-anchors, 1 mobile beacon RADAR [48] 3m N/A dg=3, 3 anchors Kernel-based Learning [49] 3.5m N/A grid deployment of 25 anchors and 81 nodes LaSLAT [51] 1.9cm for ultrasound ranging N/A dg=10, total 27 nodes cal cases. Similarly, researches on privacy of nodes' locations mostly focus on preventing the locations of data sources or base stations from being exposed to adversaries [72,73].…”

Sparse multidimensional scaling for blind tracking in sensor networks

“…Hence the term sparsity penalized MDS. The cost function of the dwMDS algorithm [9] is motivated by the variational formulation of the classical MDS, which attempts to find sensor location estimates that minimize the inter-sensor distance errors. Keeping in mind that it is the geometry of the sensor network which is crucial for tracking, we present a novel extension of the dwMDS algorithm through the addition of the sparseness inducing l p -constraint.…”

“…Among the popular approaches are adaptive trilateration [32,39] and successive refinement [9,23] algorithms. In trilateration, each sensor gathers information about its location with respect to anchor nodes, also referred to as seeds [31], through a shortest path.…”

“…In this chapter, we present a sparsity constrained dwMDS algorithm, which can localize the relative positions of the sensor nodes even in the absence of anchor nodes. The dwMDS algorithm proposed in [9] is a successive refinement method, where a global cost function is divided into multiple local cost functions at each sensor location and the computational load involved in finding the sensor location estimates is divided among the sensors in a distributed fashion. The allocation of non-negative continuous weights to the measured data overcomes the problem of combining local maps to one global map, a problem that is common to other decentralized methods [23].…”