On distributed geolocation by employing spring-mass systems

Abstract

Recently, finding the geographic whereabouts of nodes became a key service for many distributed applications, e.g., online games or localizing delivered content. However, an exact localization may be impossible because of GPS signals being unavailable, receivers too expensive, or energy too scarce. Hence,alternatives emerged that typically rely on central databases, which in turn are often found to be inaccurate, though. Facing that problem, we study a complementary idea: By constructing a delay-weighted spring-mass embedding of nodes and augmenting the system with geographic hints, e.g., those of traditional location databases, we efficiently estimate geographic positions of nodes by multilateration and solely distributed means. We will show that peer positions can be estimated with an accuracy of a few hundred kilometers in the average case. The proposed system is evaluated by simulations that are based on real-world PlanetLab latency data.

Towards distributed geolocation by employing a delay-based optimization scheme

“…Furthermore, the estimation errors strictly decrease with an increasing ratio of location hints, i.e, given a fair ratio of 30% anchors, the median error is 172 km, where the mean error equals 250 km. At a first glance, the curve shapes are comparable to a previous study [8], but the reached accuracy is considerably higher. This applies in particular to the dataset, consisting of North American and European nodes: In contrast to the early approach that suffered from inhomogeneities of the underlying network, the introduced neighborhood selection strategies reduce the corresponding influence now.…”

“…Simulation-based schemes typically scale better. The most popular example is perhaps Vivaldi [4] that makes use of a spring-mass-model and in our previous work [8], we studied a Vivaldi-inspired geolocation approach. However, the achievable accuracy was not entirely satisfying, in particular because the algorithm suffered from conceptual weaknesses of the spring-mass approach, e.g., frequent erroneous embedding at local minima.…”

“…The measured delays are mapped to real distances by f : R → R. As global latencies are not only affected by the propagation delay, but also other delay types (especially varying queuing delay) and potential inaccuracies [8] one cannot expect f to return accurate distances, but to derive meaningful approximates. For this article, we will assume a directly proportional relation between delay and distance.…”

“…Taking into account previous work on a delay-based springmass model [8], we contribute an alternative approach, where nodes are embedded on a sphere and local positioning errors are periodically minimized by an iterative Internet delaybased multilateration technique. By including a fair amount of position hints, we efficiently estimate node positions by distributed means.…”

Best Practice in RSS Measurements and Ranging

“…Range-based approaches, on the other hand, make use of distance estimates obtained by processing signals exchanged by the nodes, an operation that is commonly referred to as ranging. Once a sufficient number of range estimates between pairs of nodes have been collected, it is possible to estimate the nodes position in the area by using multilateration algorithms [15], [16], semidefinite programming [17]- [19], maximum likelihood estimators [20], [21], or spring-mass relaxation approaches [22]- [24].…”