Reducing the number of flips in trilateration with noisy range measurements

Abstract

Many applications in wireless networks depend on accurate localization services to operate properly. Trilateration is a widely used range-based localization method that can operate in polynomial time, given that the distance measurements are precise. However in real-world, range measurements tend to have errors due to internal and external factors. Flip ambiguities that occur during trilateration as a consequence of imprecise range measurements turn localization via trilateration into an intractable problem. In this paper, we analyze flip ambiguities due to range measurement errors and propose a heuristic solution that tries to minimize the number of flips in trilateration even in highly noisy environments. We simulate our algorithms under various noise scenarios and observe that the use of our heuristic based solution e↵ectively decreases the number of flips in trilateration and increases the accuracy of the localization.

A Localization Method Avoiding Flip Ambiguities for Micro-UAVs with Bounded Distance Measurement Errors

“…Akcan et al [22] proposed a heuristic solution based on the notion of a "safe-triangle" to mitigate the problem of FA in a trilateration network with range noise. First proposed here, a safe-triangle is formed by three nodes with known location, where the distance of any node to the line passing through two other nodes is larger than a set threshold.…”

“…However, even if the network is globally rigid in the presence of errors, FA may still occur. In trilateration, the three measured distances may locate their connected node to a false side, which causes FA due to errors in the measurements [22], [23].…”

Detecting high indoor crowd density with Wi-Fi localization: a statistical mechanics approach

“…It has been argued that one of the biggest source of errors, when using RSS values for localization, is the absence of a single global optimum [15]. In the fingerprinting approaches the phenomenon is called "fingerprinting twins" [14,15], while in the multilateration approaches it is known as "flip ambiguity" [16,17,28]. We also sampled randomly 20 MAC addresses from the sensation data, under various crowd conditions, and plotted the estimations of their coordinates through time.…”

“…This figure shows the estimated x-coordinates (in meters) through time of a static MAC device that was persistent for 24 h (most probably an AP). The "twins" phenomenon originates from the fact that the environmental settings and the temporal variations in the RSS create opportunities for multiple local optima [17], in case of trilateration, or geographically distant positions to share the same RSS vectors [15], in case of fingerprinting. (Note: we call them 'twins' because the empirical evidence suggests so far that there are no 'triplets'; however, theoretically the latter are not excluded.)…”

“…Despite the recent success in using wireless technologies for indoor positioning and crowd counting, several problems remain open. Firstly, there is the problem of ambiguity when attempting wireless indoor localization [14][15][16][17], which is a major source of localization errors. Secondly, when a phone is not 'connected' , its Media Access Control (MAC) address may change (be "randomized") over time [18], complying to privacy policies, thus making it impossible to track the user over time.…”