aalto1 untyped-item.component.html
Optimal transport for 2D multisource localization
Loading...
URL
Journal Title
Journal ISSN
Volume Title
Perustieteiden korkeakoulu |
Bachelor's thesis
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.
Authors
Date
Department
Major/Subject
Mcode
SCI3029
Degree programme
Language
en
Pages
39
Series
Abstract
The radio frequency (RF) localization of multiple sources from time difference of arrival (TDOA) measurements presents a dual challenge: the data association problem of assigning TDOAs to the correct source, and the localization problem of determining the sources' physical positions. This thesis evaluates an optimal transport (OT) framework to solve these two problems concurrently. The analysis focuses on a four-receiver configuration, which is the minimum setup required for always getting a unique 2D location estimate.
Multilateration, the process of localizing a single transmitter based on its TDOA measurements, is an established localization method that uses hyperbolas to model the TDOAs. The intersection points of these hyperbolas correspond to the true locations of the transmitters. Thus, at least three (linearly independent) TDOA measurements are needed to always form a unique location estimate in two dimensions.
Having multiple active transmitters simultaneously complicates the analysis significantly because it is now not known which TDOA measurement corresponds to which transmitter. In this case, one cannot simply find the intersection points of random hyperbolas to locate the emitter. Furthermore, the system can generate false TDOA measurements, for example, when the same signal is reflected from an obstacle to the receivers due to multipath propagation. Such a false measurement can appear genuine and thus add more error in the localization results. For this reason, a method is needed that correctly associates true TDOA measurements with distinct transmitters.
The method developed in this thesis simultaneously solves the localization and data association problems. The employed multilateration method initially generates a large set of possible location estimates using various TDOA measurement combinations. Subsequently, OT is used to associate estimated locations to TDOAs, thereby finding points with the largest hyperbola density. The whole localization method is based on the fact that there are more TDOA hyperbolas that intersect at the true transmitter locations than intersect at other estimate locations. Therefore, denser clusters of hyperbola intersections are formed which are used to find the locations of the transmitters.
Since TDOA measurements always contain some noise, the shape of the hyperbolas deviates slightly from the ideal. Therefore, three hyperbolas do not intersect at the exact same point. A non-linear least squares method is applied to each group of three hyperbolas to find the point that is as close as possible to all three. These points serve as individual location estimates for further analysis.
The localization accuracy of the method, measured as the mean Euclidean distance between the estimates and the true locations, was evaluated in four different simulation scenarios, all of which used a four-receiver system for localization. These simulations considered the effect of noise level, the number of transmitters, and false TDOA measurements on localization accuracy. Additionally, a more accurate, ideal solver was compared with a lower complexity and less accurate solution method. The simulation results indicate that the proposed method can find correct associations and achieve good localization accuracy in the considered two-dimensional scenarios.