Localization using Distance Geometry: Minimal Solvers and Robust Methods for Sensor Network Self-Calibration

Research output: ThesisDoctoral Thesis (compilation)

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Abstract

In this thesis, we focus on the problem of estimating receiver and sender node positions given some form of distance measurements between them. This kind of localization problem has several applications, e.g., global and indoor positioning, sensor network calibration, molecular conformations, data visualization, graph embedding, and robot kinematics. More concretely, this thesis makes contributions in three different areas.
First, we present a method for simultaneously registering and merging maps. The merging problem occurs when multiple maps of an area have been constructed and need to be combined into a single representation. If there are no absolute references and the maps are in different coordinate systems, they also need to be registered. In the second part, we construct robust methods for sensor network self-calibration using both Time of Arrival (TOA) and Time Difference of Arrival (TDOA) measurements. One of the difficulties is that corrupt measurements, so-called outliers, are present and should be excluded from the model fitting. To achieve this, we use hypothesis-and-test frameworks together with minimal solvers, resulting in methods that are robust to noise, outliers, and missing data. Several new minimal solvers are introduced to accommodate a range of receiver and sender configurations in 2D and 3D space. These solvers are formulated as polynomial equation systems which are solved
using methods from algebraic geometry.
In the third part, we focus specifically on the problems of trilateration and multilateration, and we present a method that approximates the Maximum Likelihood (ML) estimator for different noise distributions. The proposed approach reduces to an eigendecomposition problem for which there are good solvers. This results in a method that is faster and more numerically stable than the state-of-the-art, while still being easy to implement. Furthermore, we present a robust trilateration method that incorporates a motion model. This enables the removal of outliers in the distance measurements at the same time as drift in the motion model is canceled.
Original languageEnglish
QualificationDoctor
Supervisors/Advisors
  • Oskarsson, Magnus, Supervisor
  • Åström, Kalle, Assistant supervisor
  • Lindquist, Björn, Assistant supervisor, External person
Award date2022 Oct 28
Place of PublicationLund
Publisher
ISBN (Print)978-91-8039-377-5
ISBN (electronic) 978-91-8039-378-2
Publication statusPublished - 2022

Bibliographical note

Defence details
Date: 2022-10-28
Time: 13:15
Place: Lecture hall MH:Gårding, Centre of Mathematical Sciences, Sölvegatan 18, Faculty of Engineering LTH, Lund University, Lund. The dissertation will be live streamed but part of the premises is to be excluded from the live stream.
External reviewer(s)
Name: Wymeersch, Henk
Title: Prof.
Affiliation: ChaImers Institute of Technology, Gothenburg.
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Subject classification (UKÄ)

  • Geometry

Keywords

  • localization
  • TDOA
  • TOA
  • trilateration
  • multilateration
  • distance geometry
  • registration
  • sensor network self-calibration

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