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Related Experiment Video

Updated: Oct 13, 2025

Author Spotlight: Insights into the Analysis of Human Interaction with 3D Virtual Objects

Author Spotlight: Insights into the Analysis of Human Interaction with 3D Virtual Objects

Published on: October 18, 2024

Novel Solutions to the Three-Anchor ToA-Based Three-Dimensional Positioning Problem.

Mohamed Khalaf-Allah¹

¹Institute of Traffic Telematics, Technische Universität Dresden, 01062 Dresden, Germany.

Sensors (Basel, Switzerland)

|November 13, 2021

Summary

This summary is machine-generated.

New algorithms enable accurate 3D positioning using only three anchor nodes (ANs) and time-of-arrival (ToA) data. This reduces the need for excessive nodes in applications like unmanned aerial vehicle (UAV) navigation.

Keywords:

direct method (DM)particle filter (PF)three-dimensional (3D) positioning time of arrival (ToA)unmanned aerial vehicle (UAV)

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Area of Science:

Robotics and Control Systems
Wireless Sensor Networks
Geospatial Positioning

Background:

Accurate three-dimensional (3D) positioning typically requires at least four non-coplanar anchor nodes (ANs) for time-of-arrival (ToA) methods.
Existing methods face challenges with fewer ANs or specific spatial arrangements.

Purpose of the Study:

To develop and validate algorithms for 3D positioning using only three ANs.
To assess the feasibility of these algorithms in scenarios with horizontally coplanar ANs.
To enable real-time positioning applications with reduced infrastructure.

Main Methods:

Developed a Direct Method (DM) reducing the problem to solving a quadratic equation.
Implemented a Particle Filter (PF) using 1000 particles to estimate the 3D position.
Utilized ToA measurements for particle importance weighting and posterior probability density function (PDF) updating.

Main Results:

Both DM and PF algorithms demonstrated viability in simulations.
Algorithms achieved accuracy and computational efficiency in pursuit and circumnavigation scenarios.
Successful positioning was shown even with a horizontally coplanar arrangement of three ANs.

Conclusions:

The developed DM and PF algorithms enable accurate 3D positioning with only three ANs.
This significantly reduces the number of ANs required for real-time positioning applications.
Enables applications like unmanned aerial vehicle (UAV) autonomous docking and circling without excessive ANs.