Particle Filtering for Three-Dimensional TDoA-Based Positioning Using Four Anchor Nodes

In this article, the four-anchor time difference of arrival (TDoA)-based three-dimensional (3D) positioning by particle filtering is addressed. The implemented particle filter uses 1000 particles to represent the probability density function (pdf) of interest, i.e., the posterior pdf of the target node’s state (position). A resampling procedure is used to generate particles in the prediction step, and TDoA measurements are used to determine the importance, i.e., weight, of each particle to enable updating the posterior pdf and estimating the position of the target node. The simulation results show the feasibility of this approach and the possibility to employ it in indoor positioning applications under the assumed working conditions using, e.g., the ultra-wideband (UWB) wireless technology. Therefore, it is possible to enable unmanned air vehicle (UAV) positioning applications, e.g., inventory management in large warehouses, without the need for an excessive number of anchor nodes.

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

Sensors ◽

10.3390/s21217325 ◽

2021 ◽

Vol 21 (21) ◽

pp. 7325

Author(s):

Mohamed Khalaf-Allah

Keyword(s):

Direct Method ◽

Computational Cost ◽

Three Dimensional ◽

Quadratic Equation ◽

Position Estimation ◽

Time Of Arrival ◽

Posterior Probability Density ◽

Resampling Procedure ◽

Posterior Probability Density Function ◽

3D Positioning

At least four non-coplanar anchor nodes (ANs) are required for the time-of-arrival (ToA)-based three-dimensional (3D) positioning to enable unique position estimation. Direct method (DM) and particle filter (PF) algorithms were developed to address the three-anchor ToA-based 3D positioning problem. The proposed DM reduces this problem to the solution of a quadratic equation, exploiting the knowledge about the workspace, to first estimate the x- or z-coordinate, and then the remaining two coordinates. The implemented PF uses 1000 particles to represent the posterior probability density function (PDF) of the AN’s 3D position. The prediction step generates new particles by a resampling procedure. The ToA measurements determine the importance of these particles to enable updating the posterior PDF and estimating the 3D position of the AN. Simulation results corroborate the viability of the developed DM and PF algorithms, in terms of accuracy and computational cost, in the pursuit and circumnavigation scenarios, and even with a horizontally coplanar arrangement of the three ANs. Therefore, it is possible to enable applications requiring real-time positioning, such as unmanned aerial vehicle (UAV) autonomous docking and circling a stationary (or moving) position, without the need for an excessive number of ANs.

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UWB Localization with Battery-Powered Wireless Backbone for Drone-Based Inventory Management

Sensors ◽

10.3390/s19030467 ◽

2019 ◽

Vol 19 (3) ◽

pp. 467 ◽

Cited By ~ 12

Author(s):

Nicola Macoir ◽

Jan Bauwens ◽

Bart Jooris ◽

Ben Van Herbruggen ◽

Jen Rossey ◽

...

Keyword(s):

Inventory Management ◽

Ultra Wideband ◽

Human Errors ◽

Personnel Costs ◽

Accurate Localization ◽

Current Consumption ◽

Anchor Nodes ◽

Update Rate ◽

Average Current ◽

Low Costs

Current inventory-taking methods (counting stocks and checking correct placements) in large vertical warehouses are mostly manual, resulting in (i) large personnel costs, (ii) human errors and (iii) incidents due to working at large heights. To remedy this, the use of autonomous indoor drones has been proposed. However, these drones require accurate localization solutions that are easy to (temporarily) install at low costs in large warehouses. To this end, we designed a Ultra-Wideband (UWB) solution that uses infrastructure anchor nodes that do not require any wired backbone and can be battery powered. The resulting system has a theoretical update rate of up to 2892 Hz (assuming no hardware dependent delays). Moreover, the anchor nodes have an average current consumption of only 27 mA (compared to 130 mA of traditional UWB infrastructure nodes). Finally, the system has been experimentally validated and is available as open-source software.

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