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

Abstract

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.

Emitter Location with Azimuth and Elevation Measurements Using a Single Aerial Platform for Electronic Support Missions

“…Therefore, the PF can simultaneously deal with nonlinear models and non-Gaussian or multimodal distributions. The PF approximates the posterior probability density function (PDF), p(p e |Z) , as a weighted combination of particles [41]:…”

“…The implementation of Equation ( 31) has to account for the rare case of getting zero values for the two summation terms to avoid division by zero. The estimate of the emitter location,p e , is obtained by the weighted trimmed average estimate (WTAE) [41,42], in which a number L, L < P, of the best-weighted particles, is selected and their weights are normalized as:p…”

A Survey of Smartphone-Based Indoor Positioning System Using RF-Based Wireless Technologies

“…In TDOA based localization, the distance difference between the tag device and APs is calculated based on time difference measurements as shown in Figure 3. Here, the difference of distance to APs and to the AP where the signal first arrives is [88]:…”

“…Here, the difference of distance to APs and to the AP where the signal first arrives is [ 88 ]: where and are the time instant of signal reception from AP i and j , respectively. Geometrically, with a given TDOA measurement, the tag device must lie on a hyperboloid with a constant range difference between the two APs.…”

Lora RTT Ranging Characterization and Indoor Positioning System

“…In the early days, the Kalman filter positioning algorithm is mainly used to solve the problem achieving efficient state estimation for linear Gaussian systems [24]. Moreover, to deal with unwanted errors and nonlinear distortions, particle filter (PF) is applied as a nonparametric filter to location, which is recursive implementations of Monte Carlo-based statistical processing [25][26][27] and performs well in localization efficiency, stability, and accuracy.…”