Article
A Novel Hybrid NN-ABPE-Based Calibration Method for
Improving Accuracy of Lateration Positioning System
Milica Petrovi´c
1,
*
,†
, Maciej Ci˛e
˙
zkowski
2,†
, Sławomir Romaniuk
2
and Adam Wolniakowski
2
and Zoran Miljkovi´c
1
Citation: Petrovi´c, M.; Ci˛e
˙
zkowski,
M.; Romaniuk, S.; Wolniakowski, A.;
Miljkovi´c, Z. A Novel Hybrid
NN-ABPE-Based Calibration Method
for Improving Accuracy of Lateration
Positioning System. Sensors 2021, 21,
8204. https://doi.org/10.3390/
s21248204
Academic Editors: YangQuan Chen,
Nunzio Cennamo, M. Jamal Deen,
Subhas Mukhopadhyay, Simone
Morais and Junseop Lee
Received: 3 November 2021
Accepted: 3 December 2021
Published: 8 December 2021
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4.0/).
1
Faculty of Mechanical Engineering, University of Belgrade, 11120 Belgrade, Serbia; zmiljkovic@mas.bg.ac.rs
2
Faculty of Electrical Engineering, Białystok University of Technology, 15-351 Białystok, Poland;
m.ciezkowski@pb.edu.pl (M.C.); s.romaniuk@pb.edu.pl (S.R.); a.wolniakowski@pb.edu.pl (A.W.)
* Correspondence: mmpetrovic@mas.bg.ac.rs
† These authors contributed equally to this work.
Abstract:
Positioning systems based on the lateration method utilize distance measurements and the
knowledge of the location of the beacons to estimate the position of the target object. Although most
of the global positioning techniques rely on beacons whose locations are known a priori, miscellaneous
factors and disturbances such as obstacles, reflections, signal propagation speed, the orientation of
antennas, measurement offsets of the beacons hardware, electromagnetic noise, or delays can affect
the measurement accuracy. In this paper, we propose a novel hybrid calibration method based on
Neural Networks (NN) and Apparent Beacon Position Estimation (ABPE) to improve the accuracy
of a lateration positioning system. The main idea of the proposed method is to use a two-step
position correction pipeline that first performs the ABPE step to estimate the perceived positions
of the beacons that are used in the standard position estimation algorithm and then corrects these
initial estimates by filtering them with a multi-layer feed-forward neural network in the second step.
In order to find an optimal neural network, 16 NN architectures with 10 learning algorithms and
12 different activation functions for hidden layers were implemented and tested in the MATLAB
environment. The best training outcomes for NNs were then employed in two real-world indoor
scenarios: without and with obstacles. With the aim to validate the proposed methodology in a
scenario where a fast set-up of the system is desired, we tested eight different uniform sampling
patterns to establish the influence of the number of the training samples on the accuracy of the system.
The experimental results show that the proposed hybrid NN-ABPE method can achieve a high level
of accuracy even in scenarios when a small number of calibration reference points are measured.
Keywords:
neural networks; Apparent Beacon Position Estimation; positioning systems; calibration;
ultra wide band; non line of sight
1. Introduction
One of the founding principles in the Industry 4.0 paradigm is the emphasis on the
autonomy of the agents participating in the technological process. In order to achieve the
autonomy of the mobile agents, e.g., Automated Guided Vehicles (AGVs) or mobile robots,
it is paramount to provide a source of reliable navigational data, such as the information
about the position of the agent or the layout of the environment it is working in. The former
is handled by employing various types of positioning systems.
Accurate, precise, and reliable navigational data are especially important in applica-
tions where a given AGV has to cooperate with another vehicle or object, e.g., warehouse
inventory inspection [
1
], cargo carriage in storehouse [
2
], or autonomous picking and
palletizing [
3
]. Another example of an implementation of the reliable positioning system
that is worth mentioning is customer navigation in a retail shop [
4
]. Demesure et al. [
5
]
presents a navigation approach of mobile agents in the AGV-based manufacturing system.
Sensors 2021, 21, 8204. https://doi.org/10.3390/s21248204 https://www.mdpi.com/journal/sensors
