Citation: Zhou, G.; Wang, Y.; Wu, K.;
Wang, H. Localization Approach for
Underwater Sensors in the Magnetic
Silencing Facility Based on Magnetic
Field Gradients. Sensors 2022, 22,
6017. https://doi.org/10.3390/
s22166017
Academic Editors: Enrico Meli and
Shafiqul Islam
Received: 11 June 2022
Accepted: 8 August 2022
Published: 12 August 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Localization Approach for Underwater Sensors in the Magnetic
Silencing Facility Based on Magnetic Field Gradients
Guohua Zhou, Yufen Wang *, Kena Wu and Hanming Wang
School of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China
* Correspondence: wangzimai2022@163.com
Abstract:
Localization of the underwater magnetic sensor arrays plays a pivotal role in the magnetic
silencing facility. A localization approach is proposed for underwater sensors based on the optimiza-
tion of magnetic field gradients in the inverse problem of localization. In the localization system,
a solenoid coil carrying direct current serves as the magnetic source. By measuring the magnetic
field generated by the magnetic source in different positions, an objective function is established. The
position vector of the sensor is determined by a novel multi-swarm particle swarm optimization with
dynamic learning strategy. Without the optimization of the magnetic source’s positions, the sensors’
positions, especially in the z-axis direction, struggle to meet the requested localization. A strategy is
proposed to optimize the positions of the magnetic source based on magnetic field gradients in the
three directions of x, y and z axes. Compared with the former method, the model experiments show
that the proposed method could achieve a 10 cm location error for the position type 2 sensor and
meet the request of localization.
Keywords: localization; underwater sensors; magnetic field gradients; magnetic silencing facility
1. Introduction
Marine vessels, such as submarines and ships, consist of ferromagnetic material which
can disturb the Earth’s magnetic field [
1
,
2
]. The significance of a marine vessel’s magnetic
field has been proverbial since Germany blockaded Britain with magnetic naval mines,
causing great losses to the British Navy in World War II. Magnetic silencing facilities
(MSF) are utilized to reduce the risk of damaging submarines and ships from mines and
the magnetic airborne detection [
3
]. Its key elements are magnetic sensor arrays on the
seafloor, whose efficacious performance depends on the accuracy of the sensors installed
and the accuracy of locating the sensors after installation [
4
]. According to the technique of
installing sensors, the magnitude of the position deviation vector in the three-axis direction
is no more than 30 cm, which could bring magnetic field errors more than 100 nT and have
repercussions for the magnetic assessment of marine vessels. The existence of the position
deviations directly reduces the accuracy of the ship’s measured magnetic field and affects
the assessment of the ship’s magnetic protection capability.
For the magnetic silencing facilities, underwater sensors are installed at a depth of
15~20 m from the pier plane, where a high-sensitivity GPS hardly works in the sea as it is
incompatible with water [
5
–
7
]. In addition, due to seaweed organisms, accumulated sedi-
ment and murky water, there are complex conditions in seafloor environments. Therefore,
it is difficult to provide precision with the localization methods which use both acoustic
and optical signals [
8
]. Comparatively, using a magnetic signal is more useful in a shallow
maritime environment with the advantage of energy efficiency and low cost. Many meth-
ods have explored how to locate underwater sensors [
9
,
10
]. Callmer explored a method to
locate underwater sensors by using an extended Kalman Filter and a vessel with known
static magnetic signature, but it is hard to obtain highly accurate data for the ragged static
magnetic signature [
11
]. Yang proposed a method to simplify the 3D position problem
Sensors 2022, 22, 6017. https://doi.org/10.3390/s22166017 https://www.mdpi.com/journal/sensors
