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Quantifying the advantage of vector over scalar magnetic sensor networks for undersea surveillance

Wenchao Li, Xuezhi Wang, Qiang Sun, Allison N. Kealy, Andrew D. Greentree

TL;DR

The paper addresses undersea magnetic surveillance by comparing scalar and vector magnetometer networks using a centralized unscented Kalman filter to track a magnetic dipole target. It formulates a dipole-based target model, two measurement modalities, and a UKF fusion framework, complemented by Fisher information and CRLB analyses. The key finding is that vector magnetometer networks yield substantial tracking gains (over a factor of three) and greater resilience than scalar networks, enabling sparser configurations to outperform denser scalar deployments. The work informs practical design choices for persistent undersea monitoring, suggesting vector-based sensors (e.g., diamond in fibre) as a promising path, while acknowledging the challenges of robust underwater deployment.

Abstract

Magnetic monitoring of maritime environments is an important problem for monitoring and optimising shipping, as well as national security. New developments in compact, fibre-coupled quantum magnetometers have led to the opportunity to critically evaluate how best to create such a sensor network. Here we explore various magnetic sensor network architectures for target identification. Our modelling compares networks of scalar vs vector magnetometers. We implement an unscented Kalman filter approach to perform target tracking, and we find that vector networks provide a significant improvement in target tracking, specifically tracking accuracy and resilience compared with scalar networks.

Quantifying the advantage of vector over scalar magnetic sensor networks for undersea surveillance

TL;DR

The paper addresses undersea magnetic surveillance by comparing scalar and vector magnetometer networks using a centralized unscented Kalman filter to track a magnetic dipole target. It formulates a dipole-based target model, two measurement modalities, and a UKF fusion framework, complemented by Fisher information and CRLB analyses. The key finding is that vector magnetometer networks yield substantial tracking gains (over a factor of three) and greater resilience than scalar networks, enabling sparser configurations to outperform denser scalar deployments. The work informs practical design choices for persistent undersea monitoring, suggesting vector-based sensors (e.g., diamond in fibre) as a promising path, while acknowledging the challenges of robust underwater deployment.

Abstract

Magnetic monitoring of maritime environments is an important problem for monitoring and optimising shipping, as well as national security. New developments in compact, fibre-coupled quantum magnetometers have led to the opportunity to critically evaluate how best to create such a sensor network. Here we explore various magnetic sensor network architectures for target identification. Our modelling compares networks of scalar vs vector magnetometers. We implement an unscented Kalman filter approach to perform target tracking, and we find that vector networks provide a significant improvement in target tracking, specifically tracking accuracy and resilience compared with scalar networks.
Paper Structure (10 sections, 8 equations, 7 figures, 2 tables)

This paper contains 10 sections, 8 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Centralized Unscented Kalman Filter
  4. Fisher information matrix
  5. Performance comparison of scalar and vector arrays
  6. Scenario I
  7. Scenario II
  8. Part I
  9. Part II
  10. Conclusions

Figures (7)

  • Figure 1: Estimating the target's true location $\mathbf{X}_{t,k}$ at time $k$ via centralized fusion and sensor network composing with $n$ sensors. These sensors are located at $\mathbf{x}_{i}$ and can provide magnetic scalar measurement or magnetic field measurement to the fusion center for tracking target.
  • Figure 2: Calculated $\sqrt{\text{Tr}(CRLB)}$ with three sensors (scalar measurement) located at $[10, 10, -25]$ m, $[10, -10, -25]$ m and $[-10, -10, -25]$ m as well as $M=[600, 0, 0]^T$ Am. The results are plotted in $\log_{10}$ scale.
  • Figure 3: Calculated $\log_{10}\left(\sqrt{\text{Tr}(CRLB)}\right)$ with 3 sensor (vector measurement) located at $[0, 0, -25]$ m and different $M$. (a) $M=[600, 0, 0]^T$ Am; (b) $M=[600, 600, 2]^T$ Am
  • Figure 4: The plot of $\log_{10}\left(\sqrt{\text{Tr}(CRLB)}\right)$ over the interested area and true trajectory. The std of noise is $10$ pT and sensors' depth is fixed at $z=-25$ m. (a) scalar model; (b) vector model; (c) the $\sqrt{\text{Tr}(CRLB)}$ along the trajectory.
  • Figure 5: The plot of $\log_{10}\left(\sqrt{\text{Tr}(CRLB)}\right)$ over the interested area and true trajectory. The std of noise is $10$ pT and sensors' heights are fixed to $-80$ m. (a) scalar model; (b) vector model; (c) the $\sqrt{\text{Tr}(CRLB)}$ along the trajectory.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Remark