# Millimeter-Scale Magnetic Positioning Using a Single AMR Sensor and BP Neural Network

## TL;DR

This paper introduces a low-cost, high-precision positioning system using a single magnetic sensor and a neural network for millimeter-scale tracking.

## Contribution

The novel use of a single AMR sensor with a BP neural network enables accurate, compact magnetic positioning.

## Key findings

- Simulation RMSEs for X and Z axes are 0.27 mm and 0.26 mm, respectively.
- Actual test RMSEs for X, Y, and Z axes are 0.83 mm, 1.15 mm, and 0.85 mm.

## Abstract

Unlike conventional positioning systems that rely on multiple sensors, the positioning system proposed in this study uses a single anisotropic magnetoresistive (AMR) sensor to measure the magnetic field of a target permanent magnet. This approach significantly reduces the system hardware cost and complexity, facilitating the miniaturization of positioning systems. Leveraging a BP neural network model, which is shown to be fast and accurate, the positioning system obtains the real-time magnetic field of the target magnet using a single sensor, subsequently converting three-axis magnetic field data into coordinate information to achieve real-time tracking and localization. The results show that the root mean square errors (RMSEs) for the X and Z axes in the simulation are 0.27 mm and 0.26 mm, respectively, while the RMSEs for the X, Y, and Z axes in the actual test are 0.83 mm, 1.15 mm, and 0.85 mm, respectively. It is also observed that the positioning error correlates with variations in the magnetic field with respect to position, which originate from the strong distance-dependent nonlinearity of the magnetic field. This method not only reduces hardware costs but also maintains accuracy. It is particularly well-suited to applications requiring high-precision positioning and tracking, achieving millimeter-level accuracy within a volume of 50 × 40 × 40 mm3. It has potential applications in aerospace intelligent connectors, medical devices and automation systems, where space and signal lines are limited.