# In Situ Calibration Method for an MGT Detection System Based on Helmholtz Coils

## TL;DR

This paper introduces a new in-place calibration method for magnetic sensors that improves accuracy and reduces errors without needing to rotate the sensors.

## Contribution

A novel in situ calibration method for MGT systems using stationary sensors and Helmholtz coils, eliminating rotational errors and enhancing precision.

## Key findings

- Tensor invariant CT decreased from 6287.84 nT/m to 7.57 nT/m with reduced variance.
- Inter-sensor output differences were suppressed to 1–3 nT, and magnetic field magnitude error dropped to 3 × 10−4 nT.
- The method achieved a 5–6-order-of-magnitude enhancement in calibration precision.

## Abstract

What are the main findings?
Proposing an In Situ Calibration Method for Magnetic Gradient Tensor (MGT) Systems Based on Three-Axis Helmholtz Coils.A two-stage calibration process was established: Single-element nonlinear calibration and Array relative calibration.Closed-loop generation method for constant-magnitude random magnetic fields has been realized.

Proposing an In Situ Calibration Method for Magnetic Gradient Tensor (MGT) Systems Based on Three-Axis Helmholtz Coils.

A two-stage calibration process was established: Single-element nonlinear calibration and Array relative calibration.

Closed-loop generation method for constant-magnitude random magnetic fields has been realized.

What are the implications of the main findings?
Achieve stationary calibration without rotation, eliminating rotational errors and noise.Simultaneously compensates for magnetic sensor array scaling factors, non-orthogonality, soft iron/hard iron effects, and attitude inconsistencies.Significantly enhance the calibration stability and repeatability of magnetometer arrays.

Achieve stationary calibration without rotation, eliminating rotational errors and noise.

Simultaneously compensates for magnetic sensor array scaling factors, non-orthogonality, soft iron/hard iron effects, and attitude inconsistencies.

Significantly enhance the calibration stability and repeatability of magnetometer arrays.

Vector magnetometer arrays are essential for ferromagnetic target detection and MGT measurement, but their performance is limited by proportional factor errors, triaxial non-orthogonality, soft/hard iron interference, and inconsistent array orientations. Traditional rotation-based scalar calibration requires magnetic-free turntables or manual multi-orientation operations, introducing mechanical noise, orientation perturbations, and poor repeatability. This paper proposes an in situ rapid calibration method for MGT systems using triaxial Helmholtz coils. By generating three-dimensional magnetic field sequences of constant magnitude and random directions while keeping the sensors stationary, the method replaces conventional rotational excitation. A two-stage rapid calibration algorithm is developed to achieve individual sensor error modeling and array relative calibration. Experimental results show substantial improvements. The tensor invariant CT decreased from 6287.84 nT/m to 7.57 nT/m, with variance reduced from 1.46 × 106 to 13.47 nT2/m2; inter-sensor output differences were suppressed to 1–3 nT; and the magnetic field magnitude error dropped from ~940 nT to 3 × 10−4 nT, achieving a 5–6-order-of-magnitude enhancement. These results verify the method’s effectiveness in eliminating rotational errors, improving array consistency, and enabling high-precision in situ calibration with strong engineering value.