Multi -Modality Joint Localization Method for Magnetic Sources Based on Tensor Invariants

The tensor invariant based positioning method has a broad application prospect in the detection field due to its insensitivity to attitude changes. However, the traditional method, which uses the gradient direction of tensor invariants as the target vector direction, is limited by non-spherical errors, resulting in low positioning accuracy. This paper proposes a new joint positioning method. By analyzing rotational invariants unaffected by relative attitude, and combining the total field gradient magnitude of the magnetic target with tensor contraction quantities, we obtain the real-time relative distance from the target to the measurement point center. This approach achieves multipoint joint positioning in various application scenarios. It effectively overcomes the non-spherical error issues present in traditional methods, significantly reduces the structural complexity of the magnetometer, and retains the advantage of tensor rotational invariants being less affected by attitude changes. Experimental results show that this method can achieve high-precision real-time positioning of magnetic anomaly targets under low signal-to-noise ratio conditions, demonstrating significant engineering application value.