Eigenvector Constraint-Based Method for Eliminating Dead Zone in Magnetic Target Localization

Abstract

Magnetic target localization using the magnetic gradient tensor (MGT) plays a significant role in underwater localization. However, this method inherently has a localization dead zone, which presents challenges for real-world applications. This paper delves into the root cause of this dead zone, identifying the non-invertibility of the MGT when the magnetic moment vector is orthogonal to the position vector from the target to the observation point. To tackle this issue, a method based on the eigenvector constraints is proposed. By constructing an objective function with eigenvector constraints and leveraging the property that its gradient at the observation point is zero, we derive an equivalent expression for the inverse of MGT that always holds and further develop a dead-zone-free localization method. To validate the robustness and efficacy of the proposed localization method, a comparative analysis with other methods is conducted. Simulation results in a 10 m × 10 m area under Gaussian noise demonstrate the proposed method’s capability to eliminate the dead zone and achieve an average localization error of 0.032 m. Experimental results further demonstrate that the proposed method eliminates the localization dead zone and exhibits greater robustness than the dominant method in the normal region. In summation, this paper provides an effective method for eliminating localization dead zone, offering a more stable and reliable method for magnetic target localization in practice.