Magnetic Dipole Two-Point Tensor Positioning Based on Magnetic Moment Constraints

Magnetic target positioning methods that use magnetic gradient tensors have wide application prospects in unexploded ordnance detection, moving magnetic target tracking, and so on. However, the commonly used positioning methods, such as Nara, Frahm, and scalar triangulation and ranging (STAR), still have some problems. Namely, these methods cannot avoid the influence of the geomagnetic field, depend highly on sensor accuracy, and have poor tolerances to environmental noise, all of which severely restrict their practical applications. To overcome the aforementioned bottleneck, this article proposes a new two-point tensor positioning (TPTP) method based on a magnetic moment constraint. First, a two-point magnetic gradient tensor-measurement structure is built, and a target positioning function is constructed in which a penalty term with target magnetic moment information is introduced. Second, through simulation and comparative analysis, the approximate value range of the optimal penalty coefficient is delimited, and the objective function with penalty items greatly improves the optimization success rate. Finally, we compare the TPTP with state-of-the-art methods in various scenarios, including cases with and without geomagnetic fields, with different sensor accuracies, and with different levels of environmental noise. The experimental results indicate that the proposed TPTP method can effectively avoid the influence of the geomagnetic field. This method can also be used to realize the positioning and tracking of a magnetic target, even if the sensor accuracy is relatively low or the environmental noise is relatively large.