Two-Point Positioning Method with Magnetic Gradient Tensor Invariant Constraints

Abstract

Single-point magnetic gradient tensor positioning methods are greatly affected by geomagnetic field estimation errors, and multi-point magnetic gradient tensor positioning methods are easy to get trapped in local optima. To address these issues, a two-point magnetic gradient tensor positioning method was proposed. Based on the single-point magnetic gradient tensor positioning algorithm, this method used two-point magnetic gradient tensor measurement data and superimposed the constraints of tensor geometric invariants to construct a nonlinear objective function about the target position coordinates, and it used the natural selection-based particle swarm optimization(NSPSO) algorithm to solve the target position coordinates. Simulation experiments demonstrate that the proposed method is less affected by geomagnetic field estimation errors and can search for global optima. It exhibits high localization accuracy. The simulation analysis considers the positioning performance of the proposed method for magnetic targets under different system baseline lengths and magnetometer sensitivities. The results indicate that as the system baseline length and the magnetometer sensitivity improve, the positioning error for magnetic targets decreases.

Keywords

• magnetic gradient tensor
• geometric invariant
• two-point positioning
• natural selection-based particle swarm optimization algorithm