Cramer-Rao Lower Bound for Geomagnetic Matching and Its Approximation Method

Geomagnetic matching positioning is a promising autonomous positioning technique that relies on the Earth's magnetic field. The Cramer-Rao lower bound (CRLB) is commonly employed to assess the positioning accuracy of various positioning technologies, and it can formalize the main factors that affect positioning accuracy. This article establishes a refined error model for geomagnetic matching that accounts for multiple sources of error, based on which the CRLB for geomagnetic matching is derived. Building on this, a geomagnetic matching method is proposed, which achieves performance close to the theoretical optimal accuracy. The method accomplishes geomagnetic matching by fitting the weighted mean square difference curve/surface. Monte Carlo simulations demonstrate that the CRLB effectively characterizes the optimal accuracy of geomagnetic matching. In addition, CRLB can serve as a practical criterion to guide magnetic sensor selection, area suitability assessment, and configuration of the matching window.