Lower Bounds on Magnetic Navigation Performance as a Function of Magnetic Anomaly Map Quality

Magnetic Navigation (MagNav) is a rising form of alternative navigation which uses a map of the Earth's crustal magnetic field over a given area of interest, and compares the mapped value at an estimated prior position to the measured output of a quantum magnetometer in order to update the estimate. A key concern with this technology is the relationship between map information content and navigation accuracy. This paper explores the use of the Cramér-Rao Lower Bound (CRLB) as a metric to quantify this accuracy. Two approaches are proposed in this paper: 1) Extended Kalman Filter (EKF) with a unimodal Gaussian distribution modeling the measurement error uncertainty, 2) a version of the EKF that supports the use of a multimodal Gaussian mixture measurement uncertainty. Both methods use information from a measurement residual histogram generated by SandboxAQ's machine-learning models trained on data collected during flight campaigns. These methods are evaluated on synthesized aircraft trajecto-ries over a given region of interest. The results are presented in the form of CRLB values superimposed on a regional map, which is compared with the directional magnetic gradient over a region in the same heading as the trajectory. This demonstrates the correlation between the magnetic information present in the map, indicated by the gradient values, with navigation performance bounds when using the map in MagNav. Simulation results for a 250 × 400 km² region with a grid spacing of 0.5 km using the North American Magnetic Anomaly Map (NAMAM) show a strong correlation between the gradient map and the CRLB heatmap where areas with higher gradient values result in lower CRLB values, indicating better navigation performance. Moreover, results show a significant reduction in the CRLB value for Method 2 when compared to Method 1 due to a more accurate noise model representation. Finally, the analysis in this paper allows the development of tools that can be used to compare magnetic anomaly maps obtained from different sources and different data collection initiatives.