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Session C5: Navigation and Positioning

Magnetic Calibration for Navigation Interpretation and Applicability
Brandon Blakely, Jonnathan Bonifaz, and Aaron Nielsen, AFIT/ANT Center
Date/Time: Friday, Sep. 20, 11:48 a.m.

Magnetic anomaly navigation relies on Tolles-Lawson calibration to accurately model an aircraft's magnetic disturbance fields (permanent, induced, and eddy-current), allowing the extraction of the Earth's magnetic anomaly for navigation purposes. The standard tolles-lawson calibration application calculates static (constant in time) coefficients to model the aircraft disturbance field. This study seeks to improve the accuracy and robustness of the Tolles-Lawson calibration while ensuring that the coefficients make physical sense and the calibration is repeatable. We investigate the use of the L2-norm (ridge regression), the L-1 norm using Lasso (Least Absolute Shrinkage and Selection Operator), and other techniques to solve for the Tolles-Lawson coefficients. These techniques have the potential to mitigate overfitting, improve generalization, and enhance the physical interpretability of the results.
Previous research has focused on utilizing Tolles-Lawson calibration but has often neglected understanding the physical meaning of the calculated coefficients and doing so in a broadly applicable way. Our study examines how to obtain coefficients that align with the expected behavior of the aircraft's magnetic fields. For example, we explore maintaining consistent estimates of the permanent magnetic field regardless of whether only permanent and induced coefficients, or a full model with eddy-current coefficients, are used. For example, when solving for the permanent and induced fields only, the permanent fields are not the same as when solving for the permanent, induced, and eddy-current coefficients. This is while ensuring that the same exact data is used for getting the coefficients. Similar effects are seen when calculating tolles-lawson coefficients at different altitudes or for different flight patterns. Coefficients from the same flight while flying the same flight pattern calculated at 5334 m in altitude differ from those calculated at 9144 m in altitude. At 5334m the permanent coefficients are 2299.35, -4122.95, 1574.46. While the coefficients at 9144m are 2916.09, -4329.24, and 859.66. Additionally, coefficients calculated using a rectangular flight pattern differ from a cloverleaf pattern. Sometimes the difference is not significant, but other times it is significant. Nonetheless, there are inconsistencies that need to be investigated and analyzed.

Our goals are to mitigate this disparity between the coefficients calculated under different conditions as much as possible, come up with a more consistent way to calculate these coefficients, and make physical sense of what is going on. To accomplish this, we analyze various flights from the F-16 dataset to compare coefficient calculation methods (linear, ridge regression, Lasso) and develop a more consistent and broadly applicable approach. This F16 dataset contains flight data at various different altitudes where the aircraft performs a diverse set of flight paths. Performing tolle’s lawson calibration at different altitudes can change the tolles-lawson coefficients, and the coefficients are also affected by the flight pattern to some extent. Testing on this diverse range of data allows us to show how repeatable this method is for calculating the tolles-lawson coefficients and gives us a better understanding of what exactly causes the coefficients to change. Comparing the different methods for solving for the tolles-lawson coefficients will also simplify the coefficient calculation process across various flights and offer insights into the reasons behind superior performance.

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