Derivation and Extensions of the Tolles-Lawson Model for Aeromagnetic Compensation

TL;DR

This paper revisits and extends the Tolles-Lawson linear aeromagnetic compensation model, providing detailed derivations, calibration procedures, and enhancements like second-order corrections for improved aircraft magnetic field modeling.

Contribution

It offers a detailed derivation of the Tolles-Lawson model, clarifies assumptions, and introduces extensions such as second-order corrections and vector field construction methods.

Findings

Derived a more rigorous formulation of the Tolles-Lawson model

Outlined a calibration procedure for model coefficients

Proposed second-order correction and vector field construction methods

Abstract

This note is intended to serve as a straightforward reference that summarizes and expands on the linear aeromagnetic compensation model first introduced by Tolles and Lawson in 1950. The Tolles-Lawson model provides a simple, physical representation of an aircraft's magnetic field, composed of permanent, induced, and eddy current terms, and applies an approximation (a Taylor expansion) to enable fitting coefficients with a general linear model. Here, the Tolles-Lawson model is derived, paying stricter attention to where assumptions are made, the model calibration procedure is described, and some additional comments on a second-order correction and a means of constructing the vector aircraft field are provided.