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

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.