We consider the problem of estimating systematic errors in a network of magnetic direction finders using bearing data from a historical record containing a large number of lightning flash observations. It is clear that this problem is linked with the flash location estimation problem and that the two are statistically confounded in the sense that the effect of one cannot be separated from the other. We formalize mathematically a connection between the two problems to arrive at a self-consistent system. In this paper we parameterize the site errors as two-cycle sinusoidal functions and show that the estimation equations can be described by a model which separates into linear and nonlinear parameters. We take advantage of this separation to decouple large-dimensional equations into smaller dimensional equations. Through these equations we show the link between the site error and flash location estimation problems. Validation of our modeling procedures is done by heuristic arguments and analysis of residuals. The latter reveals that not all of the residuals have been explained by sinusoidal site errors but that some residuals might result from the geometry of the network. This appears to be an important problem and is presently under study. Also, there is a need to test the site error estimation algorithm developed in this paper against some ground truth.