“…In addition to fitting the IFT footprints, we also require the magnetic field model to fit, in a least squares sense, the in situ magnetometer observations obtained by spacecraft. The data available include measurements obtained by the vector helium magnetometers on Pioneer 10 and 11 [Smith et al, 1974[Smith et al, , 1975 as determined previously [Connerney et al, 1982]. In the linearized system, y is a column vector of the model residuals (observed minus modeled field or equatorial crossing distance), x is a column vector of parameter corrections required to bring the model into closer agreement with the data, and the matrix A is a matrix of partial derivatives relating the observations to the model parameters.…”