Our choice of calculation frame simplifies greatly the numerical technique. We transform the spacecraft measurement frame via a rotation which aligns the
axis with the measured velocity
such that
. The scalar quantity
remains the same, as does the trace of the pressure tensor. The transformed quantities can be directly inferred from the measured values, so the details of the rotation matrix do not need to be known. As only the magnitude of the velocity is needed, we can use the measured direction of the velocity to recover the corrected velocity vector from the speed derived in our calculation.
The algorithm converges to a solution by improving on a set of initial guesses. The values of initial guess we use were derived from a series of tests in which, given a set of Maxwellian parameters, we simulated measured moments given a range of and energy cut-offs. We ran our algorithm on these inputs to recover the initial underlying Maxwellian values. The initial guesses were then chosen to be the average values for which the alorithm converged successfully for a range of parameter space which represents typical plasma environments encountered by spacecraft.