MHD Shock Fitting Algorithm

A variation of the basic Lepping-Argentiero shock fitting algorithm gives fits of the MHD shock jump conditions to magnetic field and velocity data from a single spacecraft that are unique and rapidly convergent assuming that the sources of error in the data are uncorrelated gaussian noise. The algorithm is a simple iterative procedure that enforces coplanarity through the use of a Lagrange multiplier and successively minimizes the residuals between model and data. It typically converges to machine accuracy in a dozen iterations or so and works well for signal to noise ratios as low as about unity. Standard techniques from nonlinear programming theory demonstrate that each numerically determined solution is a strict local minimum. The theory of pseudoconvex functions applied to the Lagrangian and the coplanarity constraint condition then shows that the local minima so determined in the twelve dimensional parameter space are global, i.e. unique. Expressions for error estimates for the shock normal and shock speed as functions of the signal to noise ratio are determined analytically. Quality factors based on noise levels estimated from the data are used to determine an objective measure of the goodness of fit. Numerical solutions for the normal and speed based on simulated shocks with uncorrelated gaussian noise are shown as functions of signal to noise ratio and compared to the results of other methods.