Electric potential estimation with line-of-sight measurements using basis function optimization

Given line-of-sight drift-velocity measurements at points on the Earth, our goal is to estimate the electric potential distribution to match the drift velocity pattern. The electric potential is first expressed as a coefficient expansion of radial basis functions, and based on this expansion the expressions for the velocities are derived. A least-squares problem is then set up to minimize the error between the estimated velocity and the measurements. The coefficient vector obtained by solving the least squares problem is used to reconstruct the potential pattern. To further improve the fit, optimization of basis function parameters are also considered. Necessary gradient expressions are derived, which are then used in a quasi-Newton optimization algorithm. The new technique is demonstrated with a test problem and with real data.