Estimating the vector electric field using monostatic, multibeam incoherent scatter radar measurements

An algorithm has been developed to image the local structure in the convection electric field using multibeam incoherent scatter radar (ISR) data. The imaged region covers about 4 degrees in magnetic latitude and 8 degrees in magnetic longitude for the specific geometry considered (that of the Poker Flat ISR). The algorithm implements the Lagrange method of undetermined multipliers to regularize the underdetermined problem posed by the radar measurements. The error on the reconstructed image is estimated by mapping the mathematical form to a Bayesian estimate and observing that the Lagrangian method determines an effective a priori covariance matrix from a user-defined regularization metric. There exists a unique solution when the average measurement error is smaller than the average measurement amplitude. The algorithm is tested using synthetic and real data and appears surprisingly robust at estimating the divergence of the field. Future applications include imaging the current systems surrounding auroral arcs in order to distinguish physical mechanisms.