GALS – Gradient Analysis by Least Squares

Abstract

We present a method, GALS (Gradient Analysis by Least Squares) for estimating the gradient of a physical field from multi-spacecraft observations. To obtain the best possible spatial resolution, the gradient is estimated in the frame of reference where structures in the field are essentially locally stationary. The estimates are refined iteratively by a least squares method. We show that GALS is not very sensitive to the spacecraft configuration and resolves structures much smaller than the characteristic size of the spacecraft distribution. Furthermore, GALS requires little user input. GALS has been tested on synthetic magnetic field data and data from the Cluster FGM instrument. GALS will also be useful for other types of data. The results indicate that GALS is robust and superior to the curlometer method for estimating the current from magnetic field measurements.