Wavelength and direction filtering by magnetic measurements at satellite arrays: Generalized minimum variance analysis

The main goal of the Cluster mission, consisting of four identical spacecraft, is the spatial resolution of plasma structures. For the determination of the wave vectors of a wave field from four positions, classical Fourier analysis is inappropriate. We develop a generalized minimum variance technique which gives a high wave vector resolution though the spatial grid is restricted to only a few sampling positions. This technique uses the amplitude and phase information of the magnetic field from the four satellite positions and determines the optimum wave field corresponding to the measured data. The components of the magnetic field are assumed to be normally distributed. The divergence-free nature of the magnetic field is used as a constraint. Using the magnetic data measured at four positions allows up to seven different wave vectors at one frequency to be uniquely resolved.