Constellation of N Spacecraft : the Aliasing Problem

Constellations of N spacecraft allow to separate spatial and temporal variations of the electromagnetic field in space as demonstrated by achievements of CLUSTER and MMS missions. Future missions in preparation, involving more than four spacecraft, will offer new opportunities beside proper technological progress in sensors and electronic design : the genuine and promising aspect is the number of spacecraft larger than four. Four spacecraft is the minimal configuration to estimate gradients and to do spatial filtering in three dimensions. More than four spacecraft gives additional degrees of freedom by weighting the constellation ; a numerical weight is attributed to each spacecraft for computing gradients or doing spatial filtering. It has been early recognized that spatial filtering by a constellation of spacecraft is limited by spatial aliasing ; theoretical considerations, for example dispersion relations, allow to discriminate aliased energy peaks. Discriminating aliased energy peaks with more than four space spacecraft is possible just by changing the weighting of the constellation as will be shown for the simplest case N=5. First the aliasing equation is reminded, then the fundamental cell is defined and visualized, and it is shown that aliased peaks are moving when changing the weighting. Meanwhile non-aliased peaks are unaffected.