Analysis of three-spacecraft data using planar reciprocal vectors: methodological framework and spatial gradient estimation

In the context of ESA's Cluster mission, four-point array techniques are widely used to analyze space plasma phenomena such as shocks and discontinuities, waves and turbulence, and spatial gradients. Due to failures of single instruments on the Cluster spacecraft fleet, there is also need for array processing of three-point measurements. In this paper we identify planar reciprocal vectors as a generic tool for this purpose. The class of three-point techniques introduced here includes methods for discontinuity analysis, wave identification, and spatial gradient determination. Parameter vectors can be resolved fully in the spacecraft plane but further assumptions or physical constraints have to be specified to estimate the normal components. We focus on the gradient estimation problem where we check and illustrate our approach using Cluster measurements.