Robust Adaptive Spacecraft Array Derivative Analysis

Abstract

Multispacecraft missions such as Cluster, Themis, Swarm, and MMS contribute to the exploration of geospace with their capability to produce gradient and curl estimates from sets of spatially distributed in situ measurements. This paper combines all existing estimators of the reciprocal vector family for spatial derivatives and their errors. The resulting framework proves to be robust and adaptive in the sense that it works reliably for arrays with arbitrary numbers of spacecraft and possibly degenerate geometries. The analysis procedure is illustrated using synthetic data as well as magnetic measurements from the Cluster and Swarm missions. An implementation of the core algorithm in Python is shown to be compact and computationally efficient so that it can be easily integrated in the various free and open source packages for the Space Physics and Heliophysics community.