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Multi-spacecraft missions allow the gradient of important physical quantitiesin the terrestrial environment to be determined. The gradient can be computedfrom four simultaneous measurements in a straightforward way, but thiscomputation does not produce proper error estimates, making it hard to assessthe meaningfulness of the result. Recently developed least-squares gradientcomputation techniques offer the possibility to obtain more precise resultswith all-inclusive error estimates, provided that information about thenon-linearity of the space and time variations of the observed quantity isgiven. The present paper describes several heuristics for estimating thesevariations, thereby enabling a fully automatic computation of the gradientand the associated error estimates. The performance of these heuristics isillustrated with synthetic data corresponding to 4- and 10-spacecraftconfigurations

Least-squares multi-spacecraft gradient calculation with automatic error estimation