Analysis of Three-Spacecraft Data Using Planar Reciprocal Vectors

Multi-point analysis methods have been developed for multi-spacecraft missions such as ESA's Cluster, NASA's THEMIS or the upcoming Crosscale designed to study structures such as gradients, shocks, or waves. Although four is the minimum number of resolve fully the spatio-temporal ambiguity, data is sometimes available only at three spacecraft. In this work we demonstrate the use and applicability of planar reciprocal vectors for three-point analysis. We construct robust linear estimators that can fully resolve structures of interest in the three-spacecraft plane. For reconstructing the structure component normal to the three- spacecraft plane, we employ additional assumptions or physical constraints, such as stationarity or the magnetostatic case. We have previously shown that the mathematical framework, based on a least-squares minimization problem, is the same for several classes of applications, such as gradient estimation, wave vector identification, or boundary crossing times. The validation of our method targeted gradient estimations of the magnetic field using simulated Harris sheet structures and data from the Fluxgate Magnetometer (FGM) experiment on Cluster. The FGM is operational on all four spacecraft and thus provides a good comparison between the four- and three-spacecraft techniques. Results indicate the expected robust behavior of the estimate of the gradient component in the three-spacecraft plane for both the simulated and the real data. Estimates of the normal gradient components using different physical constraints and assumptions are promising, although a greater sensibility to the field variability characteristics is observed in this case. We envision applying our technique also for estimating gradients of scalar fields such as pressure measured with the Cluster Ion Spectrometry (CIS) experiment, which operates on only three of the four Cluster spacecraft. Future work includes generalizing the mathematical framework of this technique to wave- vector estimation applications.