Modelling of attitude error in vector magnetic data: application to Ørsted data

Abstract

Analysis of data from the Ørsted satellite indicates that the largest source of error arises from an anisotropic attitude uncertainty, related to poorly determined rotation about the axis of the star imager. For two data sets from May and December 1999, I quantify this error, and review and apply a formalism designed to allow for this problem. I argue that, when modelled correctly, this attitude uncertainty should not significantly damage the main field models obtained from Ørsted data.

Candidate models for the IGRF-11th generation making use of extrapolated observatory data

“…Ørsted data were weighted using an anisotropic scheme, to reflect the uncertainty related to attitude provided by the Star Imager (Holme, 2000). In contrast, as the selected CHAMP data were all acquired when both CHAMP star imagers were operating, all CHAMP data were isotropically weighted.…”

Use of the Comprehensive Inversion method for Swarm satellite data analysis

“…As such, these transformations will be degraded by random errors due to physical limitations of the STRs and should therefore be accounted for in the error analysis of the estimators. In a series of papers (Holme andBloxham, 1995, 1996;Holme, 2000) a mechanism was developed in order to account for these errors that will henceforth be referred to as "HB theory". This theory has been used successfully in such models as the Oersted Initial Field Model (OIFM) (Olsen et al, 2000) and Comprehensive Model-4 (CM4) (Sabaka et al, 2004) for instance.…”

“…This formula was chosen because it appears, for instance, that Holme (2000) would advocate its use in this case. In both the CI and HB cases, B CRF was computed from Eq.…”

“…Likewise, satellite scalar measurements are treated as uncorrelated with all other data and the variance is denoted by σ 2 F . For satellite vector measurements, the formalism of Section 4 is employed to account for the CRF attitude error while an additional isotropic term is added to account for instrument noise (Holme, 2000) and is chosen here to match the scalar variance, which is assumed the same for each spacecraft fluxgate magnetometer. Therefore,…”

“…Here a methodology, termed "Selective Infinite Variance Weighting" (SIVW), is developed to handle non-zero mean error due to, for instance, theory inadequacies through the use of bias estimation which exploits Signal-to-Noise ratio (SNR) levels in different data subsets in order to extract the best models. In addition, the methodology of Holme andBloxham (1995, 1996) and Holme (2000) to account for attitude error present in vector magnetometer measurements due to star tracker instabilities is revised in order to improve parameter estimates in the CI algorithm. The entire error treatment mechanism is then placed in the context of robust estimation by applying a Huber weighting scheme to mitigate the effects of outliers (Constable, 1988;Walker and Jackson, 2000;Olsen, 2002).…”