High-quality aeromagnetic data are important in guiding new knowledge of the solid earth in frontier regions, such as Antarctica, where these data are often among the first data collected. The difficulties of data collection in remote regions often lead to less than ideal data collection, leading to data that are sparse and four-dimensional in nature. Standard aeromagnetic data collection procedures are optimised for the (nearly) 2D data that are collected in industry-standard surveys. In this work we define and apply a robust magnetic data correction approach that is optimised to these four dimensional data. Data are corrected in three phases, first with operations on point data, correcting for spatio-temporal geomagnetic conditions, then operations on line data, adjusting for elevation differences along and between lines and finally a line-based levelling approach to bring lines into agreement while preserving data integrity. For a large-scale East Antarctic survey, the overall median cross-tie error reduction error reduction is 93%, reaching a final median error of 5 nT. Error reduction is are spread evenly between phase 1 and phase 3 levelling operations. Phase 2 does not reduce error directly but permits a stronger error reduction in phase 3. Residual errors are attributed to limitations in the ability to model 4D geomagnetic conditions and also some limitations of the inversion process used in phase 2. Data have improved utility for geological interpretation and modelling, in particular quantitative approaches, which are enabled with less bias and more confidence.