High-quality magnetic 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, comparison with more traditional processing approaches demonstrates superiority, gains in this case are relatively marginal for phase 1 (3-5%) but more substantial for phase 2 (10-35%). For the full implementation, median cross-tie error reduction is 89%, reaching a final error of 8-9 nT. Residual errors are attributed to limitations in the models used for in predicting the 4D geomagnetic conditions and also some limitations of the inversion process used in phase 2. Nevertheless, data have improved utility for tectonic and glacio-tectonic interpretation and modelling, in particular quantitative approaches, which are enabled with less bias and more confidence compared to conventional processing.