Interpolating with data-space prediction-error filters

The Madagascar sea elevation dataset presents a problem where data are collected along crossing tracks. These tracks are not straight, and are therefore irregular in the model space. Previous methods assumed that the data were regularly sampled in the model space coordinate system, or did not take into account the regularities in the acquisition of the data. Instead of attempting to find a prediction-error filter in the model space, I estimate two prediction-error filters in a coordinate system based on the data’s spatial distribution, and show how to regularize the data with these filters with promising results. I then show how this strategy can be applied to 2D and 3D land surveys when data predicted by reciprocity is included.