What is this approximation/error-reduction method called?
There is a high risk that you are "overfitting": you are fitting to noise, not to signal.  If that's indeed what is happening, your method won't actually be useful.

The way to find out whether your method is actually making any real improvements (or whether you're just fooling yourself) is to have a holdout set: a separate set of signals, that you haven't used during the error correction.  In other words, you have a training set (one set of signals) and a test set (a separate list of signals, with no overlap with the training set).  You do all of the correction, corrections to the corrections, etc., on the training set.  Then, once you've done that, you measure how effective your resulting corrected algorithm is on the test set.  This will give you a sense of how effective your approach is.