In estimating parameters in a discrete time model I've often seen the use of filters applied to the input data, before its applied to least squares processing. I've been told that the filters are useful if one wishes to remove bias or high frequency noise that's not considered a part of the model.
But I'm currently working with a problem where I'm using the Moore Penrose pseudoinverse to calculate the least squares. I'm filtering the input data with a lowpass filter to remove high frequency noise well beyond the model dynamics, but the choice of the filter pole seems to have a significant affect on the outcome of the estimate. And in any case the residues are near zero (they don't seem to be better or worse according to pole selection).
How should one chose to filter input data, and should it affect the estimate?