I'm not sure what's you model is.
Let's say it is something like:
$$ y = H x + n $$
Now, using the Least Squares model is optimal (In the MSE sense) when $ n $ is AWGN (It is the linear optimal estimator if the noise is white).
So unless the noise in your model is colored, no gain by filtering the data before applying the Least Squares method.
Now, what ...