Using an error prediction filter for filtering a semi-known signal I'm trying to wrap my head around the proper use of a Wiener or error-prediction filter for filtering data. It seems to me that it is only a whitening filter, so how is it used when the data you want to recover isn't an AWGN signal?

For instance, I have a signal that has several distint interfering signals - I can see them on a PSD, but I don't know that they are a) stationary and b) what properties they have. I can use a method like Yule-Walker equations to recover the AR model for the whole signal, but in this case I only want to recover the model of the interfering signals, not the portion I want to recover. 

I tried implementing an adaptive LMS notch filter, with the reference signal being a single sinewave, but this turned out to me much too narrow and didn't track frequency changes in the signal very well.

I guess basically my question is this, if I'm using an error prediction filter to filter real data, then how do I separate the data portion from the noise portion? In other words, I don't want to whiten the whole signal, only the noise portion. What am I missing?
i am not sure i understand correctly the question (feel free to update me if not so).

There is the MUSIC algorithm, which extracts signals embedded in a background noise, as a sum of sinusoidals signals

There is also the option to use SVD (or Karhunen-Loeve transform) and reduce the dimensionality of the input data while retaning maximum information (this will discard most of the background noise components).

If this is online or real-time, this could be done adaptively.

Hope this helps