Using an error prediction filter for filtering a semi-known signal
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