If non-white noise is added to an output it appears that the time constants are over-estimated(minor bug)

It is possible that this is a good case for re-introducing some filtering of the output y before identification?

At least, by subtracting the modelled Y from the real Y, it should be possible to determine if the noise appears white or not, after identification, and that could be used to apply a method that is more suitable to this sort of process.

LIkely, the time-constant "smoothes" out the model and this is somehow advantageous for the objective function in this case - but it is not based on reality.

Maybe if the process is "non-white noise" it is more appropriate to disable time-constants altogether?