Consider the problem of recognizing speech that has gone through a filtering channel, using a standard recognizer trained on unfiltered speech. The match between spectrally distorted speech and undistorted templates won't be very good.
One possibility is to apply an inverse filter to compensate for the channel. The problem is noise. The inverse filter will reemphasize the portions of features that were deemphasized by the channel, but it will also emphasize noise. The more emphasized portions are less reliable, and should be treated as such. This can be done by calculating a "measure of reliability", and passing it to the recognizer together with the reemphasized data (as in scheme #5 above).
A second possibility is to give the recognizer a model of the distortion, that it can apply to its templates or models before matching the input data to them. This implies a third input channel.
Both schemes should work. The second is a bit more flexible.