How do you apply Kalman Filter to track a signal?
The power of the Kalman filter lies in the effect that it predicts the next "state" of the signal/object by using an internal model of the process. That why it is very effective for physical processes, because they can (often) be modelled with quite large precision.

The fact that you point out that it is impossible to derive a model for your signal renders the effect of using (and even the possibility of using)  Kalman filter usesless/impossible.