A graph showed us that rather than converge, we began to oscillate about the desired point, with the oscillations growing. For a long filter, mu must be smaller. This experiment provided several insights. First, the change in the noise must be relatively smooth, that is, no sharp changes. Upon review of the weighting algorithm, this makes sense, since it uses the gradient of the error function to compute new weights.
Quick changes make for large derivative values.
More importantly, this experiment made us realize that our noise samples were too simplistic. In a real world muffler situation, the noise issued by the engine via the muffler and the noise as picked up by a microphone would differ in phase and frequency. This led us to try more the more complicated simulations described below. In this simulation, we used sensors attached to the skin to record the electrical activity associated with muscle movement. An examination of the signal revealed that the noise was shifted in phase and varied in amplitude.