Stochastic peak tracking and the Kalman filter

The peak tracking problem can be reduced to a Kalman falter problem [1] with the additional variable of the excursion amplitude
c
, which is then obtained by maximizing the expected peak. In the special case where the parameters do not change, the method yields two tracking procedures depending on the criterion used: 1) Tracking for a limited time and then settling for the parameter value so determined. It is shown that the expected error is proportional to t
^-1
, where
t
is the tracking time [2]. 2) A procedure which agrees with the Kiefer-Wolfowitz stochastic approximation method [3]. It is shown further that the expected total reduction in peak value (due to error and hunting loss) is proportional to
t^{-1/2}.