Stochastic peak tracking and the Kalman filter
S. Chang · IEEE Transactions on Automatic Control · 1968
The peak tracking problem can be reduced to a Kalman falter problem [1] with the additional variable of the excursion amplitudec, 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, wheretis 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 tot^{-1/2}.