Steady state estimation using kernel estimator and stochastic approximation

This work applies passive stochastic approximation method to steady state estimation. The underlying problem can be formulated as: Find the roots of f¯(x)=0 provided only noise measurements y_n =f(x_n,ξ_n) are available, where the sequence {x_n} is also contaminated by noise and Ef(x,ξ_n)=f¯(x). The main difficulty lies in that the sequence (x_n) is generated passively and randomly, and cannot be adjusted in accordance with our wish. To circumvent the difficulty, another sequence {z_n} is generated to approximate the roots of f¯(x)=0. A class of recursive algorithms is proposed with non-additive noise, constant step size and constant window width, and correlated random processes. After reviewing some recent results on the asymptotic properties of the algorithms obtained by the authors, the effort is directed to the numerical experiments and simulations