PASSIVE STOCHASTIC-APPROXIMATION WITH CONSTANT STEP-SIZE AND WINDOW WIDTH

Motivated by the desire to solve a steady-state estimation and detecti on problem in chemical engineering, and inspired by the recent progres s in passive stochastic approximation, recursive algorithms combining stochastic approximation and kernel estimation are studied and develop ed in this work, The underlying problem can be stated as finding the r oots (f) over bar(x) = 0 provided only noisy measurements y(n) = f(x(n ),xi(n)) are available, where E f(x, xi(n)) = (f) over bar(x). The mai n difficulty lies in that unlike the traditional approach in stochasti c approximation, the sequence {x(n)} is generated randomly and cannot be adjusted in accordance with our wish. Similar to those used in the decreasing step size algorithms, another sequence {z(n)} is generated to approximate the roots of (f) over bar(x) = 0 Some of the features o f the algorithms include: constant step size and constant window width and correlated random processes, Under fairly general conditions, it is proven that a weak convergence result holds for an interpolated seq uence of the iterates, Error bounds are obtained and a local limit the orem is also derived, The algorithm is then applied to an estimation p roblem in chemical engineering, Simulation has shown promising results .