On Stochastic Approximation Method and Optimal Filtering Theory

摘要

This paper establishes some connections among the maximum likelihood estimate, the optimal filtering and the stochastic approximation solutions to the following well-known problem: Consider the vector-matrix equations Ax + v sub k = b sub k = 1, 2, ... where A is a given r x n matrix; x is an unknown n-vector; v sub k is a random r-vector with E(v sub k) = 0 and E(v sub k v sub j) = I delta(k - j) b sub k is a r-vector of observation. It is desired to determine an estimate x for the unknown parameters x which is optimal in some sense.