Some aspects of recursive parameter estimation

The aim of this paper is to develop a unified view of the nature of the recursive, Stochastic Approximation (SA) and Model Reference methods for estimating the parameters of a lumped model of a dynamic system, Thus it is shown how, by sequential minimization of an average prediction error, it is possible to construct recursive algorithms (Predict ion Error Recursions, I'KRs) for almost any lumped parametric model. For a general class of recursions (including I'ERs and SAs) an informal analysis of convergence is given by considering the first order moment behaviour of the recursion (viewed as a stochastic difference equation). This leads to equations given by Ljung. Continuing however yields a second order analysis that provides the asymptotic variance behaviour (Central Limit Theorem) of the algorithms.