On convergence of the recursive identification algorithms

The paper is concerned with identification of a linear dynamic system through recursive algorithms of the approximate maximum likelihood (AML) method. In all papers on the convergence of the recursive AML procedure, no matter what method of analysis is used, a certain rather restrictive positive real condition is imposed on the model of disturbance. In this work, it is shown that recursive AML algorithms converge with probability one under a fairly broad (also positive real) condition which significantly expands the AML application area. The well-known principle of averaging from physics is used as a tool of analysis. A sketch of the proof of the principle of averaging for stochastic difference equations is given.