The use of stochastic approximation to solve the system identification problem

The identification or modeling of a given plant or system seems to be of current interest with regard to control problems. In particular, attention is often focused upon the case in which the given system is assumed to be linear and time invariant with a rational transfer function whose order is known not to exceed some number
n
. In this case it is desired to estimate the poles and zeros of the transfer function or, alternatively, the coefficients of the numerator and denominator polynomials. This paper describes a method of estimating the coefficients based on certain results in stochastic approximation and optimum filter theory. This method is computationally simple and has a rate of convergence inversely proportional to the observation time. The method requires a knowledge of the correlation properties of the observation noise.