Parameter estimation of delay systems

An algorithm for parameter estimation of a class of stochastic hereditary systems, including state-space systems and systems with delays, is presented. In particular, the form of a linear input-output operator A is assumed subject to the determination of a vector of parameters γ. Measurements are made of the process x= A(γ)z, where z is a Gaussian noise process. The maximum likelihood estimate of γ given the (discrete or continuous) measurements of x is obtained by minimizing a Hilbert space norm. The norm is differentiable, so efficient optimization software is applicable. A pair of simple examples are given to show the style and versatility of the method