抄録
This paper presents some results obtained through analysis of a parameter identification problem for linear stochastic systems in the framework of functional analysis. A procedure is formulated for the identification of unknown parameters where a class of adaptation mechanisms is used to improve the filter dynamics so that the filtering residual provides an innovation process, i.e., a Brownian motion process independent of observation. The adaptation mechanisms are assumed to be modelled mathematically as a class of dynamical systems driven by the filtering residuals so as to provide a mapping from the function space made up of parameter estimation processes into itself. Sufficient conditions are obtained for the mapping to have a fixed point. The uniqueness of the fixed point is also proved to clarify the conditions for the parameter estimate, which is computed as the fixed point of a locally convergent adaptation mechanism, provides the unknown parameter asymptotically.
