Recursive Identification of Continuous-Time Linear Stochastic Systems – An Off-Line Approximation

We consider multi-variable continuous-time linear stochastic systems given in innovation form, with system matrices depending on an unknown parameter that is locally identifiable. A computable continuous-time recursive maximum likelihood (RML) method with resetting has been proposed in our ECC 09 paper. Resetting takes place if the estimator process hits the boundary of a pre-specified compact domain, or if the rate of change, in a stochastic sense, of the parameter process would hit a fixed threshold. An outline of a proof of convergence almost surely and in Lq was given, under realistic conditions. In the present paper we show that the RML estimator differs from the off-line estimator by an error of the magnitude of logT/T in an appropriate sense. With this result a conjecture formulated back in 1984 has been settled.