MODELING CONTINUOUS-TIME STOCHASTIC PROCESSES USING INPUT-TO-STATE FILTERS

A novel direct approach for modeling continuous-time stochastic processes is proposed in this paper. First the observed data is passed through an input-to-state filter and the covariance of the output state is computed. The properties of the state covariance matrix is then exploited to estimate the positive real spectrum of the observed data at a set of prescribed points on the right half plane. Finally, the continuous-time parameters are obtained from the positive real spectrum estimates by solving a Nevanlinna-Pick interpolation problem. The estimated model is stable. The analytical results are illustrated using numerical simulations.