Identification of Linear Stochastic Systems Through Projection Filters

A novel method is presented for identifying a state-space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relationship between the state-space model and the finite difference model of linear stochastic systems derived through projection filters. It is proved that least-squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model. In estimating the corresponding state estimator gain, a z-domain method is used. First the deterministic component of the output is subtracted out, and then the state estimator gain is obtained by whitening the remaining signal. An experimental example is used to illustrate the feasibility of the method.