Stochastic system transformation using generalized orthonormal basis functions with applications to continuous-time system identification

This paper studies the system transformation using generalized orthonormal basis functions that include the Laguerre basis as a special case. The transformation of the deterministic systems is studied in the literature, which is called the Hambo transform. The aim of the paper is to develop a transformation theory for stochastic systems. The paper establishes the equivalence of continuous and transformed-discrete-time stochastic systems in terms of solutions. The method is applied to the continuous-time system identification problem. It is shown that using the transformed signals the PO-MOESP subspace identification algorithm yields consistent estimates for system matrices. An example is included to illustrate the efficacy of the proposed identification method, and to make a comparison with the method using the Laguerre filter.