Continuous-time system identification of nonparametric models with constraints

Although structural constraints such as model order and time delay have been incorporated in the continuous time system identification since its origin, the constraints on the estimated model parameters were rarely enforced. This paper proposes a continuous time system identification approach with constraints. It shows that by incorporating physical parameter information known a priori as hard constraints, the traditional parameter estimation schemes are modified to minimize a quadratic cost function with linear inequality constraints. Using the structure of Frequency Sampling Filters as the vehicle, the paper shows that the constraints can be readily imposed on continuous time frequency response estimation and step response estimation. In particular, a priori knowledge in both time-domain and frequency domain is utilized simultaneously as the constraints for the optimal parameter solution. A Monte-Carlo simulation study with 100 noise realization is used to demonstrate the improvement of the estimation results in terms of continuous time frequency response and continuous time step response.