Weighted Complex Orthogonal Estimator for Identifying Linear and Nonlinear Continuous Time Models from Generalised Frequency Response Functions.

A new weighted orthogonal least squares algorithm is derived to estimate linear and nonlinear continuous time differential equation models from complex frequency response data. The algorithm combines the properties and advantages of both weighted and orthogonal least squares algorithms. A weighted complex orthogonal estimator, obtained by combining the proposed algorithm with the modified error reduction ratio test provides an effective and robust way of detecting the correct model structure or determining which terms to include in the model and identifying the unknown parameters. Since the estimation procedure does not involve any numerical differentiation of the noisy data, the performance of the estimator under the influence of significant noise is quite satisfactory. The proposed estimator has been successfully applied to a variety of both linear and nonlinear systems.