On-line Structure Detection and Parameter Estimation with Exponential Windowing for Nonlinear Systems

A new recursive orthogonal estimation algorithm is derived which updates both the model structure and the parameters of nonlinear models on-line. Techniques developed for on-line modification of the structure of linear models are not generally suitable when nonlinear systems are considered, because the vector-shift properties no longer hold for nonlinear models and the demands of real-time processing on data storage make on-line structure detection much more difficult. In the present study a new on-line orthogonal estimation algorithm based on the polynomial NARMAX model is derived by extending the family of orthogonal QR decomposition algorithms to include on-line model structure selection. The new algorithm which includes exponential data windowing based on a stable Givens routine minimises the loss function at every selection step by selecting significant regression variables, computes the parameter estimates and maintains the orthogonality of the vector space for continuous computation. Simulated examples are included to demonstrate the performance of the new algorithm.