COMPACT AND ACCURATE LINEAR AND NONLINEAR AUTOREGRESSIVE MOVING AVERAGE MODEL PARAMETER-ESTIMATION USING LAGUERRE FUNCTIONS

A linear and nonlinear autoregressive moving average (ARMA) identifica tion algorithm is developed for modeling time series data. The algorit hm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiene r kernals. However, instead of estimating linear and nonlinear system dynamics via moving average models, as is the case for the Volterra-Wi ener analysis, we propose an ARMA model-based approach. The proposed a lgorithm is essentially the same as LEK, but this algorithm is extende d to include past values of the ouput as well. Thus, all of the advant ages associated with using the Laguerre function remain with our algor ithm; but, by extending the algorithm to the linear and nonlinear ARMA model, a significant reduction in the number of Laguerre functions ca n be made, compared with the Volterra-Wiener approach. This translates , into a more compact system representation and makes the physiologica l interpretation of higher order kernels easier. Furthermore, simulati on results show better performance of the proposed approach in estimat ing the system dynamics than LEK in certain cases, and it remains effe ctive in the presence of significant additive measurement noise.