Compact and accurate linear and nonlinear autoregressive moving average model parameter estimation using Laguerre functions |
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Authors: | Ki H Chon Richard J Cohen Niels-Henrik Holstein-Rathlou |
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Institution: | (1) Department of Molecular Pharmacology, Physiology and Biotechnology, Brown University, Box G-B397, 02912 Providence, RI, USA;(2) Department of Medical Physiology, University of Copenhagen, Copenhagen, Denmark |
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Abstract: | A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series
data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating
linear and nonlinear system dynamics via moving average models, as is the case for the Volterra-Wiener analysis, we propose
an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include
past values of the ouput as well. Thus, all of the advantages associated with using the Laguerre function remain with our
algorithm; but, by extending the algorithm to the linear and nonlinear ARMA model, a significant reduction in the number of
Laguerre functions can be made, compared with the Volterra-Wiener approach. This translates into a more compact system representation
and makes the physiological interpretation of higher order kernels easier. Furthermore, simulation results show better performance
of the proposed approach in estimating the system dynamics than LEK in certain cases, and it remains effective in the presence
of significant additive measurement noise. |
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Keywords: | Volterra-Wiener kernel NARMA Difference equation Impulse response |
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