Theoretical and Experimental Study of Order Estimation

Abstract

We consider estimation of system order and parameters for ARX systems with martingale difference noise. The order estimation criterion used is the accumulated prediction error (or predictive least-square error) criterion which generates strongly consistent order estimates. High computational load and over- complex (when real data are processed) models are two glaring problems occurring in order estimation. We develop a fast and parallel algorithm for strongly consistent estimation of system order and parameters. This shows that order estimation by minimizing the APE cost function could be performed on-line. We also modify the APE criterion by adding a device for tradeoffs between model complexity and model accuracy. This modification helps to solve the over-complexity problem. Furthermore, we present a simulation study on order estimation to complement the theoretical analysis.