A Fast Time & Order Recursive Algorithm for Parameter Estimation of a Set of ARX Systems

It would be useful in control system design and signal processing to be able to determine a family of least squares (LS) ARX models of different order (p,q) for a physical system (p: AR order, q: order of the exogenous input part), and then select the best model according to some criterion for evaluating the resulting models. A practical problem is how to obtain such a family of models efficiently. To solve this, a time and order recursive algorithm (TORA) is developed in this paper. For uniformly bounded input and output processes, the strong consistency of the parameter estimates generated by the recursive LS algorithm guarantees that the TORA produces strongly consistent parameter estimates. The TORA can be useful, by combining it with other relevant techniques, in stochastic modeling, adaptive IIR filtering, quantification of unmodeled dynamics, and self-tuning control.