ARMAX Model Identification with Unknown Process Order and Time-Varying Parameters

Abstract

Identification of a system, in which the generating mechanisms are unknown, has been a central issue in the field of signal processing for many years. The aim of this paper is two-fold: first to investigate and present a method for simultaneously selecting the order and identifying the time-varying parameters of an AutoRegressive Moving Average model with eXogenous input (ARMAX), and second to evaluate the method via computer experiments. The proposed algorithm is based on the reformulation of the problem in the standard state space form and the subsequent implementation of a bank of Kaiman filters, each fitting a different order model. Then the problem is reduced to selecting the true model, using the well-known multi-model partitioning theory for general (not necessarily Gaussian) data pdf’s. Simulations illustrate that the proposed method selects the correct model order and identifies the model parameters in a sufficiently small number of iterations, even when the true model order does not belong to the bank of Kaiman filters. Furthermore, the method is adaptive, in the sense that it can successfully track changes in the model structure in real time. Finally, the algorithm can be implemented in parallel and a VLSI implementation is also feasible.