On ARX modeling with the ASYM method for errors-in-variables problems

ARX models are often used in system identification. Using high-order ARX models one can well describe arbitrary output noise. Combining high-order ARX models and model reduction techniques, several two-step identification methods are formed, such as the asymptotic method (ASYM) (Zhu, 1998). To extend these methods into errors-in-variables (EIV) problems, it is crucial to get reliable ARX models with input noise effects compensated. The methods based on bias-compensation are classical solutions for such a purpose. By investigating the effects of input variance determination on the parameter estimates, this paper reveals that there is a fundamental limitation in these methods: one has to make a compromise between a full compensation and a reliable model. If the input variance estimate is not well selected, large biases can occur. This difficulty increases as the order of the ARX model increases. Three ways, including a revised bias-compensating method, a generalized instrumental variable estimator (GIVE) and a frequency-domain method are then proposed to avoid unreliable estimates. A comparative simulation study between ASYM and maximum likelihood (ML) methods is also included, showing that ASYM can provide estimates with nearly optimal performance.