Direct and two-step methods for closed-loop identification: a comparison of asymptotic and finite data set performance

The asymptotic and ®nite data behavior of some closed-loop identi®cation methods are investigated. It is shown that, when the output power is limited, closed-loop identi®cation can generally identify models with smaller variance than open-loop identi®cation. Several variations on some two-step identi®cation methods are compared with the direct identi®cation method. High order FIR models are used as process models to avoid bias issues arising from inadequate model structures for the processes. Comparisons are, therefore, made based on the variance of the identi®ed process models both for asymptotic situations and for ®nite data sets. Process model bias resulting from improper selection of the noise and sensitivity function models is also investigated. In this con- text, the results support the use of direct identi®cation methods on closed-loop data.