Identification in closed loop: asymptotic high order variance for restricted complexity models

Asymptotic high order variance expressions for identified models have found widespread use in, for example, optimal experiment design, analysis of model accuracy and control. The expressions derived in the 1970´s and 1980´s by Berk, Ljung and others are valid for a wide range of operating conditions and models such as restricted complexity models identified from open loop data as well as full order models identified from closed loop data. Throughout the 1990´s much attention has been devoted to the issue of identification of models based on closed loop data. In order to, at least asymptotically in the model order, be able to analyze the quality of such models a corresponding high order variance theory for restricted complexity models identified from closed loop data is necessary. The paper provides this for models with a fixed noise model. A novel variance expression, valid for Gaussian signals, is derived. Simulations show that this expression is surprisingly accurate also for non-Gaussian signals.