Subspace identification from closed loop data

So called subspace methods for direct identiication of linear models in state space form have drawn considerable interest recently. They have been found to work well in many cases but have one drawback { they do not yield consistent estimates for data collected under output feedback. This contribution points to the reasons for this and also shows how to modify the basic algorithm to handle closed loop data. We stress how the basic idea is to focus on the estimation of the state-variable candidates { the k-step ahead output predictors. By re-computing these from a \non-parametric" (or, rather, high order ARX) one-step ahead predictor model, closed loop data can be handled.