Initialisation aspects for subspace and output-error identification methods

This paper is inspired by a recent contribution by Rao and Garnier about identification of continuous time models. They show examples where methods that directly estimate continuous time models, based on smoothed differentiated input-output data outperform methods that are based on discrete time model estimation. The reasons for that situation are investigated in this contribution. It turns out that the key problem is that ARX-type models are very biased for the example in that study, which leads to problems for initializations for output error models both based on ARX/IV techniques and on subspace (CVA estimation techniques). The remedy is to decrease the ARX-bias via low pass data filtering, which in turn also explains why the direct continuous-time estimation techniques (with inherent data smoothing) do not suffer from this problem.