On estimating initial conditions in unstructured models

Estimation of structured models is an important problem in system identification. Some methods, as an intermediate step to obtain the model of interest, estimate the impulse response parameters of the system. This approach dates back to the beginning of subspace identification and is still used in recently proposed methods. A limitation of this procedure is that, when obtaining these parameters from a high-order unstructured model, the initial conditions of the system are typically unknown, which imposes a truncation of the measured output data for the estimation. For finite sample sizes, discarding part of the data limits the performance of the method. To deal with this issue, we propose an approach that uses all the available data, and estimates also the initial conditions of the system. Then, as examples, we show how this approach can be applied to two methods in a beneficial manner. Finally, we use a simulation study to exemplify the potential of the approach.