System identification using an over-parametrized model class - Improving the optimization algorithm

The use of an over-parametrized state-space model for system identification has some clear advantages: A single model structure covers the entire class of multivariable systems up to a given order. The over-parametrization also leads to the possibility to choose a numerically stable parametrization. During the parametric optimization the gradient calculations constitute the main computational part of the algorithm. Consequently using more than the minimal number of parameters required slows down the algorithm. However, we show that for any chosen (over)parametrization it is possible to reduce the gradient calculations to the minimal amount by constructing the parameter subspace which is orthonormal to the tangent space of the manifold representing equivalent models.