An analysis of separable least squares data driven local coordinates for maximum likelihood estimation of linear systems

In this paper we study a novel parametrization for state-space systems, namely separable least squares data driven local coordinates (slsDDLC). The parametrization by slsDDLC has recently been successfully applied to maximum likelihood estimation of linear dynamic systems. In a simulation study, the use of slsDDLC has led to numerical advantages in comparison to the use of more conventional parametrizations, including data driven local coordinates (DDLC). However, an analysis of properties of slsDDLC, which are relevant to identification, has not been performed up to now. In this paper, we provide insights into the geometry and topology of the slsDDLC construction and show a number of results which are important for actual identification, in particular for maximum likelihood estimation. We also prove that the separable least squares methodology is indeed guaranteed to be applicable to maximum likelihood estimation of linear dynamic systems in typical situations.