Data driven local coordinates for normalized state-space systems: orthoDDLC

A new approach to the question of parametrizing state-space systems is considered. The approach consists of using input-normal state-space representations. These representations are unique up to an isometric state isomorphism. By decomposing the tangent space of the set of normalized controllable matrix pairs into the tangent space of the equivalence class and the orthogonal complement one obtains an interesting set of local coordinates with a number of remarkable properties. Here the approach is presented in the context of a separable least squares approach to maximum likelihood estimation of a linear system.