A Differential Geometric Viewpoint on Local Identifiability and Identification, Part 1: Theory

The questions of local identifiability and identification of nonlinear sytems are treated from a differential geometric point of view. It is shown how identifiability can be interpreted in the framework of Lie groups, which provides convenient tools for unifying concept of identifiability. Three different notions of identifiability are interpreted in this framework. Furthermore parameter identification itself is also treated. It is shown how a parameter estimator can be formulated in a coordinate-free setting. In this setting it can be clearly determined to what extent the underlying geometric structure and the coordinate-specific parameterization of the system influence the properties of the estimator.