Persistence of excitation properties for the identification of time-varying systems

The identification of time varying parameters requires that a certain level of information is present in the data through time. Only in this case it is in fact possible to track the parameter variability and form a reliable estimate. This consideration has led to the introduction in the literature of a variety of persistence of excitation notions ranging from the deterministic ones (in the ´80s) to more sophisticated stochastic definitions proposed in the last decade. This paper presents an overview of the existing stochastic excitation notions and discusses important issues like their necessity for tracking and their applicability in different contexts. It appears that the present state of the art is not completely satisfying in terms of completeness and generality of the available results