State Observability and Parameters Identifiability of Stochastic Linear Systems

A new representation of stochastic linear time-invariant systems is presented. This representation generalizes in a rigorous way the concept of observability to parameters identifiability. The state of the augmented system is a combination of the state of the original system and the unknown parameters. It is shown that simultaneous state observability and parameters identifiability of linear time-invariant system is an observability problem of an augmented linear time-variant system. It is shown that the well known results derived by Least Squares(LS) algorithms evolve as a special case of the new representation. The representation yields necessary and sufficient conditions on the simultaneous state observability and parameters identifiability. These conditions apply to estimation in open and closed loop without further restrictions. Simulation results demonstrate the performance of estimation with this new approach.