Kalman Filter for Unobservable Systems and Its Application to Time Scale Generation by Atomic Clock Ensembles

This paper proposes Kalman filter algorithms for unobservable systems. The proposed algorithms are effective in the time scale generation by atomic clock ensembles with undetectable modes. Applying the conventional Kalman filter (CKF) to an undetectable system causes numerical instability due to the divergence of the error covariance matrix. The proposed algorithm can prevent numerical instability while providing the same estimation as that of the CKF if the system has undetectable modes only on the unit circle. In addition, we also propose the steady-state form of the proposed algorithm. Numerical simulations confirm the validity of these algorithms for time scale generation by atomic clock ensembles.