  In this article, we present a structured Kalman filter associated with the
transformation matrix for observable Kalman canonical decomposition from
conventional Kalman filter (CKF) in order to generate a more accurate time
scale. The conventional Kalman filter is a special case of the proposed
structured Kalman filter which yields the same predicted unobservable or
observable states when some conditions are satisfied. We consider an
optimization problem respective to the transformation matrix where the
objective function is associated with not only the expected value of prediction
error but also its variance. We reveal that such an objective function is a
convex function and show some conditions under which CKF is nothing but the
optimal algorithm if ideal computation is possible without computation error. A
numerical example is presented to show the robustness of the proposed method in
terms of the initial error covariance
