One-state and twice Kalman filter time scale algorithms
Abstract
We first propose a one-state Kalman filter time scale algorithm, and derive the analytical expressions of the weights and the predictions. Based on the analytical expressions, we introduce the virtual Kalman sampling time. The theoretical analyses and the simulations both validate that we can optimize the frequency stability on any one of the certain observation intervals of the time scale by means of choosing a certain virtual Kalman sampling time. Then, based on this algorithm, we propose a twice Kalman filter time scale algorithm, and describe the principle of the algorithm. The forming time scale only involves walk random frequency modulation noise (RWFM), and does not involve white frequency modulation noise (WFM). The weights are in inverse proportion to the intense of RWFM. The short-term and middle-term frequency stability of the time scale is higher.
