Kalman filter time scale algorithm based on noise characteristics of optically pumped cesium clock

Abstract The time scale algorithm plays an important role in time keeping. Currently, the time scale algorithm primarily adopts the predictability weighting algorithm for microwave clocks. Due to the different working principles and performance of optically pumped small cesium clocks compared with microwave clocks, a new time scale algorithm must be developed to adapt to optically pumped clocks. Based on the noise characteristics of the optically pumped clocks, the state model is established and the time scale is calculated using the Kalman filtering algorithm. The state model of the optically pumped clocks simultaneously considers the effects of white frequency modulation, flicker frequency modulation, and random walk frequency modulation. The proposed algorithm models the flicker frequency modulation for filtering estimation, which effectively improves the stability of the time scale. Here, the flicker frequency modulation is modeled through the linear combination of Markov processes, and the impact of different numbers of Markov processes on the time scale stability is analyzed. Compared with the predictability weighted algorithm, the results obtained by the proposed algorithm demonstrate that the frequency stability of the Kalman filtering time scale based on the noise characteristics was better than that of the predictability algorithm. Taking rapid Coordinated Universal Time (UTCr) as a reference, the frequency stabilities of the time scale based on three optically pumped clocks obtained by the proposed algorithm were 1.14 × 10 −14 for 15 days and 5.50 × 10 −15 for 30 days.