Rubidium atomic clocks have been used extensively in various fields, with applications such as a core component of Global Navigation Satellite Systems (GNSS). However, they exhibit inherently poor long-term stability. This paper presents the development of a control system for rubidium atomic clocks. It introduces an adaptive Kalman filtering algorithm for the disciplining of a rubidium atomic clock, utilizing autocovariance least squares (ALS) to estimate the clock’s noise parameters. The experimental results demonstrate that the proposed algorithm achieves a high estimation accuracy. The standard deviation of the clock error between the steered rubidium atomic clock 1 Pulse Per Second (1PPS) and Coordinated Universal Time (UTC) provided by the National Time Service Center (NTSC) is better than 2.568 nanoseconds(ns), with peak-to-peak values improving to within 11.358 ns. Notably, its frequency stability is reduced to 3.06 × 10⁻¹³ @100,000 s. The results for the rubidium atomic clock demonstrate that the adaptive Kalman filtering algorithm proposed herein constitutes an accurate and effective control strategy for the rubidium atomic clock discipline.

The BeiDou-3 Navigation Satellite System (BDS-3) precise point positioning (PPP) service through the B2b signal (PPP-B2b) leverages precise correction data disseminated by satellites to eliminate or mitigate key error sources, including satellite orbit errors, clock biases, and ionospheric delays, thereby enabling high-precision timing and positioning. This paper investigates the disparities in time comparison and positioning capabilities associated with the PPP-B2b signals transmitted by the BDS-3 Geostationary Earth Orbit (GEO) satellites (C59 and C61). Three stations in the Asia–Pacific region were selected to establish two time comparison links. The study evaluated the time transfer accuracy of PPP-B2b signals by analyzing orbit and clock corrections from BDS-3 GEO satellites C59 and C61. Using multi-GNSS final products (GBM post-ephemeris) as a reference, the performance of PPP-B2b-based time comparison was assessed. The results indicate that while both satellites achieve comparable time transfer accuracy, C59 demonstrates superior stability and availability compared to C61. Additionally, five stations from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) were selected to assess the positioning accuracy of PPP-B2b corrections transmitted by BDS-3 GEO satellites C59 and C61. Using IGS/iGMAS weekly solution positioning results as a reference, the analysis demonstrates that PPP-B2b enables centimeter-level static positioning and decimeter-level simulated kinematic positioning. Furthermore, C59 achieves higher positioning accuracy than C61.

This paper addresses the issue of limited timing accuracy in complex environments for both the BeiDou system (BD) and the long-range navigation system (LORAN). We delve into the correction algorithm for LORAN timing signals and an adaptive fusion timing algorithm based on the extended Kalman filter (EKF). First, we introduce the advantages and limitations of the BD and LORAN systems in timing applications, as well as the principles of the EKF algorithm and its application in multisource information fusion. Next, we propose a correction algorithm signal to address the significant fluctuations in LORAN timing signals. Building on this, we continue to study an adaptive BD and LORAN fusion timing algorithm based on the EKF. This involves optimising system noise covariance through adaptive adjustments and establishing a fusion timing algorithm model based on the EKF. Finally, we construct a test platform to verify the effectiveness of the proposed algorithms. The experimental results demonstrate that, compared to a single navigation system, the adaptive BD and LORAN fusion timing algorithm based on the EKF significantly improves the accuracy and stability of system timing. Additionally, correcting the LORAN timing results before fusion further enhances system fusion timing performance metrics. The algorithm still maintains high performance in complex environments, showing great application prospects.

Three stations in the Asia-Pacific region are selected to form two time comparison links. By comparing the correction accuracy of the satellite orbits and clock deviations of the PPP-B2b messages broadcast by the two GEO satellites of BDS-3 C59 and C61, and taking the time comparison results obtained by the GBM post-ephemeris as a reference, the accuracy of the time comparison of the PPP-B2b messages broadcast by the two GEO satellites C59 and C61 was evaluated. The results show that the accuracy of time comparison between C59 and C61 is similar, but the stability and availability of C59 are better than those of C61. In addition, five IGS/IGMAS stations were selected to evaluate the accuracy of the PPP-B2b message transmitted by the C59 and C61 GEO satellites for BDS-3 positioning, using the IGS/IGMAS weekly solution positioning results as a reference. The results show that the static positioning of PPP-B2b broadcasted by C59 and C61 can reach centimeter level, and the simulated kinematic positioning can reach decimeter level. The positioning accuracy of C59 is higher than that of C61.

This paper explores effective methods for taming rubidium atomic clocks with longwave timing signals. In an in-depth analysis of the time-difference data between the 1PPS timing signal output from the ground-wave signal received by a long-wave receiver and the 1PPS signal from UTC, we observe that the time-difference data has significant short-term jitter and long-term periodicity effects. To meet this challenge, we adopt several innovative strategies. First, we use the Fourier transform algorithm to analyse the time-frequency characteristics of the time-difference data in detail and accordingly propose a de-jittering correction algorithm for the long-wave timing data, which is aimed at improving the stability of the long-wave timing signals. Secondly, the time difference model of the rubidium clock is innovatively modified, and a quadratic polynomial superimposed with a periodic fluctuation term is constructed, which can accurately solve and eliminate the periodic components and obtain smoother time difference data. Finally, the parameters of the rubidium clock are accurately estimated by the least-squares method using the corrected smoother time difference data, and the output frequency of the rubidium clock is adjusted accordingly so that the rubidium clock is tamed effectively by the long-wave timing signal successfully. The experimental results show that the long-term stability of the tamed rubidium clock is significantly improved to 3.52 × 10⁻¹³/100,000 s; meanwhile, the phase deviation of the output 1PPS from the UTC of the tamed rubidium clock after entering the stabilisation period is kept within 25 ns.

Gravity-assisted navigation is an important means for underwater vehicles to achieve autonomous, passive, and long-endurance navigation. Among its key procedures, correcting the inertial navigation system (INS) based on gravity matching positions is of critical significance. In this paper, using shipborne measured INS data and gravity data together with a gravity database inverted from satellite altimetry data, the entire process of gravity-assisted navigation was experimentally validated through the normal time-frequency transform (NTFT) and Kalman filtering. NTFT is mainly used for gravity error correction, while Kalman filtering is primarily applied to matching algorithms. The analysis of the results shows that after 68.8 h, gravity-assisted navigation technology (GANT) can maintain navigation accuracy within 2 n mile (1 n mile ≈ 1852 m). Through comparison of different calibration methods, it is concluded that open-loop calibration applied only in the longitude direction is feasible and achieves satisfactory navigation performance. This surface vessel-based gravity-assisted navigation experiment addresses aspects such as experimental conditions and algorithmic techniques, serving as an important foundation for further underwater navigation applications.