Time synchronization is a critical prerequisite for unmanned aerial vehicle ad hoc networks (UANETs) to facilitate navigation and positioning, formation control, and data fusion. However, given the dynamic changes in UANETs, improving the convergence speeds of distributed consensus time synchronization algorithms with only local information poses a major challenge. To address this challenge, this study first establishes a convex model on the basis of graph theory and relevant theories of random matrices to approximate the original problem. Subsequently, three acceleration schemes for consensus algorithms are derived by minimizing the Frobenius norm of the iteration matrix. Additionally, this study provides a new upper bound for constant communication weights and discusses the limitations of existing metrics used to measure the convergence speeds of consensus algorithms. Finally, the proposed schemes are compared with existing ones through simulation. Our results indicate that the three proposed schemes can achieve faster convergence while maintaining high-precision synchronization in scenarios with static or known topological structures of networks. In scenarios where the topological structure of a UANET is time-varying and unknown, the scheme proposed in this paper achieves the fastest convergence speed.

To improve the positioning accuracy of the Loran system and meet the requirements of Loran/BDS integrated positioning and timing, it is necessary to enhance the traditional Loran hyperbolic positioning method, making its pseudorange calculation consistent with the BDS positioning and timing solution. The existing pseudorange algorithm based on the Andoyer-Lambert formula has issues such as strict initial value selection range and susceptibility to singularities during calculations. This study proposes a new Loran pseudorange calculation method based on the Vincenty distance formula and conducts a simulation analysis of it. The results show that, in the absence of noise interference, the positioning and timing errors of this pseudorange algorithm are close to zero, demonstrating high accuracy. When subjected to random noise with a standard deviation of less than 100 ns, the latitude and longitude errors are both less than 10 m, and the timing error is less than 10⁻⁴ ns, meeting the requirements of Loran positioning and timing. Compared to the pseudorange algorithm based on the Andoyer-Lambert formula, the one based on the Vincenty formula has comparable positioning longitude accuracy but superior timing accuracy. Moreover, the latter offers a wider range of initial value selection and can avoid more singularity issues during calculations.

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.

High-frequency (HF) communication is critical for applications such as over-the-horizon positioning and ionospheric detection. However, precise time-delay estimation in complex HF channels faces significant challenges from multipath fading, Doppler shifts, and noise. This paper proposes a Modulation Signal-based Adaptive Time-Delay Estimation (MATE) algorithm, which effectively decouples carrier and modulation signals and integrates phase-locked loop (PLL) and delay-locked loop (DLL) techniques. By leveraging the autocorrelation properties of 8PSK (Eight-Phase Shift Keying) signals, MATE compensates for carrier frequency deviations and mitigates multipath interference. Simulation results based on the Watterson channel model demonstrate that MATE achieves an average time-delay estimation error of approximately 0.01 ms with a standard deviation of approximately 0.01 ms, representing a 94.12% reduction in mean error and a 96.43% reduction in standard deviation compared to the traditional Generalized Cross-Correlation (GCC) method. Validation with actual measurement data further confirms the robustness of MATE against channel variations. MATE offers a high-precision, low-complexity solution for HF time-delay estimation, significantly benefiting applications in HF communication systems. This advancement is particularly valuable for enhancing the accuracy and reliability of time-of-arrival (TOA) detection in HF-based sensor networks and remote sensing systems.

Time synchronization is a crucial element of cooperativity among underwater acoustic sensor networks (UWASNs), and it plays an indispensable role in the application of and research into UWASNs. Although plenty of previous studies on time synchronization for UWASNs have been proposed and applied, most of them cannot perform well when the nodes have high mobility, and they are characterized by low energy efficiency. Tri-Message is a scheme proposed for networks in high-latency and resource-constrained environments, but it works unsatisfactorily when the nodes are movable. In that case, there is no such scheme for high-speed UWASNs with low energy consumption. Herein, we propose LT-Sync, a lightweight time synchronization scheme for high-speed mobile UWASNs. This adopts a Doppler-shift-estimating method to derive the propagation delay of high-speed UWASNs when the unsynchronized node moves uniformly in a single direction. In addition, an underwater spread-spectrum method is adopted for signal receiving to obtain the accurate Doppler shift. The simulation results show that LT-Sync is more feasible for high-speed UWASNs compared to existing methods and has high energy efficiency.

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.