The pure inertial navigation system (INS) contains three inherent periodic oscillations, namely, Schuler periodic oscillation (SPO, 84.4 min), Foucault periodic oscillation (FPO), and Earth periodic oscillation (EPO, 24 h), which can decrease the navigation accuracy, especially in long-term and low-velocity applications, such as ships and submarines. This article applies the inaction method (IM) to restrain SPO. Compared to external damping network technology (EDNT) and integrated navigation technology (INT), the IM is more independent, as it does not require auxiliary reference information. The IM is based on the so-called normal time–frequency transform (NTFT), and its uniqueness lies in recognizing and extracting instantaneous amplitude, frequency, and phase from a harmonic/quasi-harmonic signal directly and exactly. In this article, simulation data and experimental data are analyzed, and both show that the IM is effective. Moreover, the calculation results show that IM has wider applicability and higher stability than internal damping network technology (IDNT) and bandpass (BP) filtering. Compared to pure INS, the root mean square (rms) of the velocity error decreases significantly; the rmss of the latitude and longitude errors decrease as well. The IM can restrain SPO, and FPO is also restrained. However, the IM has no effect on the divergence of longitude error, and the edge effect is a drawback that needs to be addressed in the future.

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.

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.

Low-frequency (LF) time code timing technology holds significant importance in civilian applications such as radio-controlled clocks. This study focuses on the design and implementation of a high-precision Binary Phase Code (BPC) LF time code signal generator. A generator system was constructed, demonstrating good stability, superior resolution, and flexible adjustment capabilities for both amplitude and phase. The system employs an ARM + FPGA cooperative architecture: the ARM processor is responsible for parsing and scheduling the time code data, while the FPGA implements carrier wave generation and high-precision digital modulation. This digital processing is combined with analog circuitry to achieve digital-to-analog (D/A) signal conversion. Compared to traditional methods, carrier generation is achieved using Direct Digital Synthesis (DDS) technology. Digital modulation techniques enable the precise control of the modulation depth (adjustable between 70% and 90%) and phase (with a resolution of 1 ns). A sliding window algorithm was utilized for time difference calculation and compensation. Testing confirmed the stability of key signal parameters, including integrity, carrier frequency and modulation depth. These results validate the feasibility and superiority of the digital LF time code generation technology proposed in this study, providing a valuable reference for the development of next-generation timing equipment.