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.

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.

To enhance the long-term endurance navigation and positioning capabilities of inertial navigation systems (INSs), external auxiliary information is typically required for calibration. However, in certain challenging environments, obtaining continuous reliable and high-precision auxiliary information becomes difficult, and only sparse and low-precision position information may be available. Investigating methods to utilize this unfavorable information for calibrating INSs holds significant practical value. Building upon the inherent error characteristics of INSs, this study introduces a novel position calibration methodology. The first step is to make a comprehensive judgment by combining the position calculated by the INS and the reference position and selecting the usable sparse and low-precision reference position that meets the judgment conditions. The second step is to calibrate the INS with reference positions that meet the judgment conditions. Finally, a simulation static test and dynamic test were carried out; in the simulation static test, the std value of the latitude error decreased from 0.3250 $\mathrm{n} \mathrm{mile}$ to 0.2245 $\mathrm{n} \mathrm{mile}$, and the accuracy improved by 30.92%; the max value of the longitude error decreased from 8.2168 $\mathrm{n} \mathrm{mile}$ to 1.1629 $\mathrm{n} \mathrm{mile}$, and the accuracy improved by 85.85%; and the max value of the position error decreased from 8.2168 $\mathrm{n} \mathrm{mile}$ to 1.2003 $\mathrm{n} \mathrm{mile}$, and the accuracy improved by 85.39%. In the simulation dynamic test, the std value of the latitude error decreased from 0.4501 $\mathrm{n} \mathrm{mile}$ to 0.2384 $\mathrm{n} \mathrm{mile}$, and the accuracy improved by 47.03%; the max value of the longitude error decreased from 3.5907 $\mathrm{n} \mathrm{mile}$ to 0.9383 $\mathrm{n} \mathrm{mile}$, and the accuracy improved by 73.87%; and the max value of the position error decreased from 3.5931 $\mathrm{n} \mathrm{mile}$ to 1.0581 $\mathrm{n} \mathrm{mile}$, and the accuracy improved by 70.55%. The results of these tests show that the cumulative error which grows with time in INSs is obviously suppressed.