The time of a satellite navigation system is primarily generated by the main control station of the ground system. Consequently, when ground stations fail, there is a risk to the continuous provision of time services to the equipment and users. Furthermore, the anticipated launch of additional satellites will further strain the satellite–ground link. Next-generation satellite navigation systems will rely on time deviation measurements from inter-satellite links to independently establish and maintain a space-based time reference, enhancing the system’s reliability and robustness. The increasing number of low-Earth-orbit satellite navigation constellations provides ample resources for establishing a space-based time reference. However, this also introduces challenges, including extensive time scale computations, increased link noise, and low clock resource utilization. To address these issues, this paper proposes a Distributed Kalman Plus Weight (D-KPW) algorithm, which combines the benefits of Kalman filtering and the weighted average algorithm, balancing the performance with computational resources. Furthermore, an adaptive clock control algorithm, D-KPW (Control), is developed to account for both the short-term and long-term frequency stability of the time reference. The experimental results demonstrate that the frequency stability of the time reference established by the D-KPW (Control) algorithm reaches $7.40\times {10}^{-15}$ and $2.30\times {10}^{-15}$ for sampling intervals of 1000 s and 1,000,000 s, respectively, outperforming traditional algorithms such as ALGOS. The 20-day prediction error of the time reference is 1.55 ns. Compared to traditional algorithms such as AT1, ALGOS, Kalman, and D-KPW, the accuracy improves by 65%, 65%, 66%, and 67%, respectively.

Doppler positioning, as an early form of positioning, has regained significant research interest in the context of Low Earth Orbit (LEO) satellites.Given the LEO mega-constellation scenario, the objective function of Doppler positioning manifests significant nonlinearity, leading to ill-conditioning challenges for prevalent algorithms like iterative least squares (LS) estimation, especially in cases where inappropriate initial values are selected. In this study, we investigate the causes of ill-posed problems from two perspectives. Firstly, we analyze the linearization errors of the Doppler observation equations in relation to satellite orbital altitude and initial value errors, revealing instances where traditional algorithms may fail to converge. Secondly, from an optimization theory perspective, we demonstrate the occurrence of convergence to locally non-unique solutions for Doppler positioning. Subsequently, to address these ill-conditioning issues, we introduce Tikhonov regularization terms in the objective function to constrain algorithm divergence, with a fitted model for the regularization coefficient. Finally, we conduct comprehensive simulation experiments in both dynamic and static scenarios to validate the performance of the proposed algorithm. On the one hand, when the initial values are set to 0, our algorithm achieves high-precision positioning, whereas the iterative LS fails to converge. On the other hand, in certain simulation scenarios, the iterative LS converges to locally non-unique solutions, resulting in positioning errors exceeding 50 km in the north and east directions, several hundred kilometers in the vertical direction, and velocity errors surpassing 120 m/s. In contrast, our algorithm demonstrates typical errors of a position error of 6.8462 m, velocity error of 0.0137 m/s, and clock drift error of 8.3746 × ${10}^{-6}$ s/s. This work provides an effective solution to the sensitivity issue of initial points in Doppler positioning and can serve as a reference for the algorithm design of Doppler positioning receivers with LEO mega-constellations.

When a pseudolite is used to provide positioning services to users, it needs to provide position information by broadcasting ephemeris parameters. As part of resilient positioning, navigation, and timing (PNT), a UAV pseudolite system can serve users independently as a GNSS backup system, but unlike satellites that move periodically, the motion of UAVs is often variable, so it brings difficulties for how to make accurate predictions of the UAV's trajectory in a future segment within the ephemeris parameter update period. Therefore, based on a cruise UAV, we proposed an ephemeris based on a prediction method combined with Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) networks. The true position is divided into positions on the intended route and their deviations by mapping, and we use the motion model, the Singer model with Kalman filter and the CNN-LSTM networks to predict the position. Moreover, the network updates are achieved by a network monitoring loop and adaptive adjustment of the parameter update period is achieved by a prediction accuracy monitoring loop. Moreover, the ephemeris parameters are obtained by fitting the prediction results. The experimental results verify the performance of the designed ephemeris, the root mean squared error (RMSE) value of ephemeris parameter characterization error is less than 5 m, and the average occupied bits is about 35 bits; even using the sample data of UAV maneuvering at extreme speed with poor control performance, the RMSE of ephemeris parameter characterization error is 6.56 m, and the average occupied bits is 69.0 bits.

The global satellite navigation system represented by global position systems (GPS) has been widely used in civil and military fields, and has become an important cornerstone of space-time information services. However, the frequency band of satellite navigation signals is open, and the frequency points overlap with some radars and communication systems, which brings challenges to the application of satellite navigation. Time-domain adaptive filtering technology is a typical anti-jamming method which can suppress the narrow-band interference faced by satellite navigation. However, in the process of suppressing narrow-band interference, the navigation signal will be distorted, which is mainly reflected in the distortion of the spectrum of the navigation signal, which will lead to the enhancement of the side lobes in the correlation function. In this paper, we focus on time-domain adaptive anti-jamming, study the mechanism of correlation function sidelobes lift caused by narrow-band interference suppression, and propose a correlation function sidelobes suppression method based on time-domain adaptive anti-jamming, which can be realized without losing anti-jamming performance. The simulation experiment verifies the validity of the mechanism analysis of the sidelobes lift of the correlation function and the effectiveness of the proposed method. The analysis results and the proposed method are of great significance, which is reflected in the improvement of the anti-jamming performance and acquisition performance of satellite navigation receivers.

Deep space exploration utilizing high-orbit vehicles is a vital approach for extending beyond near-Earth space, with orbit information serving as the foundation for all functional capabilities. The performance of orbit determination is primarily influenced by observation types, errors, geometrical structures, and physical perturbations. Currently, research on orbit determination for high-orbit spacecraft predominantly focuses on single observation methods, error characteristics, multi-source fusion techniques, and algorithms. However, these approaches often suffer from low observation accuracy and increased costs. This paper advocates for the comprehensive utilization of existing multi-source observation methods, such as GNSS (Global Navigation Satellite System), SLR (Satellite Laser Ranging), and VLBI (Very Long Baseline Interferometry), in research. The decoupled Kalman filter reveals a positive correlation between measurement positioning accuracy and orbit determination accuracy, and it derives a simple orbit performance evaluation model that considers the influence of observation value types and geometric configurations, without the need to introduce complex dynamic models. Simulations are then employed to verify and analyze antenna gain, observation values, and performance evaluation. The results indicate the following: (1) Under simulated conditions, the optimal strategy involves employing the SLR/VLBI dual system during periods when VLBI orbit determination is feasible, yielding an average Weighted Position Dilution of Precision (WPDOP) of 26.79. (2) For periods when VLBI orbit determination is not feasible, the optimal approach is to utilize the GNSS/SLR/VLBI triple system, resulting in an average WPDOP of 16.32. (3) The orbit determination performance of the triple system is not significantly impacted by the use of global SLR stations compared to using only Chinese SLR stations. However, the global network enables continuous, round-the-clock orbit determination capabilities.