For the downward continuation method of gravity field, the frequency domain continuation method has different requirements for data noise and continuation distance, and there is no clear conclusion yet. This paper analyzes seven frequency domain downward continuation methods, including Milne method, Taylor series expansion method, integral iteration method, Tikhonov regularization method, CGNR method, iterative least squares method, and Landweber iterative method. The model was tested using simulation data and aviation measured data, and the results were compared and studied. The results show that the Milne method and the Taylor series expansion method can be used for continuation of point distances less than 14 times under noise-free conditions; the integral iteration method has better stability when continuation of point distances 1 to 20 times without noise, but is more sensitive to noise; the Tikhonov regularization method has significant advantages when it contains noise and is greater than 5 times of point distances, and can obtain higher accuracy; the CGNR method, iterative least squares method and Landweber iterative method have wide applicability, and can maintain high accuracy when continuation of point distances 1 to 20 times under different noise conditions. Among them, the noise resistance of the Landweber iterative method is the most outstanding, and the latter four methods show certain advantages in actual data experiments, and can obtain stable downtime results.

To address the low computational efficiency of serial programs in integral calculations for marine gravity anomaly inversion, this study takes the inverse Vening-Meinesz formula as a case study to optimize the spherical harmonic synthesis and integration processes. Two parallel computing methods, OpenMP and MPI, are compared, with an improved task allocation strategy proposed for MPI. MPI is ultimately selected to implement the rapid computation of marine gravity anomaly inversion using the remove-restore technique. The results demonstrate that parallel computing significantly enhances the efficiency of integral inversion calculations. OpenMP exhibits higher parallel efficiency, while MPI demonstrates stronger acceleration capabilities on cluster servers. By employing the MPI-based parallel method with optimized task allocation, the inversion process requires only 20.87 seconds under the following conditions: a cluster server with 80 processes (CPU model: Intel Xeon E5-2670 v2 @ 2.50 GHz), a computational region of 10°×10°, an inversion resolution of 1'×1', and an integration radius of 60'. The computational accuracy of this approach slightly surpasses that of the FFT method.

In response to the issue that existing cycle slip detection methods lack systematic performance evaluation tools, this paper proposes a comprehensive evaluation approach that considers all epochs. By uniformly introducing cycle slips across all epochs, the method comprehensively reflects the true performance of different cycle slip detection algorithms over the entire observation period. Starting from three dimensions: combined noise, test statistic detection performance, and cycle slip detection results, three performance indicators are constructed: the root mean square error (RMSE) of the test statistic, the ratio of test statistic variation to RMSE, and the missed detection probability over all epochs. These indicators are used to systematically evaluate the performance differences of five cycle slip detection algorithms: Melbourne-Wübbena (MW), sliding window improved MW, triple-frequency pseudorange and phase, triple-frequency geometry-free (GF), and triple-frequency second-order time-difference phase ionospheric residual (STPIR). The results show that for all cycle slips within two weeks of the B1C/B2a/B3I signals, the triple-frequency GF cycle slip detection algorithm with a combination coefficient of (1, 2, -3) performs the best. Its test statistic RMSE is 0.006 2, the ratio of test statistic variation to RMSE is 100.56, and the missed detection probability over all epochs is only 7.28%. This performance evaluation method provides an objective quantitative basis for comparing the performance of cycle slip detection algorithms.

In urban environments, range measurement errors caused by non-line-of-sight (NLOS) signals significantly impact the precise positioning performance of global navigation satellite systems (GNSS), especially for low-cost devices and precise point positioning (PPP) that require accurate error processing. To address this issue, this paper designs a method for detecting NLOS signals based on the inertial navigation system (INS) and fisheye camera, and proposes an equivalent weight matrix update scheme for NLOS signals based on observation residuals to mitigate the adverse effects of NLOS signals on PPP. In the experiments, low-cost helical antennas and u-blox boards were used to collect two sets of vehicle-mounted data in Wuhan and Zhengzhou. The results show that the proportion of NLOS signal occurrences varies significantly across different scenarios, with tree shading and building blockage being the main factors causing NLOS signals. The optimized PPP achieves significant improvements in positioning accuracy and stability, especially in bridge-shaded and tree-shaded environments. The positioning errors were reduced from 21.259 m and 11.814 m to 17.071 m and 9.239 m, respectively, with improvement rates of 19.7% and 21.8%.

The BDS-3 and Galileo both provide five-frequency signal services. To fully utilize the multi-frequency signal data, a BDS-3/Galileo multi-frequency single point positioning (SPP) model based on the ionosphere-free combination is established, and the multi-frequency ionosphere-free combination coefficients are determined. Data from 48 multi-GNSS experiment (MGEX) stations are selected to systematically evaluate the performance of multi-frequency pseudorange SPP based on the ionosphere-free combination. The experimental results show that multi-frequency combined observations help to improve the SPP positioning accuracy of the BDS-3, Galileo, and BDS-3/Galileo systems. Compared with three-frequency SPP positioning, the positioning accuracy of four-frequency and five-frequency SPP has been improved to varying degrees. The improvement is most significant for the BDS-3 system. For the BDS-3 three-frequency SPP positioning, the RMS mean values in the E, N, U directions are 0.56 m, 0.59 m, 1.46 m, respectively, while the RMS mean values for four-frequency and five-frequency positioning are similar, at 0.53 m, 0.55 m, 1.40 m and 0.52 m, 0.55 m, 1.38 m, respectively. Compared with the single BDS-3 and Galileo systems, the five-frequency SPP positioning accuracy of the BDS-3/Galileo combined system has increased by 30.8%, 29.1%, 25.4% and 28.0%, 30.4%, 25.9%, respectively.

Traditional satellite orbit determination methods primarily rely on post-processing on the ground, which results in significant time delays and fails to meet the real-time requirements of autonomous on-board tasks. To address this issue, this paper proposes an autonomous real-time orbit determination algorithm based on the extended Kalman filter (EKF). The algorithm integrates quality control of observational data, dynamic orbit integration, and parameter estimation techniques to achieve real-time orbit determination for low-Earth orbit (LEO) satellites. The accuracy of the algorithm was assessed by comparing the real-time and predicted orbits with the ground-based post-processed precise reference orbits. Results show that, after accumulating 72 hours of observational data, the three-dimensional position error of real-time orbit determination was 15.18 cm, and the three-dimensional position error of orbit prediction within 2 hours was better than 18.75 cm, meeting the requirements for autonomous mission planning. Moreover, validated on an embedded platform, the algorithm has a single calculation cycle of less than 35 seconds and a memory footprint of less than 4 MB, complying with the onboard resource requirements. This study not only provides a theoretical and technical foundation for the design of autonomous navigation systems for medium and high Earth orbit satellites but also holds engineering value for enhancing the real-time response capabilities of satellites in orbit.

At present, the common detection method of integrated navigation system soft faults is to combine the sequential probability ratio test (SPRT) algorithm with the residual Chi-square detection algorithm. However, this algorithm has the defects of low detection accuracy and inability to detect multiple consecutive soft faults. Aiming at this problem, this paper first proposes an improved SPRT detection algorithm based on fading factor to reduce the influence of historical information on fault detection statistics and enhance the effect of current information on fault detection statistics. Then, the fault check statistic of the improved SPRT detection algorithm is designed, and combined with the residual Chi-square detection algorithm, an integrated navigation soft fault detection algorithm is proposed. Finally, based on GNSS/SINS integrated navigation system, this article has carried on the integrated navigation system soft failure detection simulation experiment.The experimental results show that compared with the classical algorithm, residual Chi-square detection algorithm, the improved algorithm not only has high precision and can accurately detect multiple consecutive soft faults, which can guarantee the stability of the integrated navigation system.

We conduct a detailed analysis of the spatial configuration of Beidou-3 constellation, and construct a dynamic link constraint model from two aspects: satellite visibility and antenna directivity. We obtain the real satellite orbit parameters through two line elements (TLE) file, construct the Beidou-3 constellation based on STK, and comprehensively analyze the topology characteristics of Beidou inter-satellite link. The simulation results have important guiding significance for further completing the link budget, achieving autonomous orbit determination and time synchronization between satellites.

This paper employs the spherical radial basis function (SRBF) method to integrate terrestrial gravity and airborne gravity data for the computation of the gravity quasi-geoid. Experiments are conducted from aspects such as terrain effects, model order, and basis function parameters to investigate the impact and variation patterns of different parameters.The results show that: 1) The burial depth, effective distance, and expansion order of the basis function all affect the quality of the quasi-geoid refined by the SRBF method. The precision difference of the geoidal height anomalies corresponding to different parameter settings can reach up to 2.4 cm; 2) Considering the terrain effects when calculating residual gravity data can improve the final quasi-geoid precision by 21.6%; 3) Using two sets of GNSS/leveling points with different precisions and distributions for external validation of the quasi-geoid results, the best validation precision differs by 4.3 cm; 4) In mountainous areas, by optimizing parameters to integrate terrestrial and airborne data, the optimal precision of the quasi-geoid result can reach 2.7 cm.

Heat flow (HF) refers to the heat energy transmitted from the Earth's interior to the surface. It can reveal various processes occurring in the deep Earth and information about energy balance. In the Antarctic region, understanding heat flow is of great significance for simulating the dynamic changes of ice sheets. This study employs the Stacking algorithm in machine learning to construct a heat flow prediction model for Antarctica. The model integrates 13 types of geological and geophysical features related to heat flow as observational input data and incorporates six machine learning algorithms commonly used for regression prediction problems, namely GBDT, XGBoost, RF, LightGBM, ET, and MLP, to predict the distribution characteristics of heat flow. The experimental results show that the prediction accuracy of the Stacking model is superior to that of several benchmark models. The new Antarctic heat flow distribution prediction map obtained through this model is more in line with the actual distribution of heat flow in Antarctica compared with the large-scale estimated heat flow distribution maps drawn by traditional methods, demonstrating more excellent performance.