Low Earth Orbit (LEO) satellites utilizing Doppler measurements can be an effective supplementary positioning solution when Global Navigation Satellite System (GNSS) signals are unavailable. LEO satellites pose challenges to the efficiency and stability of real-time satellite selection algorithms due to their high dynamic and large number. The traditional satellite selection algorithms have the problems of high computational complexity and significant hardware dependence. In contrast, the intelligent optimization algorithm significantly improves the accuracy and real-time performance of satellite selection through global search and efficient processing. According to the characteristics of LEO satellites, a Multi-Strategy Fusion Grey Wolf Optimization (MSFGWO) algorithm is proposed for satellite selection. The experimental results show that when six satellites are selected, the average Doppler Geometric Dilution of Precision (DGDOP) value of the MSFGWO algorithm is 222.08. Compared with the DGDOP ratio of the traversal method, it is 1.03. The three-dimensional positioning accuracy is 192.86 m, and the positioning error is improved by 54.43% compared with the positioning accuracy of the traditional GWO algorithm. The longest continuous observation was achieved for 45 s, during which no switching of six satellites occurred at adjacent moments. The calculation time of the algorithm was only 0.0174 s, and the efficiency was improved by 93.43%. The MSFGWO algorithm proposed in this paper not only improves the overall optimization ability of the Grey Wolf Optimizer (GWO) algorithm and effectively reduces the DGDOP value but also significantly reduces the satellite switching number and prolongates the continuous observation time, thus improving the stability and accuracy of the positioning solution.

With the modernization of GLONASS, four M+ and two K satellites are able to broadcast code-division multiple-access signals at a G3 frequency. The evaluation of the G3 frequency is necessary, among which the satellite-induced code pseudorange variation is one of the most important indicators. Using the code-minus-carrier (CMC) combination, it was found that the magnitude of the code pseudorange variations at the G3 frequency is about 1 m, which is primarily caused by the fact that G3 is transmitted from a different antenna, the same as G1 and G2. However, different from BDS-2 medium Earth orbit and inclined geo-synchronous orbit satellites, the code pseudorange variations at the GLONASS G3 frequency have a very weak relationship with the elevation angle, while a strong correlation exists with the time series, by using wavelet transformation and correlation analysis. Validation is carried out using a single-site model and a continuous multi-site model over 24 h, and the correction performance of these two models is comparable. The systematic deviation of the CMC and Melbourne–Wübbena combinations are significantly corrected, so only random errors remain. With a more concentrated distribution of the pseudorange residuals of single point positioning, the standard deviation of the pseudorange residuals is reduced.

To address the limitations of Global Navigation Satellite Systems (GNSSs), such as vulnerability to electromagnetic interference and weak ground signal power, signal of opportunity (SOP) provided by low Earth orbit (LEO) satellites can serve as a backup positioning method. By simulating a LEO constellation, the impact of satellite visibility, Doppler geometric dilution of precision (DGDOP), and positioning accuracy was explored. Considering positioning errors such as satellite clock drift rate, ionospheric delay rate, tropospheric delay rate, and Earth rotation effects, the instantaneous positioning performance with satellite orbital errors and satellite velocity errors of different magnitudes was simulated. The results show that satellite visibility and DGDOP are negatively correlated. In a typical atmospheric environment with orbital errors of 10 m and satellite velocity errors of 0.1 m/s, positioning accuracy within 30 m can be achieved. This confirms that Doppler-based positioning with LEO satellites can be used as a backup method for GNSSs.

In dynamic environments, the traditional relative positioning methods based on the Kalman filter model suffer from low accuracy and stability due to the influence of noise and outliers. This paper proposes a variational Bayesian filtering algorithm based on the combination of four-frequency observations from BDS (BeiDou Navigation Satellite System) and models the observation noise using the T-distribution to enhance the stability of filtering. Firstly, a geometrically correlated ambiguity resolution model is constructed based on the characteristics of the combined observations, effectively improving the precision of float ambiguity resolution and fixing rate. Moreover, considering the characteristics of outliers that are likely to occur in dynamic conditions, a T-distribution-based variational Bayesian filtering approach is employed to estimate the time-varying observation noise and system states. Experimental results demonstrate that the proposed method exhibits robustness and stability in dynamic short baseline scenarios, leading to further improvements in positioning accuracy, float ambiguity resolution precision, and fixing rate.