The BeiDou Navigation Satellite System (BDS) features a heterogeneous constellation so that it is difficult to mitigate the multipath in the coordinate-domain. Therefore, mitigating the multipath in the observation-domain becomes more important. Sidereal filtering is commonly used for multipath mitigation, which needs to calculate the orbit repeat time of each satellite. However, that poses a computational challenge and damages the integrity at the end of the multipath model. Therefore, this paper proposes a single-difference model based on the multipath hemispherical map (SD-MHM) to mitigate the BDS-2/BDS-3 multipath in a short baseline. The proposed method is converted from double-difference residuals to single-difference residuals, which is not restricted by the pivot satellite transformation. Moreover, it takes the elevation and the azimuth angles of the satellite as the independent variables of the multipath model. The SD-MHM overcomes the unequal observation time of some satellites and does not require specific hardware. The experimental results show that the SD-MHM reduces the root mean square of the positioning errors by 56.4%, 63.9%, and 67.4% in the east, north, and vertical directions; moreover, it contributes to an increase in the baseline accuracy from 1.97 to 0.84 mm. The proposed SD-MHM has significant advantages in multipath mitigation compared with the advanced sidereal filtering method. Besides, the SD-MHM also features an excellent multipath correction capability for observation data with a period of more than seven days. Therefore, the SD-MHM provides a universal strategy for BDS multipath mitigation.

With global warming, the law of climate change is more and more complex, so it is of great significance to analyze the response mechanism of vegetation change to climate change. The Loess Plateau (LP) is a vulnerable area, but we must explore the mechanism between climate and vegetation for decision-makers to make adequate plans to better govern this population-intensive but ecological-fragile area. Our study analyzed the vegetation variation in a long-term period from 1982 to 2015 and its relationship with precipitation and temperature. We innovatively leverage the weighted time-lag method to detect the different contributions of a specific climatic factor from different months to vegetation growth. Moreover, we used such weighted accumulated climatic factors to find the relationships between precipitation/temperature and different types of vegetation. The main findings are as follows: (i) For different degrees of temperature and precipitation, different vegetation has different performance characteristics in different months from 1982 to 2015. Moreover, precipitation is the major driver of vegetation growth in the LP. (ii) The response of vegetation possesses some time-lag effect on climate and exhibits spatial heterogeneity in the LP, which may be related to the characteristics of different climate zones and different vegetation. (iii) The effect of the same climatic factor on different vegetation accounts for a certain proportion of different months in the LP. Climate possesses a cumulative effect in three months on vegetation and different climatic factors have different time lags to the same vegetation type. It has a complicated interaction between vegetation growth and climate change. This paper uses the weighted time-lag method to investigate the relationship between vegetation growth and climatic factors, whilst considering how the time-lag effect can explain the changes that occur in the process of vegetation growth to a large extent.

Ultra-fast satellite clock bias (SCB) products play an important role in real-time precise point positioning. Considering the low accuracy of ultra-fast SCB, which is unable to meet the requirements of precise point position, in this paper, we propose a sparrow search algorithm to optimize the extreme learning machine (SSA-ELM) algorithm in order to improve the performance of SCB prediction in the Beidou satellite navigation system (BDS). By using the sparrow search algorithm’s strong global search and fast convergence ability, we further improve the prediction accuracy of SCB of the extreme learning machine. This study uses ultra-fast SCB data from the international GNSS monitoring assessment system (iGMAS) to perform experiments. First, the second difference method is used to evaluate the accuracy and stability of the used data, demonstrating that the accuracy between observed data (ISUO) and predicted data (ISUP) of the ultra-fast clock (ISU) products is optimal. Moreover, the accuracy and stability of the new rubidium (Rb-II) clock and hydrogen (PHM) clock onboard BDS-3 are superior to those of BDS-2, and the choice of different reference clocks affects the accuracy of SCB. Then, SSA-ELM, quadratic polynomial (QP), and a grey model (GM) are used for SCB prediction, and the results are compared with ISUP data. The results show that when predicting 3 and 6 h based on 12 h of SCB data, the SSA-ELM model improves the prediction model by ~60.42%, 5.46%, and 57.59% and 72.27%, 44.65%, and 62.96% as compared with the ISUP, QP, and GM models, respectively. When predicting 6 h based on 12 h of SCB data, the SSA-ELM model improves the prediction model by ~53.16% and 52.09% and by 40.66% and 46.38% compared to the QP and GM models, respectively. Finally, multiday data are used for 6 h SCB prediction. The results show that the SSA-ELM model improves the prediction model by more than 25% compared to the ISUP, QP, and GM models. In addition, the prediction accuracy of the BDS-3 satellite is better than that of the BDS-2 satellite.

Galileo can independently provide navigation and positioning services globally. Galileo satellites transmit quad-frequency E1, E5a, E5b, and E5 signals, which can benefit the integer ambiguity rapid resolution. Firstly, the qualities of Galileo signals from Carrier-to-Noise (C/N0), Multipath Combination (MPC), and pseudo-range and phase noise using the ultra-short baseline were evaluated. The experimental results indicated that the Galileo E5 signal has the highest C/N0, while the C/N0 of other signals is lower and almost equal. In terms of MPC, the Galileo E1 was the most severe followed by E5a and E5b, and the MPC of E5 is less severe. As for the precision of un-differenced observations, the carrier phase and pseudo-range observations of Galileo E5 had higher accuracy than those of Galileo E5a, E5b, and E1. Secondly, the quad-frequency observations allowed for various linear combinations of different frequencies, which provides some feasibility for improving the performance of ambiguity resolution. Assuming that the phase noise ${\sigma }_{\nabla \Delta \mathsf{\Phi }} = 0.01 \mathrm{m}$ and the first-order ionosphere ${\sigma }_{\nabla \Delta I_1} = 1 \mathrm{m}$, the total noise of the Extra-Wide-Lane (EWL) combination observation ((0, 0, 1, −1) and (0, −1, 1, 0)) and Very-Wide-Lane (VWL) combination observation ((0, −2, 1, 1), (0, −3, 2, 1)) are still less than 0.5 cycles. Finally, a geometry-based quad-frequency carrier ambiguities (GB-QCAR) method was developed, and all different options of linear combinations were investigated systematically from the ambiguity-fixed rate with two baselines. Experimental results demonstrated that, the ambiguity fixed rate of combination observation (0, −1, 1, 0), (0, −3, 5, −2), (1, −1, 0, 0) and (0, 0, 0, 1) is the highest and the positioning accuracy of VWL combination observation (0, −3, 5, −2) is equivalent to that of the EWL combination observation (0, −1, 1, 0). The positioning accuracies of WL combination observation (1, −1, 0, 0) are preferable to 3 cm and 10 cm in the horizontal and vertical, respectively. The positioning accuracy of NL combination observation E5 in the horizontal direction is about 1 cm, and is better than 4 cm in the vertical direction. Therefore, we can use Galileo observations to realize high-precise navigation services utilizing the proposed GB-QCAR method.

With the proliferation of mobile internet and location-based services, location-based social networks (LBSNs) have accumulated extensive user check-in data, driving the advancement of next Point-of-Interest (POI) recommendation systems. Although existing approaches can model sequential dependencies and spatio-temporal patterns, they often fail to fully capture users’ dynamic preferences under varying spatio-temporal contexts and lack effective integration of fine-grained semantic information. To address these limitations, this paper proposes Language-Guided Spatio-Temporal Context Learning for Next POI Recommendation (LSCNP). It employs a pre-trained BERT model to encode multi-dimensional spatio-temporal context—including geographic coordinates, visiting hours, and surrounding POI categories—into structured textual sequences for semantic understanding; constructs dual-graph structures to model spatial constraints and user transition patterns; and introduces a contrastive learning module to align spatio-temporal context with POI features, enhancing the discriminability of representations. A Transformer-based sequential encoder is adopted to capture long-range dependencies, while a neural matrix factorization decoder generates final recommendations. Experiments on three real-world LBSN datasets demonstrate that LSCNP consistently outperforms state-of-the-art baselines. Ablation studies and hyperparameter analyses further validate the contribution of each component to the overall performance.