Precise point positioning (PPP) is used in many fields. However, pseudorange multipath delay is an important error that restricts its accuracy. Pseudorange multipath delay can be considered as the combination of effective information and observation noise; it can be modeled after removing the observation noise. In this work, elastic nets (EN) regularization denoising method is proposed and compared with L2-norm regularization denoising method. Then, quadratic polynomial (QP) model plus autoregressive (AR) model (QP + AR) are used to model the denoised pseudorange multipath delays. Finally, the modeling results are corrected to the observations to verify the improvement of BDS-3 single-frequency PPP accuracy. Three single-frequency PPP schemes are designed to verify the effectiveness of denoising method and QP + AR model. The experimental results show that the accuracy improvement of B3I and B2a is more obvious than that of B1I and B1C when the modeling values are corrected to the pseudorange observations. The improvement of B3I and B2a in the east (E) and up (U) directions can reach 10.6%∼34.4% and 5.9%∼65.7%, and the improvement of the north (N) direction is mostly less than 10.0%. The accuracy of B1I and B1C in E and U directions can be improved by 0%∼30.7% and 0.4%∼28.6%, respectively, while the accuracy of N direction can be improved slightly or even decreased. Using EN regularization denoising and QP + AR model correction, single-frequency PPP performs better at B3I and B2a, while L2-norm regularization denoising and QP + AR model correction perform better at B1I and B1C. The accuracy improvement of B2a and B3I is more obvious than that of B1I and B1C. The convergence time after MP correction of each frequency is slightly shorter. Overall, the proposed pseudorange multipath delays processing strategy is beneficial in improving the single-frequency PPP of BDS-3 satellite.

The linear combination of multi-frequency carrier-phase and pseudorange observations can form the combined observations with special properties. The type and number of combined frequencies will directly affect the characteristics of the combined observations. BDS-2 and BDS-3 broadcast three and five signals, respectively, and the study of their linear combination is of great significance for precision positioning. In this contribution, the linear combination form of multi-frequency carrier-phase observations in cycles and meters is sorted out. Seven frequency combination modes are formed, and some special combinations for positioning are searched. Then, based on the principle of minimum combined noise, a simpler search method for the optimal real coefficients of ionosphere-free (IF) combination based on the least squares (LS) principle is proposed. The general analytical expressions of optimal real coefficients for multi-frequency geometry-based and ionosphere-free (GBIF), geometry-free and ionosphere-free (GFIF), and pseudorange multipath (PMP) combinations with the first-order ionosphere delay taken into account are derived. And the expression derivation process is given when both the first-order and second-order ionospheric delays are eliminated. Based on this, the characteristics of the optimal real coefficient combination in various modes are compared and discussed. The various combinations reflect that the accuracy of the combined observations from dual-frequency (DF) to five-frequency (FF) is gradually improving. The combination coefficient becomes significantly larger after taking the second-order ionospheric delay into account. In addition, the combined accuracy of BDS-3 is better than that of BDS-2. When only the first-order ionosphere is considered, the combination attribute of (B1C, B1I, B2a) is the best among the triple-frequency (TF) combinations of BDS-3. When both the first-order and second-order ionospheric delays are considered, the (B1C, B3I, B2a) combination is recommended.

No abstract

In this research, a preliminary mixed multi-frequency PPP solution strategy is analyzed and tested based on the combination of BDS-3 and GNSS observations. Firstly, the multi-frequency observations are combined and its coefficients are rapidly estimated by least square; then, the inter-system bias parameter and the stochastic model are introduced into the function model; finally, the mixed PPP solution and its software are developed and verified by three groups of experiments. According to experimental results of 96 stations and ten-day MGEX observations, it is indicated that the root-mean-square error (RMS) of positioning and the convergence time are significantly optimized with the aid of additional frequencies, where the accuracy improvements of multi-frequency and multi-GNSS scheme in east (E), north (N) and up (U) directions can respectively reach up to 23.2%, 13.3% and 23.8% compared with traditional BDS-3 dual-frequency ionosphere-free (IF) PPP model; and the corresponding convergence time is reduced from 18.54min to 13.18min. Meanwhile, from the results of multi-frequency BDS-3 PPP experiments, it is suggested that a better performance of positioning and convergence can be obtained, where the position RMS of E, N and U directions are reduced with 38.2%, 23.9% and 26.3%, and the convergence time is decreased from 23.86min to 12.43min for BDS-3 combined all of observations, compared with BDS-3-only solution. Furthermore, in the vehicle experiment of multi-frequency kinematics PPP, a convergence process can be found for different scenarios. Moreover, residuals series are different from each solution, in which the reducing with 71.1%, 33.3% and 77.1% in directions of E, N and U can be obtained compared with traditional BDS-3 dual-frequency IF model in kinematics experiments based on multi-GNSS and multi-frequency scenario. Therefore, it is meaningful to recommend the mixed PPP solution in GNSS community to fully use the multi-frequency and multi-GNSS observations by the adaptive combination of different observations.

Global Navigation Satellite System (GNSS) observations are subject to various errors during their propagation process. A reasonable correction of these errors can improve the positioning, navigation, and timing (PNT) service capability. The impact of multipaths on pseudorange observations can reach a decimeters or even meters level. However, their mechanism is complex and there is currently no universally accepted high-precision correction model. The correlation between the pseudorange multipaths (MP) of BDS-2 satellites and satellite elevation has been confirmed, while there have been fewer analyses of the MP characteristics for different frequencies of BDS-3 satellites. The broadcasting of multi-frequency observations in BDS-3 should theoretically make the extracted MP more accurate compared to traditional methods. Based on this, in this contribution, a multi-frequency MP extraction algorithm based on the least squares principle is proposed, which can simultaneously eliminate the influence of higher-order ionospheric delay. The analytical expression for only eliminating first-order ionospheric delay is successfully derived. Subsequently, the characteristics of the MPs extracted from different frequency combinations and the impact of combination noise on the extraction accuracy are discussed. The influence of second-order ionospheric delay on the MPs for each frequency under different combination noises, as well as the periodic behavior exhibited in long-term observations of the BDS-3 medium earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites, are also analyzed. Finally, the correlations between the MPs of each frequency of BDS satellite and elevation are quantitatively analyzed based on observations from 35 stations. Overall, this work has positive implications for the study of the MP characteristics of BDS-3 and subsequent modeling efforts.

The extraction of underground mineral sources has a significant negative impact on the local environment, results in land surface subsidence. As far as subsidence monitoring technology is concerned, leveling is the most accurate. However, leveling can only obtain discrete point data but not the whole area information of the subsidence basin. In this study, Differential Interferometric Synthetic Aperture Radar (D-InSAR) combined with Unmanned Aerial Vehicle (UAV) technology is used to study the subsidence characteristics of the whole working panel. In this analysis, the Huainan mining area is tested as a research area; measured data are compared to the elevation accuracy of the Digital Surface Model (DSM) data, which can be considered for the subsequent works of the mining area. Based on the subsidence affected area, the ground object-type information is recorded to provide basic information for the ecological restoration work after mining so that the data before and after mining can be obtained synchronously. Finally, the differential interference results and Digital Orthophoto Map (DOM) data are combined to assess the spatiotemporal evolution of working panel subsidence and its influence on surface features. The main novelty of the proposed work is combining UAV and D-InSAR to get more accurate analysis of mining subsidence. It can be done using the proposed method.