Precise Point Positioning (PPP) technique enables stand-alone receivers to obtain cm-level positioning accuracy. Observations from multi-GNSS systems can augment users with improved positioning accuracy, reliability and availability. In this paper, we present and evaluate the GPS/BDS combined PPP models, including the traditional model and a simplified model, where the inter-system bias (ISB) is treated in different way. To evaluate the performance of combined GPS/BDS PPP, kinematic and static PPP positions are compared to the IGS daily estimates, where 1 month GPS/BDS data of 11 IGS Multi-GNSS Experiment (MGEX) stations are used. The results indicate apparent improvement of GPS/BDS combined PPP solutions in both static and kinematic cases, where much smaller standard deviations are presented in the magnitude distribution of coordinates RMS statistics. Comparisons between the traditional and simplified combined PPP models show no difference in coordinate estimations, and the inter system biases between the GPS/BDS system are assimilated into receiver clock, ambiguities and pseudo-range residuals accordingly.

https://www.mdpi.com/1424-8220/16/7/1151/pdf

Modeling and Assessment of GPS/BDS Combined Precise Point Positioning.

Integrated GPS + BDS instantaneous medium baseline RTK positioning: Signal analysis, methodology and performance assessment

This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations from three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. Combining measurements from different GNSS systems introduces additional biases, including inter-system bias and hardware delays, which require rigorous modelling. Our model is based on the un-differenced and between-satellite single-difference (BSSD) linear combinations. BSSD linear combination cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. Forming the BSSD linear combination requires a reference satellite, which can be selected from any of the GPS, Galileo, and BeiDou systems. In this paper three BSSD scenarios are tested; each considers a reference satellite from a different GNSS constellation. Natural Resources Canada's GPSPace PPP software is modified to enable a combined GPS, Galileo, and BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets collected at four different IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) network are used to correct the GPS, Galileo, and BeiDou measurements in the post-processing PPP mode. A real-time PPP solution is also obtained, which is referred to as RT-PPP in the sequel, through the use of the IGS real-time service (RTS) for satellite orbit and clock corrections. However, only GPS and Galileo observations are used for the RT-PPP solution, as the RTS-IGS satellite products are not presently available for BeiDou system. All post-processed and real-time PPP solutions are compared with the traditional un-differenced GPS-only counterparts. It is shown that combining the GPS, Galileo, and BeiDou observations in the post-processing mode improves the PPP convergence time by 25% compared with the GPS-only counterpart, regardless of the linear combination used. The use of BSSD linear combination improves the precision of the estimated positioning parameters by about 25% in comparison with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for the BSSD model, which represents about 50% reduction, in comparison with the GPS-only PPP solution. The GNSS RT-PPP solution, on the other hand, shows a similar convergence time and precision to the GPS-only counterpart.

https://www.mdpi.com/1424-8220/16/6/779/pdf

Precise Point Positioning Using Triple GNSS Constellations in Various Modes.

Performance analysis of BDS/GPS precise point positioning with undifferenced ambiguity resolution

Accuracy analysis of continuous deformation monitoring using BeiDou Navigation Satellite System at middle and high latitudes in China

BDS/GPS relative positioning for long baseline with undifferenced observations

The low-cost GNSS devices are more convenient, flexible, and can be used as the low-cost Global Navigation Satellite System interferometric reflectometry (GNSS-IR) sensors. In this study, the feasibility and performance of low-cost GNSS devices for the temporary sea level measurement are assessed, by jointly utilizing signal-to-noise ratio (SNR) data from an Android smartphone Redmi Note 9 Pro and a low-cost antenna BT560 connected to a CHCNAV P5 GNSS receiver, while another identical receiver equipped with a standard geodetic-quality antenna and a pressure tide gauge (TG) were placed nearby for comparison. 80-hours of SNR data from multiple GNSS constellations were collected and processed. First, the SNR data from the three devices are compared and analyzed. In most cases, the SNR data of low-cost antennas have longer and clearer oscillations. But they are maybe more vulnerable due to the manufacturing of antennas or positioning modules. Second, quality control and height rate correction are crucial to stable sea level measurement of low-cost GNSS devices. Finally, the performance of sea level measurement of multiple GNSS constellations, dual-frequency, and dual-antenna was also assessed. It is found that the low-cost GNSS devices could yield stable sea level measurements, and have a root-mean-square error (RMSE) of about 16 cm, of which the performance is equivalent to or even slightly better than standard geodetic-quality devices, making it a promising solution for the temporary TGs. 

Feasibility and performance evaluation of low-cost GNSS devices for sea level measurement based on GNSS-IR

Evaluation of the influence of high-order ionospheric delay on GPS undifferenced and uncombined precise point positioning

With the continuous development of global navigation satellite systems (GNSS) modernization, the code bias presented in the form of observation-specific biases (OSB) is more flexible and effective when processing modern multi-frequency and multi-GNSS signals, and therefore widely accepted by the GNSS community. However, the newly reported signal distortion biases (SDB) are ignored in the existing OSB estimation methods, which may affect the reliability of the final OSB estimation. In addition, the existing studies about SDB estimation are independent of OSB estimation, and thus a set of SDB products is generated independent of OSB products, which undoubtedly brings more complicated correction operations to GNSS users. In view of it, this study proposes an approach to code OSB estimation for multi-frequency and multi-GNSS arbitrary signals by reparameterization, which considers the SDB parameter. The aim of this study is to generate a set of code OSB products that take into account SDB parameters for the GNSS users to use. Due to considering the influence of SDB on raw code observations, the OSB estimation obtained by the proposed method is related to specific satellite-receiver pairs, which makes it different from the traditional OSB estimation methods. To achieve this, an extended model for multi-frequency and multi-GNSS arbitrary signal is first established based on the undifferenced and uncombined model, in which the SDB parameter is taken into account by re-parameterization. Based on the proposed model, three types of code bias that contain the OSB information can be obtained for the subsequent OSB estimation. Then, the three types of code bias in the first step are used as virtual observations for multi-frequency and multi-GNSS arbitrary signal OSB estimation through a two-step method. The proposed method is validated with a whole month of real measured data from 418 stations in MGEX and GA CORS to generate OSBs for GPS, GLONASS, and Galileo. The comparison between the estimated OSBs and the OSB products from CAS indicates the reliability of the proposed method. Besides, all types of OSB for four receiver groups are generated based on the proposed method to analyze the relationship between OSB and receiver groups. Results indicate that the estimated OSBs are related to receiver groups, and specific differences exist between different satellites and GNSS signals. It also proves that the OSB estimation is biased by the inconsistencies of the deviation in different receiver groups, which is more obvious for GLONASS. 

Code observation-specific biases estimation for the modernized Multi-GNSS and Multi-frequency signals: an approach considering signal distortion biases

Multisatellite systems and multi‐signal‐to‐noise ratio types provide a more prosperous data basis for the inversion of sea level by GNSS‐IR technology. However, there are few studies on data reconstruction of the retrieved sea level height. This study takes the SPBY station as an example and introduces the least squares learning cross‐checking method with the Gaussian kernel model (GKM) L2 constraint. Furthermore, research on hourly sea level reconstruction based on GNSS‐IR is carried out. Compared with the measured sea level, the sea level height in 2021 obtained after the fusion of multisource data has an R of 0.905 and an RMSE of 0.144 m. And the result obtained after data reconstruction has an R of 0.958 and an RMSE of 0.090 m. Compared with the multisource data fusion results before reconstruction, R is increased by 5.9%, and RMSE is decreased by 37.5%. Finally, using the reconstructed sea level data based on Long Short‐Term Memory (LSTM) artificial neural network to carry out the research on sea level prediction, which verifies the conclusion that more reliable forecast values can be obtained based on 5 months of training data. Among them, the R from 1 to 24 hr is 0.905, and the RMSE is 0.145 m. Compared with the inversion accuracy of GNSS‐IR, the R is increased by 2.0%, and the RMSE is decreased by 21.4%. This study demonstrates the feasibility of GNSS‐IR technology and L2‐constrained least squares learning cross‐checking method based on the GKM to reconstruct sea level data with high temporal resolution and high accuracy. The reliability of the sea level prediction based on GKM reconstruction and LSTM is verified in the sea level forecast of the next 24 epochs, which has essential applications in sea level data recovery and forecasting.

Hourly Sea Level Prediction‐Based GNSS‐IR Inversions by Combining the Least Squares Learning Cross‐Checking Method With the Gaussian Kernel Model L2 Constraint and LSTM

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