GPS/BDS RTK Positioning Based on Equivalence Principle Using Multiple Reference Stations

High accuracy acceleration determination by using multiple GNSS reference stations

The fast and high-precision positioning with multiple Global Navigation Satellite Systems (multi-GNSS) has been challenging for decades. Although the single-frequency single system (SF-SS), satellite selection for multi-GNSS, and multi-GNSS-based partial ambiguity resolution (PAR) can achieve rapid positioning, the varying theoretical bases of them result in different fixed reliability of ambiguities. Hence, we provide the theory analyzing the ambiguity resolution capabilities of the named systems. By adding satellite observations, the equations giving the variance–covariance matrix variation of the original float parameters are derived. Then, the relationship between the ambiguity dilution of precision (ADOP) values of the original ambiguity vector (OAV) before and after adding observations is obtained. This is followed by the analyses of the changing trends in the OAV’s probability density function, integer least-squares pull-in region, and the R-ratio test-based integer aperture pull-in region. In terms of precision, ADOP, and R-ratio test-based fixed reliability of ambiguities, the analyses indicate that the multi-GNSS can improve the partial ambiguity estimation and validation. Besides, compared to satellite selection and SF-SS, the PAR is optimal. The BeiDou Navigation Satellite System (BDS) and the Global Positioning System (GPS)-based single-epoch positioning experiments showed that both BDS B1 and B1-based PAR outperform GPS L1 and L1-based PAR in terms of ADOP and R-ratio test-based fixed reliability. The ADOP of the former is smaller than 0.14, and both the R-ratio test-based acceptance and success rates are up to 99.64%. Finally, the false alarm, failure, and detection rates are reduced to 0.34%, 0.0%, and 0.02%, respectively.

<p>The current international and regional reference frame research is mainly realized by single GPS (Global Position System) technology. With the full deployment of BDS (Beidou Navigation System), it is urgent to study and establish the corresponding terrestrial reference frame. Since 2019, the global and regional BDS service performance has been evaluated and tested, and the long-term BDS observations of MGEX (Multi GNSS Experiment) sites distributed worldwide provide the possibility for the preliminary construction of the BDS terrestrial reference frame. We aim to preliminarily realize and evaluate the CTRF2020 (COMPASS/BDS Terrestrial Reference Frame at the epoch of 2020.0) that can be expressed with the coordinates and velocities of a series of reference sites at the epoch of 2020.0. Firstly, the actual BDS global service performance evaluation reflects BDS satellite's high visibility and change trend in recent three years, which provides primary input data for the frame. Then, the BDS observations of about 100 global sites in the recent three years are calculated by PPP (Precise Point Positioning) and NET solution, to obtain the global high-precision BDS coordinate time series. Then, the BDS time series of the two solutions are fitted and compared with the IGS14 velocity field. The results show that the series accuracy of PPP-BDS and NET-BDS solutions is equivalent, and there is an mm-level systematic deviation with IGS14 solutions. The horizontal series fitting accuracy of PPP-BDS and NET-BDS solutions is better than that of the vertical direction, the accuracy of NET-BDS solution is slightly better than PPP-BDS, and the difference of fitting accuracy is 0.12, 0.13, and 0.50 mm in the NEU direction. The velocity field accuracy of PPP-BDS and NET-BDS solution is the same, and the overall three-dimensional velocity difference is less than 0.2 mm/a. The velocity fields of PPP-BDS and NET-BDS solution have little difference from IGS14, and the overall difference is less than 0.5 mm/a. Finally, we give the limitations and improvement points of CTRF2020. The preliminary realization and evaluation of CTRF2020 may be expected to provide a reference for the future realization of a comprehensive terrestrial reference framework dominated by BDS technology and supplemented by multi-source space geodetic technology.</p>

Performance evaluation of a real-time high-precision landslide displacement detection algorithm based on GNSS virtual reference station technology

Abstract. Nowadays, the Global Navigation Satellite System (GNSS) is widely used in many applications. As a new system, China's BeiDou navigation system (BDS) is emerging in recent years. The last satellite of the third generation global BeiDou navigation system (BDS-3) has been successfully launched on June 23 in 2020, which means that BDS can offer navigation services worldwide. We evaluate the quality of BDS signals and analyze the performance of BDS positioning based on the smartphone in Espoo, Finland. The static and kinematic experiments were implemented in the parking lot of the Finish Geospatial Research Institute (FGI) and a highway route in Espoo, respectively. Experimental results show that BDS has good satellite visibility and geometric distribution. The signal carrier-to-noise density ratio (C/N0) of BDS-2 reaches 34.22 dB-Hz, which is comparable to the Global Positioning System (GPS). However, the signal carrier-to-noise density of BDS-3 is slightly lower than BDS-2, which is due to the significant number of BDS-3 satellites at low elevation angles. The horizontal precision of BDS positioning in the static and kinematic experiment is comparable to GPS in the east direction and slightly inferior to GPS in the north direction. However, the BDS shows poor precision in the up direction. In addition, the integration of BDS with other GNSS systems can significantly improve the positioning precision. This study intends to provide a reference for further research on the BDS global Positioning, Navigation, and Timing (PNT) services, particularly for LBS and smartphone positioning.

Global Navigation Satellite System (GNSS) can provide continuous and high-precision absolute displacement information and therefore has been an important technical means of landslide surface displacement monitoring. When GNSS is used for landslide monitoring, a reference station is usually set for a monitoring landslide (referred to as “one reference station for one landslide”). Through the method of short baseline relative positioning, high-precision monitoring is realized by eliminating the atmospheric propagation error with strong spatial correlation. However, this application mode has problems such as high monitoring cost, low data reuse of reference station, and heavy dependence on the single reference station for the calculation results of monitoring stations, which limit the large-scale promotion and application of GNSS in landslide monitoring. Aiming at the above problems, this study took Liujiafen Landslide in Maoxian County, Sichuan Province as a case to study the application of Continuously Operating Reference Stations (CORS) and Virtual Reference Station (VRS) issued by Natural Resource system in landslide monitoring to optimize the existing application mode of “one reference station for one landslide”. In this study, the evaluation of the quality of VRS data, the calculation accuracy of static base line, and the comparative analysis of the calculation results between virtual and physical reference stations were carried out to demonstrate the applicability of CORS in landslide monitoring. According to the results: (1) The data quality of the selected virtual reference station was good; (2) The calculation accuracy of the baseline composed of virtual reference station and monitoring station was basically equal to that of the baseline composed of physical reference station and monitoring station. In view of the regional differences in the construction density and quality of CORS reference stations, and the relationship between atmospheric propagation correction model and topographic relief, it is suggested that the application should be decided after comprehensive evaluation based on the actual distribution of reference stations and specific environmental conditions.

Global positioning system (GPS) technology is well suited for attitude determination. However, in land vehicle application, low-cost single frequency GPS receivers which have low measurement quality are often used, and external factors such as multipath and low satellite visibility in the densely built-up urban environment further degrade the quality of the GPS measurements. Due to the low-quality receivers used and the challenging urban environment, the success rate of the single epoch ambiguity resolution for dynamic attitude determination is usually quite low. In this paper, a micro-electro-mechanical system (MEMS)—inertial navigation system (INS)-aided ambiguity resolution method is proposed to improve the GPS attitude determination performance, which is particularly suitable for land vehicle attitude determination. First, the INS calculated baseline vector is augmented with the GPS carrier phase and code measurements. This improves the ambiguity dilution of precision (ADOP), resulting in better quality of the unconstrained float solution. Second, the undesirable float solutions caused by large measurement errors are further filtered and replaced using the INS-aided ambiguity function method (AFM). The fixed solutions are then obtained by the constrained least squares ambiguity decorrelation (CLAMBDA) algorithm. Finally, the GPS/MEMS-INS integration is realized by the use of a Kalman filter. Theoretical analysis of the ADOP is given and experimental results demonstrate that our proposed method can significantly improve the quality of the float ambiguity solution, leading to high success rate and better accuracy of attitude determination.

The development of the commercial multi global navigation satellite system (GNSS) dual (multi)-antenna common-clock receiver that uses time-synchronization technology has brought new opportunities for high-precision GNSS-based attitude determination. In this article, for the first time, we present a performance comparison of global positioning system (GPS) L1/Galileo navigation satellite system (Galileo) E1 attitude determination with a common-clock receiver using four different models, i.e., the loosely combined single-differenced (SD-LC) model, the tightly combined single-differenced (SD-TC) model, the loosely combined double-differenced (DD-LC) model, and the tightly combined double-differenced (DD-TC) model. We first introduce the SD-LC, SD-TC, DD-LC, and DD-TC relative positioning models with GPS L1/Galileo E1 observations from a common-clock receiver. Then, we present a performance comparison of the four models in both single-epoch and multi-epoch modes using static data collected with a Trimble BD992 common-clock receiver in terms of the ambiguity dilution of precision (ADOP), the ambiguity resolution (AR) success and failure rates, and the positioning and attitude determination accuracy. In the case of the single-epoch mode, the experimental results revealed that the results of the single-differenced (SD) models were identical to those of double-differenced (DD) models, i.e., the results of SD-LC and SD-TC models were identical to DD-LC and DD-TC models, respectively. Moreover, compared with the loosely combined model (SD-LC/DD-LC), the tightly combined model (SD-TC/DD-TC) delivered a much higher AR success rate and a lower AR failure rate, especially under a high elevation cutoff angle. The AR success rate increased by approximately 35.1% under a 40° elevation cutoff angle, while the AR failure rate decreased by approximately 4.3%. In the case of the multi-epoch mode, the experimental results confirmed the advantages of the tightly combined model over the loosely combined model as well as the SD model over the DD model. Compared with the DD-LC and SD-LC models, the AR success rates of the DD-TC and SD-TC models were improved by approximately 16.7% and 0.6% under a 45° elevation cutoff angle, respectively. The AR failure rates were reduced by approximately 12.4% and 0.3%, respectively. Moreover, compared with the DD-LC and DD-TC models, the AR success rates of the SD-LC and SD-TC models under a 45° elevation cutoff angle were improved by approximately 24.0% and 7.9%, respectively, and the AR failure rates were reduced by approximately 19.9% and 7.8%, respectively. Meanwhile, compared with the DD model, the SD model delivered comparable yaw accuracy and remarkably better pitch accuracy. The pitch accuracy was improved by approximately 65.2–75.0%.

Rapid and accurate ambiguity resolution is the core of high-precision precise point positioning (PPP) data processing. However, the ambiguity parameters in PPP observation models are easily affected by atmospheric residual and gross errors, which lead to the probability of successfully fixing decreases and computational burden increases in full ambiguity resolution. Therefore, an increasing number of partial ambiguity resolution (PAR) strategies have been proposed. The selection of the optimal subset of PAR is crucial in this method. The traditional optimal subset selection method of PAR commonly leads to a single judgment criterion and weakened geometric configuration strength because the satellites with low elevation angles are often easily eliminated during the optimal subset selection. In this paper, a multi-factor constrained optimal subset selection method for PAR was proposed, which incorporates the ambiguity variance, the ambiguity dilution of precision (ADOP), satellite position dilution of precision (PDOP) and ratio test values. In order to verify the feasibility of the proposed optimal subset selection method, PAR tests under two schemes were performed for GPS/Galileo based on the static observation data of 15 Multi-GNSS Experiment (MGEX) tracking stations. The results show that, compared with the ambiguity variance sorting method, the proposed subset selection method can further improve the accuracy of the coordinate solution and the strength of geometric figure positioning. The average root mean square of the coordinate residuals is found to decrease by about 12.90%, 6.83% and 9.39% in the eastern, northern and vertical directions, respectively. The increase in the fixed epoch rate ranged from 0.87% to 33.33%, with an average of about 8.71%.

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.

Reliable and accurate carrier phase ambiguity resolution is the key to high-precision Global Navigation Satellite System (GNSS) positioning and application. With the fast development of modern GNSS, the increased number of satellites and ambiguities makes it hard to fix all ambiguities completely and correctly. The partial ambiguity fixing technique, which selects a suitable subset of high-dimensional ambiguities to fix, is beneficial for improving the fixed success rate and reliability of ambiguity resolution. In this contribution, the bootstrapping success rate, bounded fixed-failure ratio test, and the new defined baseline precision defect are used for the selection of the ambiguity subset. Then a model and data dual-driven partial ambiguity resolution method is proposed with the above three checks imposed on it, which is named the Triple Checked Partial Ambiguity Resolution (TC-PAR). The comprehensive performance of TC-PAR compared to the full-fixed LAMBDA method is also analyzed based on several criteria including the fixed rate, the fixed success rate and correct fixed rate of ambiguity as well as the precision defect and RMS of the baseline solution. The results show that TC-PAR could significantly improve the fixed success rate of ambiguity, and it has a comparable baseline precision to the LAMBDA method, both of which are at centimeter level after ambiguities are fixed.

The Global Navigation Satellite Systems (GNSS) applications are growing and more pervasive in the modern society. The presence of multi-constellation GNSS receivers able to use signals coming from different systems like the american Global Positioning System (GPS), the european Galileo, the Chinese Beidou and the russian GLONASS, permits to have more accuracy in position solution. All the receivers provide always more reliable solution but it is important to monitor the possible presence of problems in the position computation. These problems could be caused by the presence of impairments given by unintentional sources like multipath generated by the environment or intentional sources like spoofing attacks. In this thesis we focus on design algorithms at signal processing level used to assist Integrity operations in terms of Fault Detection and Exclusion (FDE). These are standalone algorithms all implemented in a software receiver without using external information. The first step was the creation of a detector for correlation distortion due to the multipath with his limitations. Once the detection is performed a quality index for the signal is computed and a decision about the exclusion of a specific Satellite Vehicle (SV) is taken. The exclusion could be not feasible so an alternative approach could be the inflation of the variance of the error models used in the position computation. The quality signal can be even used for spoofinng applications and a novel mitigation technique is developed and presented. In addition, the mitigation of the multipath can be reached at pseudoranges level by using new method to compute the position solution. The main contributions of this thesis are: the development of a multipath, or more in general, impairments detector at signal processing level; the creation of an index to measure the quality of a signal based on the detector's output; the description of a novel signal processing method for detection and mitigation of spoofing effects, based on the use of linear regression algorithms; An alternative method to compute the Position Velocity and Time (PVT) solution by using different well known algorithms in order to mitigate the effects of the multipath on the position domain.

Influence of the input layer signals of ANNs on wind power estimation for a target site: A case study

The single-baseline solution (SBS) model has been widely adopted by the existing global navigation satellite system (GNSS) deformation monitoring systems due to its theoretical simplicity and ease of implementation. However, the SBS model neglects the mathematical correlation between baselines, and the accuracy and reliability can be degraded for baselines with long length, large height difference or frequent satellite signal occlusion. When monitoring large-area ground settlement or long-spanned linear objects such as bridges and railroads, multiple reference stations are frequently utilized, which can be exploited to improve the monitoring performance. Therefore, this paper evaluates the multi-baseline solution (MBS) model, and constrained-MBS (CMBS) model that has a prior constraint of the spatial-correlated tropospheric delay. The reliability and validity of the MBS model are verified using GPS/BDS datasets from ground settlement deformation monitoring with a baseline length of about 20 km and a height difference of about 200 m. Numerical results show that, compared with the SBS model, the MBS model can reduce the positioning standard deviation (STD) and root-mean-squared (RMS) errors by up to (47.4/51.3/66.2%) and (56.9/60.4/58.4%) in the north/east/up components, respectively. Moreover, the combined GPS/BDS positioning performance for the MBS model outperforms the GPS-only and BDS-only positioning models, with an average accuracy improvement of about 13.8 and 25.8%, with the highest accuracy improvement of about 41.6 and 43.8%, respectively. With the additional tropospheric delay constraint, the CMBS model improves the monitoring precision in the up direction by about 45.0%.

A novel method of ambiguity resolution and cycle slip processing for single-frequency GNSS/INS tightly coupled integration system