Showing papers in "Satellite Navigation in 2022"
TL;DR: In this article , the authors summarized the achievements in the precise orbit determination (POD) of BeiDou Navigation Satellite System (BDS) satellites in the past decade with the focus on observation and orbit dynamic models.
Abstract: Abstract Since the first pair of BeiDou satellites was deployed in 2000, China has made continuous efforts to establish its own independent BeiDou Navigation Satellite System (BDS) to provide the regional radio determination satellite service as well as regional and global radio navigation satellite services, which rely on the high quality of orbit and clock products. This article summarizes the achievements in the precise orbit determination (POD) of BDS satellites in the past decade with the focus on observation and orbit dynamic models. First, the disclosed metadata of BDS satellites is presented and the contribution to BDS POD is addressed. The complete optical properties of the satellite bus as well as solar panels are derived based on the absorbed parameters as well the material properties. Secondly, the status and tracking capabilities of the L-band data from accessible ground networks are presented, while some low earth orbiter satellites with onboard BDS tracking capability are listed. The topological structure and measurement scheme of BDS Inter-Satellite-Link (ISL) data are described. After highlighting the progress on observation models as well as orbit perturbations for BDS, e.g., phase center corrections, satellite attitude, and solar radiation pressure, different POD strategies used for BDS are summarized. In addition, the urgent requirement for error modeling of the ISL data is emphasized based on the analysis of the observation noises, and the incompatible characteristics of orbit and clock derived with L-band and ISL data are illuminated and discussed. The further researches on the improvement of phase center calibration and orbit dynamic models, the refinement of ISL observation models, and the potential contribution of BDS to the estimation of geodetic parameters based on L-band or ISL data are identified. With this, it is promising that BDS can achieve better performance and provides vital contributions to the geodesy and navigation.
39 citations
TL;DR: In this article , the authors summarized the achievements in the precise orbit determination (POD) of BeiDou Navigation Satellite System (BDS) satellites in the past decade with the focus on observation and orbit dynamic models.
Abstract: Abstract Since the first pair of BeiDou satellites was deployed in 2000, China has made continuous efforts to establish its own independent BeiDou Navigation Satellite System (BDS) to provide the regional radio determination satellite service as well as regional and global radio navigation satellite services, which rely on the high quality of orbit and clock products. This article summarizes the achievements in the precise orbit determination (POD) of BDS satellites in the past decade with the focus on observation and orbit dynamic models. First, the disclosed metadata of BDS satellites is presented and the contribution to BDS POD is addressed. The complete optical properties of the satellite bus as well as solar panels are derived based on the absorbed parameters as well the material properties. Secondly, the status and tracking capabilities of the L-band data from accessible ground networks are presented, while some low earth orbiter satellites with onboard BDS tracking capability are listed. The topological structure and measurement scheme of BDS Inter-Satellite-Link (ISL) data are described. After highlighting the progress on observation models as well as orbit perturbations for BDS, e.g., phase center corrections, satellite attitude, and solar radiation pressure, different POD strategies used for BDS are summarized. In addition, the urgent requirement for error modeling of the ISL data is emphasized based on the analysis of the observation noises, and the incompatible characteristics of orbit and clock derived with L-band and ISL data are illuminated and discussed. The further researches on the improvement of phase center calibration and orbit dynamic models, the refinement of ISL observation models, and the potential contribution of BDS to the estimation of geodetic parameters based on L-band or ISL data are identified. With this, it is promising that BDS can achieve better performance and provides vital contributions to the geodesy and navigation.
34 citations
TL;DR: In this article , a unified theoretical framework was developed to link the undifferenced and uncombined PPP-RTK models in a systematic way and cast them in a unified framework.
Abstract: Abstract Technique PPP–RTK combines the advantages of both the Precise Point Positioning (PPP) and the Real-Time Kinematic (RTK) positioning. With the emergence of multi-frequency Global Navigation Satellite System (GNSS) observations, it is preferable to formulate PPP–RTK functional models based on original (undifferenced and uncombined) observations. While there exist many variants of the undifferenced and uncombined PPP–RTK models, a unified theoretical framework needs developing to link these variants. In this contribution, we formulate a class of undifferenced and uncombined PPP–RTK functional models in a systematic way and cast them in a unified framework. This framework classifies the models into a code-plus-phase category and a phase-only category. Each category covers a variety of measurement scenarios on the network side, ranging from small-, medium- to large-scale networks. For each scenario, special care has been taken of the distinct ionospheric constraints and the difference between Code Division Multiple Access (CDMA) and Frequency Division Multiple Access (FDMA) signals. The key to systematically formulating these models lies in how to deal with the rank deficiency problems encountered. We opt for the Singularity-basis (S-basis) theory, giving rise to the full-rank observation equations in which the estimable parameters turn out to be the functions of original parameters and those selected as the S-basis. In the sequel, it becomes straightforward to derive for each scenario the user model as it, more or less, amounts to the single-receiver network model. Benefiting from the presented theoretical framework, the relationships and differences between various undifferenced and uncombined PPP–RTK models become clear, which can lead to the better use of these models in a specific situation.
21 citations
TL;DR: In this article , a multi-GNSS and multi-frequency PPP-RTK model was developed to evaluate its performance in urban environments from the perspectives of positioning accuracy, convergence and fixing percentage.
Abstract: Abstract PPP-RTK which takes full advantages of both Real-Time Kinematic (RTK) and Precise Point Positioning (PPP), is able to provide centimeter-level positioning accuracy with rapid integer Ambiguity Resolution (AR). In recent years, with the development of BeiDou Navigation Satellite System (BDS) and Galileo navigation satellite system (Galileo) as well as the modernization of Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS), more than 140 Global Navigation Satellite System (GNSS) satellites are available. Particularly, the new-generation GNSS satellites are capable of transmitting signals on three or more frequencies. Multi-GNSS and multi-frequency observations become available and can be used to enhance the performance of PPP-RTK. In this contribution, we develop a multi-GNSS and multi-frequency PPP-RTK model, which uses all the available GNSS observations, and comprehensively evaluate its performance in urban environments from the perspectives of positioning accuracy, convergence and fixing percentage. In this method, the precise atmospheric corrections are derived from the multi-frequency and multi-GNSS observations of a regional network, and then disseminated to users to achieve PPP rapid AR. Furthermore, a cascade ambiguity fixing strategy using Extra‐Wide‐Lane (EWL), Wide-Lane (WL) and L1 ambiguities is employed to improve the performance of ambiguity fixing in the urban environments. Vehicle experiments in different scenarios such as suburbs, overpasses, and tunnels are conducted to validate the proposed method. In suburbs, an accuracy of within 2 cm in the horizontal direction and 4 cm in the vertical direction, with the fixing percentage of 93.7% can be achieved. Compared to the GPS-only solution, the positioning accuracy is improved by 87.6%. In urban environments where signals are interrupted frequently, a fast ambiguity re-fixing can be achieved within 5 s. Moreover, multi-frequency GNSS signals can further improve the positioning performance of PPP-RTK, particularly in the case of small amount of observations. These results demonstrate that the multi-frequency and multi-GNSS PPP-RTK is a promising tool for supporting precise vehicle navigation.
19 citations
TL;DR: In this article , a unified theoretical framework was developed to link the undifferenced and uncombined PPP-RTK models in a systematic way and cast them in a unified framework.
Abstract: Abstract Technique PPP–RTK combines the advantages of both the Precise Point Positioning (PPP) and the Real-Time Kinematic (RTK) positioning. With the emergence of multi-frequency Global Navigation Satellite System (GNSS) observations, it is preferable to formulate PPP–RTK functional models based on original (undifferenced and uncombined) observations. While there exist many variants of the undifferenced and uncombined PPP–RTK models, a unified theoretical framework needs developing to link these variants. In this contribution, we formulate a class of undifferenced and uncombined PPP–RTK functional models in a systematic way and cast them in a unified framework. This framework classifies the models into a code-plus-phase category and a phase-only category. Each category covers a variety of measurement scenarios on the network side, ranging from small-, medium- to large-scale networks. For each scenario, special care has been taken of the distinct ionospheric constraints and the difference between Code Division Multiple Access (CDMA) and Frequency Division Multiple Access (FDMA) signals. The key to systematically formulating these models lies in how to deal with the rank deficiency problems encountered. We opt for the Singularity-basis (S-basis) theory, giving rise to the full-rank observation equations in which the estimable parameters turn out to be the functions of original parameters and those selected as the S-basis. In the sequel, it becomes straightforward to derive for each scenario the user model as it, more or less, amounts to the single-receiver network model. Benefiting from the presented theoretical framework, the relationships and differences between various undifferenced and uncombined PPP–RTK models become clear, which can lead to the better use of these models in a specific situation.
18 citations
TL;DR: In this article , a multi-GNSS and multi-frequency PPP-RTK model was developed to evaluate its performance in urban environments from the perspectives of positioning accuracy, convergence and fixing percentage.
Abstract: Abstract PPP-RTK which takes full advantages of both Real-Time Kinematic (RTK) and Precise Point Positioning (PPP), is able to provide centimeter-level positioning accuracy with rapid integer Ambiguity Resolution (AR). In recent years, with the development of BeiDou Navigation Satellite System (BDS) and Galileo navigation satellite system (Galileo) as well as the modernization of Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS), more than 140 Global Navigation Satellite System (GNSS) satellites are available. Particularly, the new-generation GNSS satellites are capable of transmitting signals on three or more frequencies. Multi-GNSS and multi-frequency observations become available and can be used to enhance the performance of PPP-RTK. In this contribution, we develop a multi-GNSS and multi-frequency PPP-RTK model, which uses all the available GNSS observations, and comprehensively evaluate its performance in urban environments from the perspectives of positioning accuracy, convergence and fixing percentage. In this method, the precise atmospheric corrections are derived from the multi-frequency and multi-GNSS observations of a regional network, and then disseminated to users to achieve PPP rapid AR. Furthermore, a cascade ambiguity fixing strategy using Extra‐Wide‐Lane (EWL), Wide-Lane (WL) and L1 ambiguities is employed to improve the performance of ambiguity fixing in the urban environments. Vehicle experiments in different scenarios such as suburbs, overpasses, and tunnels are conducted to validate the proposed method. In suburbs, an accuracy of within 2 cm in the horizontal direction and 4 cm in the vertical direction, with the fixing percentage of 93.7% can be achieved. Compared to the GPS-only solution, the positioning accuracy is improved by 87.6%. In urban environments where signals are interrupted frequently, a fast ambiguity re-fixing can be achieved within 5 s. Moreover, multi-frequency GNSS signals can further improve the positioning performance of PPP-RTK, particularly in the case of small amount of observations. These results demonstrate that the multi-frequency and multi-GNSS PPP-RTK is a promising tool for supporting precise vehicle navigation.
17 citations
TL;DR: In this article , the authors developed five BeiDou Satellite Navigation System (BDS) five-frequency PPP models and compared them with the traditional dual-frequency model, known as Dual-frequency IF (DF) model.
Abstract: Abstract Since its full operation in 2020, BeiDou Satellite Navigation System (BDS) has provided global services with highly precise Positioning, Navigation, and Timing (PNT) as well as unique short-message communication. More and more academics focus on multi-frequency Precise Point Positioning (PPP) models, but few on BDS five-frequency PPP models. Therefore, this study using the uncombined and Ionospheric-Free (IF) observations develops five BDS five-frequency PPP models and compares them with the traditional dual-frequency model, known as Dual-frequency IF (DF) model. Some biases such as Inter-Frequency Biases (IFB) and Differential Code Bias (DCB) are also addressed. With the data collected from 20 stations, the BDS dual- and five-frequency PPP models are comprehensively evaluated in terms of the static and simulated kinematic positioning performances. Besides, the study also analyzes some by-product estimated parameters in five-frequency PPP models such as Zenith Troposphere Delay (ZTD). The results of experiment show that five-frequency PPP models have different levels of improvement compared with the DF model. In the static mode, the one single Five-Frequency IF combination (FF5) model has the best positioning consequent, especially in the up direction, and in the simulated kinematic mode, the Three Dual-frequency IF combinations (FF3) model has the largest improvement in convergence time.
11 citations
TL;DR: In this article , the authors developed five BeiDou Satellite Navigation System (BDS) five-frequency PPP models and compared them with the traditional dual-frequency model, known as Dual-frequency IF (DF) model.
Abstract: Abstract Since its full operation in 2020, BeiDou Satellite Navigation System (BDS) has provided global services with highly precise Positioning, Navigation, and Timing (PNT) as well as unique short-message communication. More and more academics focus on multi-frequency Precise Point Positioning (PPP) models, but few on BDS five-frequency PPP models. Therefore, this study using the uncombined and Ionospheric-Free (IF) observations develops five BDS five-frequency PPP models and compares them with the traditional dual-frequency model, known as Dual-frequency IF (DF) model. Some biases such as Inter-Frequency Biases (IFB) and Differential Code Bias (DCB) are also addressed. With the data collected from 20 stations, the BDS dual- and five-frequency PPP models are comprehensively evaluated in terms of the static and simulated kinematic positioning performances. Besides, the study also analyzes some by-product estimated parameters in five-frequency PPP models such as Zenith Troposphere Delay (ZTD). The results of experiment show that five-frequency PPP models have different levels of improvement compared with the DF model. In the static mode, the one single Five-Frequency IF combination (FF5) model has the best positioning consequent, especially in the up direction, and in the simulated kinematic mode, the Three Dual-frequency IF combinations (FF3) model has the largest improvement in convergence time.
TL;DR: In this article , the authors proposed a real-time smartphone PPP method with the data processing strategies adapted for smart devices, which achieved the horizontal positioning accuracy of about 1.5 m at the 95th percentile for the vehicle-based kinematic positioning with the experimental smartphones mounted on the dashboard inside the vehicle.
Abstract: Abstract The availability of raw Global Navigation Satellite System (GNSS) measurements from Android smart devices gives new possibilities for precise positioning solutions, e.g., Precise Point Positioning (PPP). However, the accuracy of the PPP with smart devices currently is a few meters due to the poor quality of the raw GNSS measurements in a kinematic scenario and in urban environments, particularly when the smart devices are placed inside vehicles. To promote the application of GNSS PPP for land vehicle navigation with smart devices, this contribution studies the real-time PPP with smartphones. For data quality analysis and positioning performance validation, two vehicle-based kinematic positioning tests were carried out using two Huawei Mate30 smartphones and two Huawei P40 smartphones with different installation modes: the vehicle-roof mode with smartphones mounted on the top roof outside the vehicle, and the dashboard mode with smartphones stabilized on the dashboard inside the vehicle. To realize high accuracy positioning, we proposed a real-time smartphone PPP method with the data processing strategies adapted for smart devices. Positioning results show that the real-time PPP can achieve the horizontal positioning accuracy of about 1–1.5 m in terms of root-mean-square and better than 2.5 m at the 95th percentile for the vehicle-based kinematic positioning with the experimental smartphones mounted on the dashboard inside the vehicle, which is the real scenario in vehicle navigation.
TL;DR: In this article , the authors proposed a real-time smartphone PPP method with the data processing strategies adapted for smart devices, which achieved the horizontal positioning accuracy of about 1.5 m at the 95th percentile for the vehicle-based kinematic positioning with the experimental smartphones mounted on the dashboard inside the vehicle.
Abstract: Abstract The availability of raw Global Navigation Satellite System (GNSS) measurements from Android smart devices gives new possibilities for precise positioning solutions, e.g., Precise Point Positioning (PPP). However, the accuracy of the PPP with smart devices currently is a few meters due to the poor quality of the raw GNSS measurements in a kinematic scenario and in urban environments, particularly when the smart devices are placed inside vehicles. To promote the application of GNSS PPP for land vehicle navigation with smart devices, this contribution studies the real-time PPP with smartphones. For data quality analysis and positioning performance validation, two vehicle-based kinematic positioning tests were carried out using two Huawei Mate30 smartphones and two Huawei P40 smartphones with different installation modes: the vehicle-roof mode with smartphones mounted on the top roof outside the vehicle, and the dashboard mode with smartphones stabilized on the dashboard inside the vehicle. To realize high accuracy positioning, we proposed a real-time smartphone PPP method with the data processing strategies adapted for smart devices. Positioning results show that the real-time PPP can achieve the horizontal positioning accuracy of about 1–1.5 m in terms of root-mean-square and better than 2.5 m at the 95th percentile for the vehicle-based kinematic positioning with the experimental smartphones mounted on the dashboard inside the vehicle, which is the real scenario in vehicle navigation.
TL;DR: The PPP-RTK method as discussed by the authors combines the concepts of Precise of Point Positioning (PPP) and Real-Time Kinematic (RTK) to provide a centimeter-accuracy positioning service for an unlimited number of users.
Abstract: Abstract The PPP–RTK method, which combines the concepts of Precise of Point Positioning (PPP) and Real-Time Kinematic (RTK), is proposed to provide a centimeter-accuracy positioning service for an unlimited number of users. Recently, the PPP–RTK technique is becoming a promising tool for emerging applications such as autonomous vehicles and unmanned logistics as it has several advantages including high precision, full flexibility, and good privacy. This paper gives a detailed review of PPP–RTK focusing on its implementation methods, recent achievements as well as challenges and opportunities. Firstly, the fundamental approach to implement PPP–RTK is described and an overview of the research on key techniques, such as Uncalibrated Phase Delay (UPD) estimation, precise atmospheric correction retrieval and modeling, and fast PPP ambiguity resolution, is given. Then, the recent efforts and progress are addressed, such as improving the performance of PPP–RTK by combining multi-GNSS and multi-frequency observations, single-frequency PPP–RTK for low-cost devices, and PPP–RTK for vehicle navigation. Also, the system construction and applications based on the PPP–RTK method are summarized. Moreover, the main issues that impact PPP–RTK performance are highlighted, including signal occlusion in complex urban areas and atmosphere modeling in extreme weather events. The new opportunities brought by the rapid development of low-cost markets, multiple sensors, and new-generation Low Earth Orbit (LEO) navigation constellation are also discussed. Finally, the paper concludes with some comments and the prospects for future research.
TL;DR: In this article , the authors presented the BDS SBAS algorithms for these differential corrections in detail, and four types of Precise Point Positioning (PPP) function models for BDS dual-frequency (DF) and single-frequency (SF) users using the OSR and SSR parameters are also proposed.
Abstract: Abstract Satellite Based Augmentation System (SBAS) is one of the services provided by the BeiDou Navigation Satellite System (BDS). It broadcasts four types of differential corrections to improve user application performance. These corrections include the State Space Representation (SSR) based satellite orbit/clock corrections and ionospheric grid corrections, and the Observation Space Representation (OSR) based partition comprehensive corrections. The algorithms generating these SBAS corrections are not introduced in previous researches, and the user SBAS positioning performance with the contribution of BDS-3 has not been evaluated. In this paper, we present the BDS SBAS algorithms for these differential corrections in detail. Four types of Precise Point Positioning (PPP) function models for BDS Dual-Frequency (DF) and Single-Frequency (SF) users using the OSR and SSR parameters are also proposed. One week of data in 2020 is collected at 20 reference stations including the observations of both BeiDou-2 Navigation Satellite System (BDS-2) and BeiDou-3 Navigation Satellite System (BDS-3) satellites, and the PPP under various scenarios are performed using all the datasets and the BDS SBAS broadcast corrections. The results show that the performance of BDS-2/BDS-3 combination is superior to that of BDS-2 only constellation. The positioning errors in Root Mean Square (RMS) for the static DF PPP are better than 8 cm/15 cm in horizontal/vertical directions, while for the static SF PPP are 11 cm/24 cm. In the scenarios of simulated kinematic PPP, three Dimension (3D) positioning errors can reach 0.5 m in less than 10 min for the DF PPP and 30 min for the SF PPP, and the RMSs of the DF and SF PPP are better than 17 cm/21 cm and 20 cm/32 cm in horizontal/vertical directions. In a real-time single- and dual-frequency kinematic positioning test, the positioning errors of all three components can reach 0.5 m within 30 min, and the positioning accuracy after solution convergence in the N , E and U directions is better than 0.3 m.
TL;DR: In this paper , the authors proposed a method to determine the precision of the interpolated slant ionospheric delay by cross-validation, which takes the high temporal and spatial variation into consideration.
Abstract: Abstract With the high-precision products of satellite orbit and clock, uncalibrated phase delay, and the atmosphere delay corrections, Precise Point Positioning (PPP) based on a Real-Time Kinematic (RTK) network is possible to rapidly achieve centimeter-level positioning accuracy. In the ionosphere-weighted PPP–RTK model, not only the a priori value of ionosphere but also its precision affect the convergence and accuracy of positioning. This study proposes a method to determine the precision of the interpolated slant ionospheric delay by cross-validation. The new method takes the high temporal and spatial variation into consideration. A distance-dependent function is built to represent the stochastic model of the slant ionospheric delay derived from each reference station, and an error model is built for each reference station on a five-minute piecewise basis. The user can interpolate ionospheric delay correction and the corresponding precision with an error function related to the distance and time of each reference station. With the European Reference Frame (EUREF) Permanent GNSS (Global Navigation Satellite Systems) network (EPN), and SONEL (Système d'Observation du Niveau des Eaux Littorales) GNSS stations covering most of Europe, the effectiveness of our wide-area ionosphere constraint method for PPP-RTK is validated, compared with the method with a fixed ionosphere precision threshold. It is shown that although the Root Mean Square (RMS) of the interpolated ionosphere error is within 5 cm in most of the areas, it exceeds 10 cm for some areas with sparse reference stations during some periods of time. The convergence time of the 90th percentile is 4.0 and 20.5 min for horizontal and vertical directions using Global Positioning System (GPS) kinematic solution, respectively, with the proposed method. This convergence is faster than those with the fixed ionosphere precision values of 1, 8, and 30 cm. The improvement with respect to the latter three solutions ranges from 10 to 60%. After integrating the Galileo navigation satellite system (Galileo), the convergence time of the 90th percentile for combined kinematic solutions is 2.0 and 9.0 min, with an improvement of 50.0% and 56.1% for horizontal and vertical directions, respectively, compared with the GPS-only solution. The average convergence time of GPS PPP-RTK for horizontal and vertical directions are 2.0 and 5.0 min, and those of GPS + Galileo PPP-RTK are 1.4 and 3.0 min, respectively.
TL;DR: The real-time filtering method has a great potential to obtain more stable and reliable products than the ultra-rapid orbit prediction method and thus has attracted increasing attention in commercial companies and research institutes as mentioned in this paper .
Abstract: Abstract Stable and reliable high-precision satellite orbit products are the prerequisites for the positioning services with high performance. In general, the positioning accuracy depends strongly on the quality of satellite orbit and clock products, especially for absolute positioning modes, such as Precise Point Positioning (PPP). With the development of real-time services, real-time Precise Orbit Determination (POD) is indispensable and mainly includes two methods: the ultra-rapid orbit prediction and the real-time filtering orbit determination. The real-time filtering method has a great potential to obtain more stable and reliable products than the ultra-rapid orbit prediction method and thus has attracted increasing attention in commercial companies and research institutes. However, several key issues should be resolved, including the refinement of satellite dynamic stochastic models, adaptive filtering for irregular satellite motions, rapid convergence, and real-time Ambiguity Resolution (AR). This paper reviews and summarizes the current research progress in real-time filtering POD with a focus on the aforementioned issues. In addition, the real-time filtering orbit determination software developed by our group is introduced, and some of the latest results are evaluated. The Three-Dimensional (3D) real-time orbit accuracy of GPS and Galileo satellites is better than 5 cm with AR. In terms of the convergence time and accuracy of kinematic PPP AR, the better performance of the filter orbit products is validated compared to the ultra-rapid orbit products.
TL;DR: In this paper , the authors proposed a method to determine the precision of the interpolated slant ionospheric delay by cross-validation, which takes the high temporal and spatial variation into consideration.
Abstract: Abstract With the high-precision products of satellite orbit and clock, uncalibrated phase delay, and the atmosphere delay corrections, Precise Point Positioning (PPP) based on a Real-Time Kinematic (RTK) network is possible to rapidly achieve centimeter-level positioning accuracy. In the ionosphere-weighted PPP–RTK model, not only the a priori value of ionosphere but also its precision affect the convergence and accuracy of positioning. This study proposes a method to determine the precision of the interpolated slant ionospheric delay by cross-validation. The new method takes the high temporal and spatial variation into consideration. A distance-dependent function is built to represent the stochastic model of the slant ionospheric delay derived from each reference station, and an error model is built for each reference station on a five-minute piecewise basis. The user can interpolate ionospheric delay correction and the corresponding precision with an error function related to the distance and time of each reference station. With the European Reference Frame (EUREF) Permanent GNSS (Global Navigation Satellite Systems) network (EPN), and SONEL (Système d'Observation du Niveau des Eaux Littorales) GNSS stations covering most of Europe, the effectiveness of our wide-area ionosphere constraint method for PPP-RTK is validated, compared with the method with a fixed ionosphere precision threshold. It is shown that although the Root Mean Square (RMS) of the interpolated ionosphere error is within 5 cm in most of the areas, it exceeds 10 cm for some areas with sparse reference stations during some periods of time. The convergence time of the 90th percentile is 4.0 and 20.5 min for horizontal and vertical directions using Global Positioning System (GPS) kinematic solution, respectively, with the proposed method. This convergence is faster than those with the fixed ionosphere precision values of 1, 8, and 30 cm. The improvement with respect to the latter three solutions ranges from 10 to 60%. After integrating the Galileo navigation satellite system (Galileo), the convergence time of the 90th percentile for combined kinematic solutions is 2.0 and 9.0 min, with an improvement of 50.0% and 56.1% for horizontal and vertical directions, respectively, compared with the GPS-only solution. The average convergence time of GPS PPP-RTK for horizontal and vertical directions are 2.0 and 5.0 min, and those of GPS + Galileo PPP-RTK are 1.4 and 3.0 min, respectively.
TL;DR: In this paper , an ERA5-based global model for vertical adjustment of ZTD using a piecewise function is developed, which has excellent performance compared with the Global Pressure and Temperature (GPT3) model.
Abstract: Abstract Tropospheric delay is an important factor affecting high precision Global Navigation Satellite System (GNSS) positioning and also the basic data for GNSS atmospheric research. However, the existing tropospheric delay models have some problems, such as only a single function used for the entire atmosphere. In this paper, an ERA5-based (the fifth generation of European Centre for Medium-Range Weather Forecasts Reanalysis) global model for vertical adjustment of Zenith Tropospheric Delay (ZTD) using a piecewise function is developed. The ZTD data at 611 radiosonde stations and the MERRA-2 (second Modern-Era Retrospective analysis for Research and Applications) atmospheric reanalysis data were used to validate the model reliability. The Global Zenith Tropospheric Delay Piecewise (GZTD-P) model has excellent performance compared with the Global Pressure and Temperature (GPT3) model. Validated at radiosonde stations, the performance of the GZTD-P model was improved by 0.96 cm (23%) relative to the GPT3 model. Validated with MERRA-2 data, the quality of the GZTD-P model is improved by 1.8 cm (50%) compared to the GPT3 model, showing better accuracy and stability. The ZTD vertical adjustment model with different resolutions was established to enrich the model's applicability and speed up the process of tropospheric delay calculation. By providing model parameters with different resolutions, users can choose the appropriate model according to their applications.
TL;DR: The real-time filtering method has a great potential to obtain more stable and reliable products than the ultra-rapid orbit prediction method and thus has attracted increasing attention in commercial companies and research institutes as mentioned in this paper .
Abstract: Abstract Stable and reliable high-precision satellite orbit products are the prerequisites for the positioning services with high performance. In general, the positioning accuracy depends strongly on the quality of satellite orbit and clock products, especially for absolute positioning modes, such as Precise Point Positioning (PPP). With the development of real-time services, real-time Precise Orbit Determination (POD) is indispensable and mainly includes two methods: the ultra-rapid orbit prediction and the real-time filtering orbit determination. The real-time filtering method has a great potential to obtain more stable and reliable products than the ultra-rapid orbit prediction method and thus has attracted increasing attention in commercial companies and research institutes. However, several key issues should be resolved, including the refinement of satellite dynamic stochastic models, adaptive filtering for irregular satellite motions, rapid convergence, and real-time Ambiguity Resolution (AR). This paper reviews and summarizes the current research progress in real-time filtering POD with a focus on the aforementioned issues. In addition, the real-time filtering orbit determination software developed by our group is introduced, and some of the latest results are evaluated. The Three-Dimensional (3D) real-time orbit accuracy of GPS and Galileo satellites is better than 5 cm with AR. In terms of the convergence time and accuracy of kinematic PPP AR, the better performance of the filter orbit products is validated compared to the ultra-rapid orbit products.
TL;DR: In this article , the authors presented the BDS SBAS algorithms for these differential corrections in detail, and four types of Precise Point Positioning (PPP) function models for BDS dual-frequency (DF) and single-frequency (SF) users using the OSR and SSR parameters are also proposed.
Abstract: Abstract Satellite Based Augmentation System (SBAS) is one of the services provided by the BeiDou Navigation Satellite System (BDS). It broadcasts four types of differential corrections to improve user application performance. These corrections include the State Space Representation (SSR) based satellite orbit/clock corrections and ionospheric grid corrections, and the Observation Space Representation (OSR) based partition comprehensive corrections. The algorithms generating these SBAS corrections are not introduced in previous researches, and the user SBAS positioning performance with the contribution of BDS-3 has not been evaluated. In this paper, we present the BDS SBAS algorithms for these differential corrections in detail. Four types of Precise Point Positioning (PPP) function models for BDS Dual-Frequency (DF) and Single-Frequency (SF) users using the OSR and SSR parameters are also proposed. One week of data in 2020 is collected at 20 reference stations including the observations of both BeiDou-2 Navigation Satellite System (BDS-2) and BeiDou-3 Navigation Satellite System (BDS-3) satellites, and the PPP under various scenarios are performed using all the datasets and the BDS SBAS broadcast corrections. The results show that the performance of BDS-2/BDS-3 combination is superior to that of BDS-2 only constellation. The positioning errors in Root Mean Square (RMS) for the static DF PPP are better than 8 cm/15 cm in horizontal/vertical directions, while for the static SF PPP are 11 cm/24 cm. In the scenarios of simulated kinematic PPP, three Dimension (3D) positioning errors can reach 0.5 m in less than 10 min for the DF PPP and 30 min for the SF PPP, and the RMSs of the DF and SF PPP are better than 17 cm/21 cm and 20 cm/32 cm in horizontal/vertical directions. In a real-time single- and dual-frequency kinematic positioning test, the positioning errors of all three components can reach 0.5 m within 30 min, and the positioning accuracy after solution convergence in the N , E and U directions is better than 0.3 m.
TL;DR: In this article , the authors developed an improved covariance-based method to determine satellite integrity information and evaluate its performance in the range domain and position domain, and compared with the direct statistic method, the integrity bounding percentage is improved by 24.91% and the availability by 5.63%.
Abstract: Abstract Satellite integrity monitoring is vital to satellite-based augmentation systems, and can provide the confidence of the differential corrections for each monitored satellite satisfying the stringent safety-of-life requirements. Satellite integrity information includes the user differential range error and the clock-ephemeris covariance which are used to deduce integrity probability. However, the existing direct statistic methods suffer from a low integrity bounding percentage. To address this problem, we develop an improved covariance-based method to determine satellite integrity information and evaluate its performance in the range domain and position domain. Compared with the direct statistic method, the integrity bounding percentage is improved by 24.91% and the availability by 5.63%. Compared with the covariance-based method, the convergence rate for the user differential range error is improved by 8.04%. The proposed method is useful for the satellite integrity monitoring of a satellite-based augmentation system.
TL;DR: In this paper , a signal multiplexing modulation of the GPS PPP service signal that is based on the Asymmetric Constant Envelope Binary Offset Carrier (ACE-BOC) technique is proposed.
Abstract: Abstract The Precise Point Positioning (PPP) service of BeiDou-3 Navigation Satellite System (BDS-3) is implemented on its Geostationary Earth Orbit (GEO) satellites. However, its signal design is limited by the actual power of satellite and other conditions. Furthermore, the design needs to fully consider the compatibility of different service phases. Starting from the actual state of the BDS-3 GEO satellite, this paper studies the multiplexing modulation of the BDS PPP service signal that is based on the Asymmetric Constant Envelope Binary Offset Carrier (ACE-BOC) technique and proposes several feasible schemes for this signal. Comparison and optimization of these techniques are made from the aspects of transmission efficiency, multiplexing efficiency, and service forward compatibility. Based on the Type-III ACE-BOC multiplexing modulation technique, phase rotation and intermodulation reconstruction techniques are proposed to suppress the intermodulation interference issue. Finally, a signal based on improved ACE-BOC multiplexing is designed. The quality of the proposed signal was continuously monitored and tested using large-diameter antennas. The evaluation results show that the power spectrum deviation of the signal is 0.228 dB, the correlation loss is 0.110 dB, the S-curve slope deviation is 1.558% on average, the average length difference between the positive/negative chip and the ideal chip is only 0.0006 ns, and the coherence between the carrier and the pseudo code is 0.082°. All quality indicators are satisfactory, indicating that the proposed signal multiplexing modulation technique is an ideal solution that meets all the requirements of the design constraints, and can achieve efficient information broadcasting and forward compatibility of the BDS PPP service.
TL;DR: The SODIndoorLoc as mentioned in this paper is a supplementary open dataset for WiFi indoor localization based on RSS, covering three buildings with multiple floors, which includes dense and uniformly distributed Reference Points (RPs) with the average distance between two adjacent RPs smaller than 1.2 m.
Abstract: Abstract Several Wireless Fidelity (WiFi) fingerprint datasets based on Received Signal Strength (RSS) have been shared for indoor localization. However, they can’t meet all the demands of WiFi RSS-based localization. A supplementary open dataset for WiFi indoor localization based on RSS, called as SODIndoorLoc, covering three buildings with multiple floors, is presented in this work. The dataset includes dense and uniformly distributed Reference Points (RPs) with the average distance between two adjacent RPs smaller than 1.2 m. Besides, the locations and channel information of pre-installed Access Points (APs) are summarized in the SODIndoorLoc. In addition, computer-aided design drawings of each floor are provided. The SODIndoorLoc supplies nine training and five testing sheets. Four standard machine learning algorithms and their variants (eight in total) are explored to evaluate positioning accuracy, and the best average positioning accuracy is about 2.3 m. Therefore, the SODIndoorLoc can be treated as a supplement to UJIIndoorLoc with a consistent format. The dataset can be used for clustering, classification, and regression to compare the performance of different indoor positioning applications based on WiFi RSS values, e.g., high-precision positioning, building, floor recognition, fine-grained scene identification, range model simulation, and rapid dataset construction.
TL;DR: In this paper , the authors summarized the strategies, achievements, and innovations of multi-GNSS orbit/clock/bias determination in iGMAS Wuhan IAC.
Abstract: Abstract Over the past years the International Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS) Wuhan Innovation Application Center (IAC) dedicated to exploring the potential of multi-GNSS signals and providing a set of products and services. This contribution summarizes the strategies, achievements, and innovations of multi-GNSS orbit/clock/bias determination in iGMAS Wuhan IAC. Both the precise products and Real-Time Services (RTS) are evaluated and discussed. The precise orbit and clock products have comparable accuracy with the precise products of the International GNSS Service (IGS) and iGMAS. The multi-frequency code and phase bias products for Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), Galileo navigation satellite system (Galileo), and GLObal NAvigation Satellite System (GLONASS) are provided to support multi-GNSS and multi-frequency Precise Point Positioning (PPP) Ambiguity Resolution (AR). Compared with dual-frequency PPP AR, the time to first fix of triple-frequency solution is improved by 30%. For RTS, the proposed orbit prediction strategy improves the three dimensional accuracy of predicted orbit by 1 cm. The multi-thread strategy and high-performance matrix library are employed to accelerate the real-time orbit and clock determination. The results with respect to the IGS precise products show the high accuracy of RTS orbits and clocks, 4–9 cm and 0.1–0.2 ns, respectively. Using real-time satellite corrections, real-time PPP solutions achieve satisfactory performance with horizontal and vertical positioning errors within 2 and 4 cm, respectively, and convergence time of 16.97 min.
TL;DR: In this paper , the authors presented the strategies using ground-satellite-link observations to improve the accuracy of broadcast ephemeris, which are determined by the Orbit Determination and Time Synchronization (ODTS) and the Two-way Satellite Time Frequency Transfer (TWSTFT) technique, respectively.
Abstract: Abstract The BeiDou Navigation Satellite System (BDS) employs a hybrid constellation including GEO (Geosynchronous Earth Orbit), IGSO (Inclined Geosynchronous Orbit), and MEO (Medium Earth Orbit) satellites, where the GEO and IGSO satellites are critical to providing continuous and reliable Positioning, Navigation, and Timing (PNT) services in the Asia–Pacific region. To handle the inconsistency between the satellite orbits and clocks in the broadcast ephemeris, which are determined by the Orbit Determination and Time Synchronization (ODTS) and the Two-way Satellite Time Frequency Transfer (TWSTFT) technique, respectively, we present the strategies using ground-satellite-link observations to improve the accuracy of broadcast ephemeris. The clock differences between the ODTS and TWSTFT techniques are used for correcting the radial orbit component to derive the refined orbits, which are used to generate the refined broadcast ephemeris. The test results show the precision of the refined orbits is improved by 50–60% in the 3-h to 12-h predicted arcs for the GEO satellites, and by 40–50% for the IGSO satellites. Moreover, the validation using satellite laser ranging observations shows the mean precision of the refined broadcast ephemeris is improved by 27% compared to the original one. Applying the proposed strategies in the BDS Operational Control Segment (OCS), the time evolution of BDS Single Point Positioning (SPP) in the period from Jan. 2016 to April 2021 is evaluated. The SPP accuracy is improved from 1.94, 2.06 and 3.29 m to 1.39, 1.85, and 2.39 m in the north, east, and up components, respectively. Further update with the inclusion of BDS-3 satellites improve the corresponding SPP precision to 0.68, 0.70 and 1.91 m.
TL;DR: In this article , the authors developed an improved covariance-based method to determine satellite integrity information and evaluate its performance in the range domain and position domain, and compared with the direct statistic method, the integrity bounding percentage is improved by 24.91% and the availability by 5.63%.
Abstract: Abstract Satellite integrity monitoring is vital to satellite-based augmentation systems, and can provide the confidence of the differential corrections for each monitored satellite satisfying the stringent safety-of-life requirements. Satellite integrity information includes the user differential range error and the clock-ephemeris covariance which are used to deduce integrity probability. However, the existing direct statistic methods suffer from a low integrity bounding percentage. To address this problem, we develop an improved covariance-based method to determine satellite integrity information and evaluate its performance in the range domain and position domain. Compared with the direct statistic method, the integrity bounding percentage is improved by 24.91% and the availability by 5.63%. Compared with the covariance-based method, the convergence rate for the user differential range error is improved by 8.04%. The proposed method is useful for the satellite integrity monitoring of a satellite-based augmentation system.
TL;DR: In this paper , a signal multiplexing modulation of the GPS PPP service signal that is based on the Asymmetric Constant Envelope Binary Offset Carrier (ACE-BOC) technique is proposed.
Abstract: Abstract The Precise Point Positioning (PPP) service of BeiDou-3 Navigation Satellite System (BDS-3) is implemented on its Geostationary Earth Orbit (GEO) satellites. However, its signal design is limited by the actual power of satellite and other conditions. Furthermore, the design needs to fully consider the compatibility of different service phases. Starting from the actual state of the BDS-3 GEO satellite, this paper studies the multiplexing modulation of the BDS PPP service signal that is based on the Asymmetric Constant Envelope Binary Offset Carrier (ACE-BOC) technique and proposes several feasible schemes for this signal. Comparison and optimization of these techniques are made from the aspects of transmission efficiency, multiplexing efficiency, and service forward compatibility. Based on the Type-III ACE-BOC multiplexing modulation technique, phase rotation and intermodulation reconstruction techniques are proposed to suppress the intermodulation interference issue. Finally, a signal based on improved ACE-BOC multiplexing is designed. The quality of the proposed signal was continuously monitored and tested using large-diameter antennas. The evaluation results show that the power spectrum deviation of the signal is 0.228 dB, the correlation loss is 0.110 dB, the S-curve slope deviation is 1.558% on average, the average length difference between the positive/negative chip and the ideal chip is only 0.0006 ns, and the coherence between the carrier and the pseudo code is 0.082°. All quality indicators are satisfactory, indicating that the proposed signal multiplexing modulation technique is an ideal solution that meets all the requirements of the design constraints, and can achieve efficient information broadcasting and forward compatibility of the BDS PPP service.
TL;DR: In this article , a new ranging code tracking loop is designed based on the steepest descent method, which can save an early branch or a late branch compared with the narrow-spacing correlation method.
Abstract: Abstract Multipath interference seriously degrades the performance of Global Navigation Satellite System (GNSS) positioning in an urban canyon. Most current multipath mitigation algorithms suffer from heavy computational load or need external assistance. We propose a multipath mitigation algorithm based on the steepest descent approach, which has the merits of less computational load and no need for external aid. A new ranging code tracking loop is designed based on the steepest descent method, which can save an early branch or a late branch compared with the narrow-spacing correlation method. The power of the Non-Line-of-Sight (NLOS) signal is weaker than that of the Line-of-Sight (LOS) signal when the LOS signal is not obstructed and with a relatively high Carrier Noise Ratio (CNR). The peak position in the X -axis of the ranging code autocorrelation function does not move with the NLOS interference. Meanwhile, the cost function is designed according to this phenomenon. The results demonstrate that the proposed algorithm outperforms the narrow-spacing correlation and the Multipath Estimated Delay Locked Loop (MEDLL) in terms of the code multipath mitigation and computation time. The Standard Deviation (STD) of the tracking error with the proposed algorithm is less than 0.016 chips. Moreover, the computation time of the proposed algorithm in a software defined receiver is shortened by 24.21% compared with the narrow-spacing correlation.
TL;DR: In this paper , the performance of the velocity estimated based on the raw Doppler method, the time-differenced pseud-orange method, and the double-differenterenced carrier phase method, in both static and dynamic modes and in open and urban scenarios was evaluated.
Abstract: Abstract Global Navigation Satellite System (GNSS) based velocity estimation is one of the most cost-effective and widely used methods in determining velocity in geodesy and transport applications. Highly accurate and reliable velocity measurements can be obtained by exploiting the raw Doppler, carrier phase, and pseudorange measurements with a GNSS receiver. There are several approaches to GNSS-based velocity determination. This paper investigates the characteristics of the approaches which are currently popular and applicable to the observations of Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), and their combination (GPS/BDS). Specifically, it evaluates the performance of the velocity estimated based on the Raw Doppler method, the Time-Differenced Pseudorange method, the Time-Differenced Carrier Phase method, and the Double-Differenced Carrier Phase method, in both static and dynamic modes and in open and urban scenarios. The experiments show that BDS has the advantages in delivering accurate velocity determinations over GPS in the Asia–Pacific region, and the effectiveness of the GPS/BDS in improving the overall accuracy of velocity determination in complex urban scenarios.