The integrated use of GPS/GLONASS observations in network code differential positioning

We present the methodology and results of GPS/GLONASS integration in network code differential positioning for regional coverage across Poland using single frequency. Previous studies have only concerned the GPS system and relatively short distances to reference stations of up to tens of kilometers. This study is limited to using GPS and GLONASS. However, the methodology presented applies to all satellite navigation systems. The deterministic and stochastic models, as well as the most important issues in GPS/GLONASS integration are discussed. Two weeks of the GNSS observations were processed using software developed by the first author. In addition to interpolation of pseudorange corrections (PRCs) within the polygon of reference stations, the effect of their extrapolation outside that polygon is also briefly presented. It is well known that the positioning accuracy in a network of heterogeneous receivers can be degraded by GLONASS–FDMA frequency-dependent hardware biases. Our research reveals that when using such networks, the effect of these biases on the network differential GNSS (NDGNSS) positioning results as derived from both GPS and GLONASS can be reduced by simple down-weighting of GLONASS observations. We found that the same approach for the homogeneous equipment is not required; however, it can enhance performance of NDGNSS. Yet, the addition of the down-weighted GLONASS pseudoranges still improves the positioning accuracy by 14–25 %. The representative NDGNSS estimation is characterized by 0.17, 0.12 and 0.32 m RMS errors for the north, east and up component, respectively

Analysis of the accuracy of EGNOS+SDCM positioning in aerial navigation

The article presents a modified scheme of determining the accuracy parameter of SBAS (Satellite Based Augmentation System) positioning with use of two supporting systems: EGNOS (European Geostationary Navigation Overlay Service) and SDCM (System of Differential Correction and Monitoring). The proposed scheme is based on the weighted mean model, which combines single solutions of EGNOS and SDCM positions in order to calculate the accuracy of position-ing of the aerial vehicle. The applied algorithm has been tested in a flight experiment conducted in 2020 in north-eastern Poland. The phase of approach to landing of a Diamond DA 20-C1 aircraft at the EPOD airport (European Poland Olsztyn Dajtki) was subjected to numerical analysis. The Septentrio AsterRx2i geodesic receiver was installed on board of the aircraft to collect and record GPS (Global Positioning System) observations to calculate the naviga-tion position of the aircraft. In addition, the EGNOS and SDCM corrections in the “*.ems” format were downloaded from the real time server data. The computations were realized in RTKPOST library of the RTKLIB v.2.4.3 software and also in Scilab application. Based on the conducted research, it was found that the accuracy of aircraft positioning from the EGNOS+SDCM solution ranged from -1.63 m to +3.35 m for the ellipsoidal coordinates BLh. Additionally, the accuracy of determination of the ellipsoidal height h was 1÷28% higher in the weighted mean model than in the arith-metic mean model. On the other hand, the accuracy of determination of the ellipsoidal height h was 1÷28% higher in the weighted mean model than for the single EGNOS solution. Additionally, the weighted mean model reduced the resultant error of the position RMS-3D by 1÷13% in comparison to the arithmetic mean model. The mathematical model used in this study proved to be effective in the analysis of the accuracy of SBAS positioning in aerial navigatio

Precise Method of Ambiguity Initialization for Short Baselines with L1-L5 or E5-E5a GPS/GALILEO Data

This paper presents a precise and fast method of ambiguity resolution (PREFMAR) for frequencies L1/E1 and L5/E5a of GPS/GALILEO data. The developed method is designed for precise and fast determination of ambiguities in GNSS phase observations. Ambiguities are chosen based on mathematical search functions. The fact that no variance–covariance matrix (VC matrix) with a so-called float solution is needed proves the innovativeness of the developed method. The developed method enables determination of the ambiguities for short baseline double-difference (DD) observations. The presented algorithms for the developed method enable unique and reliable calculation of the ambiguity if the actual errors of code measurements of DD observations are less than 0.38 m and the relative errors of phase observations are in the range of ±3 cm. The paper presents both mathematical derivations of the functions used in the PREFMAR and numerical calculations based on real double-difference GPS observations (L1-L5). The elaborated algorithms can be easily implemented into GNSS receivers or mobile phones. Therefore, they can be widely used in many geoscience applications, as well as in precise GPS/GALILEO navigation

Performance of DGPS Smartphone Positioning with the Use of P(L1) vs. P(L5) Pseudorange Measurements

This paper presents numerical analyzes of code differential GPS positioning with the use of two Huawei P30 Pro mobile phones. Code observations on L1 and L5 frequencies were chosen for DGPS positioning analysis. For project purposes, we additionally used one high-class geodetic GNSS receiver (Javad Alpha) acting as a reference station. Smartphones were placed at the same distance of 0.5 m from the reference receiver. Such a close distance was specially planned by the authors in order to achieve identical observation conditions. Thus, it was possible to compare the DGPS positioning accuracy using the same satellites and the P(L1) and P(L5) code only, for single observation epochs and for sequential DGPS adjustment. Additionally, the precision of observations of the second differences in the observations P(L1) and P(L5) was analyzed. In general, the use of the P(L5) code to derive DGPS positions has made it possible to significantly increase the accuracy with respect to the positions derived using the P(L1) code. Average errors of horizontal and vertical coordinates were about 60–80% lower for the DGPS solution using the P(L5) code than using the P(L1) code. Based on the simulated statistical analyses, an accuracy of about 0.4 m (3D) with 16 satellites may be obtained using a smartphone with P(L5) code. An accuracy of about 0.3 m (3D) can be achieved with 26 satellites

Study Of Differential Code GPS/GLONASS Positioning

This paper presents the essential issues and problems associated with GNSS (Global Navigation Satellite System) code differential positioning simultaneously using observations from at least two independent satellite navigation systems. To this end, two satellite navigation systems were selected: GPS (Global Positioning System, USA) and GLONASS (GLObalnaya NAvigatsionnaya Sputnikovaya Sistema, Russia). The major limitations and methods of their elimination are described, as well as the basic advantages and benefits resulting from the application of the DGNSS (Differential GNSS) positioning method. Theoretical considerations were verified with the post-processed observations gathered during a six-hour measurement. The data from selected reference stations of the ASG-EUPOS (Active Geodetic Network — EUPOS) system located at different distances from the rover site was used. The study showed that the DGNSS positioning method achieves higher accuracy and precision, and improves the stability of coordinate determination in the time domain, compared to positioning which uses only one satellite navigation system. However, it was shown that its navigational application requires further studies, especially for long distances from the reference station

Operation and reliability of an onboard GNSS receiver during an in-flight test

This article presents and describes the operational capabilities of an onboard GNSS receiver to determine the reliability of the in-flight navigation parameters. An analysis was made of the operation reliability of an autonomous single-frequency Thales Mobile Mapper receiver in air navigation as compared to the technical operation of a dual-frequency Topcon HiperPro receiver. To this end, this work contains a comparison of the aircraft flight navigation parameters based on readings obtained from the Thales Mobile Mapper and Topcon HiperPro receivers. In particular, the comparison concerned the reliability of coordinate determination and flight speed parameters of an aircraft. The research experiment was conducted using a Cessna 172 aircraft, a property of the Military University of Aviation in Dęblin, Poland. Technical operation of the GNSS satellite receivers was tested in the flights of the Cessna 172 aircraft around the EPDE military airport in Dęblin. Based on the results obtained from the tests, it was found that the operational reliability of the Thales Mobile Mapper in the operational phase of the in-flight test ranged from -3.8 to +6.9 m in the XYZ geocentric frame and from -2.2 to +8.1 m in the BLh ellipsoidal frame, respectively. On the other hand, the accuracy of the Cessna 172 aircraft positioning when using the Thales Mobile Mapper receiver was higher than 1.7 m in the XYZ geocentric frame and higher than 2 m in the BLh ellipsoidal frame, respectively. Furthermore, the reliability of the Cessna 172 flight speed determination was from -3.4 to +2.4 m/s

Assessment of Static Positioning Accuracy Using Low-Cost Smartphone GPS Devices for Geodetic Survey Points’ Determination and Monitoring

Recent developments enable to access raw Global Navigation Satellite System (GNSS) measurements of mobile phones. Initially, researchers using signals gathered by mobile phones for high accuracy surveying were not successful in ambiguity fixing. Nowadays, GNSS chips, which are built in the latest smartphones, deliver code and primarily carrier phase observations available for detailed analysis in post-processing applications. Therefore, we decided to check the performance of carrier phase ambiguity fixing and positioning accuracy results of the latest Huawei P30 pro smartphone equipped with a dual-frequency GNSS receiver. We collected 3 h of raw static data in separate sessions at a known point location. For two sessions, the mobile phone was mounted vertically and for the third one—horizontally. At the same time, a high-class geodetic receiver was used for L1 and L5 signal comparison purposes. The carrier phase measurements were processed using commercial post-processing software with reference to the closest base station observations located 4 km away. Additionally, 1 h sessions were divided into 10, 15, 20 and 30 min separate sub-sessions to check the accuracy of the surveying results in fast static mode. According to the post-processing results, we were able to fix all L1 ambiguities based on Global Positioning System (GPS)-only satellite constellation. In comparison to the fixed reference point position, all three 1 h static session results were at centimeters level of accuracy (1–4 cm). For fast static surveying mode, the best results were obtained for 20 and 30 min sessions, where average accuracy was also at centimeters level

Impact of BeiDou Observations on the Accuracy of Multi-GNSS PPP in a Function of Observing Session Duration within Europe—Analysis Based on Open-Source Software GAMP

This study aims to verify whether the open-source software may provide Precise Point Positioning (PPP) with high accuracy. In this way, we address a question on the potential usability of open-source software for PPP analysis. On 31 July 2020, the full constellation of BeiDou satellites (SV) was announced. Over the European area, however, the number of visible BeiDou SVs is significantly smaller than in Asian-Pacific regions. Additionally, the system is in a modernization process, which may result in difficulties in utilizing its full potential. Ten days of multi-GNSS data were processed using the open-source software GAMP to determine how the accuracy of a derived three-dimensional PPP coordinates depends on observation session length and satellite systems used. The time series of position components of selected EUREF Permanent Network (EPN) stations generated from sub-daily (30 min and longer) solutions were analyzed. The obtained results prove that adding BeiDou observations, even in the case of using an incomplete constellation, leads to visible improvements, which can be observed both in the reduction of differences between estimated and true coordinates, as well as in the reduction of the standard deviation (SD). Improved accuracy caused by adding BeiDou data is especially noticeable for short observation sessions (in the range of 0.5 to 2.0 h) and in the case of a joint solution with GLONASS or Galileo observations. Finally, the open-source software GAMP proved to be a useful tool for multi-GNSS data processing and analysis

Dual Receiver EGNOS+SDCM Positioning with C1C and C1W Pseudo-Range Measurements

The paper presents an approach to the simultaneous use of SDCM and EGNOS corrections for two GNSS receivers placed at a constant distance. The SDCM and EGNOS corrections were applied for two GPS code measurements on L1 frequency: C1C and C1W. The approach is based mainly on the constrained least squares adjustment, but for the horizontal and vertical coordinates, the Kalman Filter was applied in order to reduce pseudo-range noises. It allows for obtaining a higher autonomous accuracy of GPS/(SDCM+EGNOS) positioning than when using only the GPS/EGNOS or GPS/SDCM system. The final dual-redundant solution, in which two SBAS systems were used (EGNOS+SDCM) and two GPS pseudo-ranges (C1C+C1W) were present, yielded RMS errors of 0.11 m for the horizontal coordinates and 0.25 m for the vertical coordinates. Moreover, the accuracy analysis in the developed mathematical model for the determined 3D coordinates with simultaneous use of EGNOS and SDCM systems proved to be much more reliable than using only a single EGNOS or SDCM system. The presented approach can be used not only for precise navigation, but also for some geoscience applications and remote sensing where the reliable accuracy of autonomous GPS positioning is required

Analysis of the determination of the accuracy parameter for dual receivers based on egnos solution in aerial navigation

The paper presents the results of research on the determination of the accuracy parameter for European Geostationary Navigation Overlay System (EGNOS) positioning for a dual set of on-board global navigation satellite system (GNSS) receivers. The study focusses in particular on presenting a modified algorithm to determine the accuracy of EGNOS positioning for a mixed model with measurement weights. The mathematical algorithm considers the measurement weights as a function of the squared inverse and the inverse of the position dilution of precision (PDOP) geometrical coefficient. The research uses actual EGNOS measurement data recorded by two on-board GNSS receivers installed in a Diamond DA 20-C airplane. The calculations determined the accuracy of EGNOS positioning separately for each receiver and the resultant value for the set of two GNSS receivers. Based on the conducted tests, it was determined that the mixed model with measurement weights in the form of a function of the inverse square of the PDOP geometrical coefficient was the most efficient and that it improved the accuracy of EGNOS positioning by 37%–63% compared to the results of position errors calculated separately for each GNSS receiver