INSIGHT INTO SPATIAL ANALYSIS OF GPS BROADCAST ORBIT ERROR TOWARDS ORBITAL IMPROVEMENT

Broadcast orbits are compared against final orbit to get the error of broadcast orbit. The errors are analysed by presenting the error over space, especially longitude. The satellite trajectory is divided into three sector namely northern, southern, and transitional sectors. Spatial analysis show that the error is correlated with the latitude and longitude. Some consistency pattern can be observed from the distribution of the error in the spatial analysis. Standard deviation (SD) is used to quantify the consistency, providing more quantitative insights into the spatial analysis. Four patterns can be observed in the error distribution, namely consistency in northern and southern sector, consistency of transitional sector, changes after transitional sector, and correlation between ΔX component and ΔY component. The spatial analysis shows potential to be used in broadcast orbit error estimation and prediction. A model that uses this predicted broadcast orbit error as a correction will be designed in the future to improve the broadcast orbit accuracy.

Analysis and Assessment of BDS-2 and BDS-3 Broadcast Ephemeris: Accuracy, the Datum of Broadcast Clocks and Its Impact on Single Point Positioning

For the global ordinary users, the broadcast ephemeris plays important roles in positioning, navigation and timing (PNT) services. With the construction of a new generation of the BeiDou navigation satellite system (BDS), the development of BDS has entered the era of globalization. It is meaningful for global users to analyze and assess the BDS-2 and BDS-3 broadcast ephemeris. Therefore, the satellite orbits and clock offsets calculated by broadcast ephemeris are compared with the precise orbit and clock offset products provided by three analysis centers (i.e., Helmholtz Centre Potsdam German Research Center for Geosciences (GFZ), Wuhan University (WHU) and Shanghai Astronomical Observatory (SHA)), and the corresponding signal-in-space range error (SISRE) and the orbit-only SISRE are analyzed to assess the accuracy of BDS broadcast ephemeris. Due to the upgrade of BDS-3 satellite hardware technology and inter-satellite links payload and the development of satellite orbit determination algorithm, the accuracy of broadcast orbit and clock offsets has been greatly improved. The root mean square (RMS) of BDS-3 broadcast orbit errors is improved by 86.30%, 89.47% and 76.86%, and the standard deviation (STD) is improved by 79.41%, 77.00% and 76.78% compared with BDS-2 in the radial, along-track and cross-track directions. The corresponding RMS and STD of all BDS-3 satellite clock offsets are improved by 40.34% and 52.49% than that of BDS-2, respectively. Meanwhile, the mean RMS and STD are 1.78 m and 0.40 m for BDS-2 SISRE, 1.72 m and 0.34 m for BDS-2 orbit-only SISRE, 0.50 m and 0.14 m for BDS-3 SISRE, and 0.17 m and 0.04 m for BDS-3 orbit-only SISRE. It is noteworthy that the average broadcast-minus-precise (BMP) clock values of BDS-2 and BDS-3 are inconsistent, which can indirectly prove that the datum of broadcast clock offsets for BDS-2 and BDS-3 are inconsistent. The inconsistency of the datum of satellite clock offsets and receiver hardware delay bias between BDS-2 and BDS-3 will result in the inter-system bias (ISB) on the receiver segment. For JAVAD TRE_3 receivers, the ISB is relatively small and thus can be ignored. However, for the TRIMBLE ALLOY, SEPT POLARX5, CETC-54-GMR-4016, CETC-54-GMR-4011, GNSS-GGR and UB4B0-13478 receivers, estimating ISB can improve the positioning accuracy of single point positioning (SPP) by 20.15%, 19.81% and 12.76% in north, east and up directions, respectively.

Analysis of Factors Affecting Asynchronous RTK Positioning with GNSS Signals

For short baseline real-time kinematic (RTK) positioning, the atmosphere and broadcast ephemeris errors can be usually eliminated in double-differenced (DD) processing for synchronous observations. However, in the case of possible communication latency time, these errors may not be eliminated in DD treatments due to their variations during latency time. In addition, the time variation of these errors may present different characteristics among GPS, GLONASS, BDS, and GALILEO due to different satellite orbit and clock types. In this contribution, the formulas for studying the broadcast orbit and clock offset errors and atmosphere error in asynchronous RTK (ARTK) model is proposed, and comprehensive experimental analysis is performed to numerically show time variations of these errors and their impacts on RTK results from short-baselines among four systems. Compared with synchronous RTK, the degradation of position precision for ARTK can reach a few centimeters, but the accuracy degradation to a different degree by different systems. BDS and Galileo usually outperform GPS and GLONASS in ARTK due to the smaller variation of broadcast ephemeris error. The variation of broadcast orbit error is generally negligible compared with the variation of broadcast clock offset error for GPS, BDS, and Galileo. Specifically, for a month of data, the root mean square (RMS) values for the variation of broadcast ephemeris error over 15 seconds are 11.2, 16.9, 7.3, and 3.0 mm for GPS, GLONASS, BDS, and Galileo, respectively. The variation of ionosphere error for some satellites over 15 seconds can reach a few centimeters during active sessions under a normal ionosphere day. In addition, compared with other systems, BDS ARTK shows an advantage under high ionosphere activity, and such advantage may be attributed to five GEO satellites in the BDS constellation.

Evaluation of Orbit, Clock and Ionospheric Corrections from Five Currently Available SBAS L1 Services: Methodology and Analysis

To meet the demands of civil aviation and other precise navigation applications, several satellite-based augmentation systems (SBASs) have been developed around the world, such as the Wide Area Augmentation System (WAAS) for North America, the European Geostationary Navigation Overlay Service (EGNOS) for Europe, the Multi-functional Satellite Augmentation System (MSAS) for Japan, the GPS (Global Positioning System) Aided GEO Augmented Navigation (GAGAN) for India, and the System for Differential Corrections and Monitoring (SDCM) for Russia. The SBASs broadcast messages to correct satellite orbit, clock, and ionosphere errors to augment the GPS positioning performance. In this paper, SBAS orbit, clock and ionospheric corrections are evaluated. Specifically, the orbit, clock and ionospheric corrections derived from SBAS messages are comprehensively evaluated using data collected from the above mentioned systems over 181 consective days. The evaluation indicates that the EGNOS outperforms other systems with signal-in-space range error (SISRE) at 0.645 m and ionospheric correction accuracy at 0.491 m, respectively. Meanwhile, the accuracy of SDCM is comparable to EGNOS with SISRE of 0.650 m and ionospheric correction accuracy of 0.523 m. For WAAS, the SISRE is 0.954 m and the accuracy of ionospheric correction is 0.505 m. The accuracies of the SBAS corrections from the MSAS and GAGAN systems, however, are significantly worse than those of others. The SISREs are 1.931 and 1.325 m and the accuracies of ionospheric corrections are 0.795 and 0.858 m, for MSAS and GAGAN, respectively. At the same time, GPS broadcast orbit, clock and ionospheric corrections are also evaluated. The results show that there are no significant improvements in the SISRE of the broadcast navigation data by applying SBAS corrections. On the other hand, the accuracy of SBAS ionospheric corrections is still much better than GPS broadcast ionospheric corrections, which could still be beneficial for single-frequency users.

VADASE Reliability and Accuracy of Real-Time Displacement Estimation: Application to the Central Italy 2016 Earthquakes

The goal of this article is the illustration of the new functionalities of the VADASE (Variometric Approach for Displacements Analysis Stand-alone Engine) processing approach. VADASE was presented in previous works as an approach able to estimate in real time the velocities and displacements in a global reference frame (ITRF), using high-rate (1 Hz or more) carrier phase observations and broadcast products (orbits, clocks) collected by a stand-alone GNSS receiver, achieving a displacements accuracy within 1–2 cm (usually better) over intervals up to a few minutes. It has been well known since the very first implementation and testing of VADASE that the estimated displacements might be impacted by two different effects: spurious spikes in the velocities due to outliers (consequently, displacements, obtained through velocities integration, are severely corrupted) and trends in the displacements time series, mainly due to broadcast orbit and clock errors. Two strategies are herein introduced, respectively based on Leave-One-Out cross-validation (VADASE-LOO) for a receiver autonomous outlier detection, and on a network augmentation strategy to filter common trends out (A-VADASE); they are combined (first, VADASE-LOO; second, A-VADASE) for a complete solution. Moreover, starting from this VADASE improved solution, an additional strategy is proposed to estimate in real time the overall coseismic displacement occurring at each GNSS receiver. New VADASE advances are successfully applied to the GPS data collected during the recent three strong earthquakes that occurred in Central Italy on 24 August and 26 and 30 October 2016, and the results are herein presented and discussed. The VADASE real-time estimated coseismic displacements are compared to the static ones derived from the daily solutions obtained within the standard post-processing procedure by the Istituto Nazionale di Geofisica e Vulcanologia.

Comparison of standalone performance between COMPASS and GPS

COMPASS or BeiDou is the new satellite navigation system under construction in China. In this paper, the standalone performance of COMPASS is compared to the Global Positioning System (GPS), including: Single Point Positioning (SPP), differential positioning (DGPS and Differential COMPASS) and single epoch ambiguity resolution and positioning. Based on the results, it was found that COMPASS SPP performance is clearly worse than that of GPS, due to larger broadcast orbit and satellite clock errors, especially the latter. Differential positioning performance of COMPASS and GPS are essentially similar, with GPS marginally better. COMPASS single epoch ambiguity resolution performance is obviously better than that of GPS due to more observed satellites and the single epoch positioning performance of COMPASS and GPS are similar.