User Range Error Research Articles

DFMC SBAS service performance analysis of multi-GNSS based on BDS-3 in different regions

Abstract The dual-frequency multi-constellation satellite-based augmentation system (DFMC SBAS) plays a crucial role in many fields, such as civil aviation and other safety-critical applications. To analyze the performance of the third generation of the BeiDou navigation satellite system (BDS-3) dual-frequency SBAS services in global major regions and the enhancement of navigation service performance by multi-Global Navigation Satellite System DFMC SBAS, four schemes are designed to conduct experiments using user end positioning in China (CHN), Europe (EUR), and Australia (AUS), and the results are analyzed under Approach with Vertical guidance I (APV-I) and Category I Precision Approach (CAT-I). In terms of the number of enhanced satellites, user range error, positioning accuracy, and DFMC SBAS service integrity, the results show that the positioning performances of the BDS-3 DFMC SBAS in the horizontal and vertical directions are 0.60 and 1.12 m for the CHN region, 0.87 and 1.39 m for the EUR region, and 0.64 and 1.11 m for the AUS region. In the CHN and AUS regions, the horizontal and vertical accuracies are comparable and better than those in the EUR region. Under the APV-I performance index, except for stations at the edge of the service range in the CHN and AUS regions, the availability and continuity of all stations were 100% and over 99% in the EUR region. The BDS-3 + Galileo + GPS DFMC SBAS service can significantly improve the positioning accuracy compared to a single constellation. Under the APV-I performance index, the availability and continuity of all stations in the three regions reached 100%, which also satisfied the minimum requirement of CAT-I service availability (99%).

An Analytical Derivation of the Signal-in-Space Root-Mean-Square User Range Error

An Analytical Derivation of the Signal-in-Space Root-Mean-Square User Range Error

Study on systematic errors of BDS-3 broadcast ephemeris and their effects with Helmert transformation

Previous studies have not evaluated the systematic errors implied in the third generation of BeiDou-3 Navigation Satellite System (BDS-3) broadcast ephemeris. In this paper we evaluate the systematic pattern described by the Helmert transformation parameters, including translations, rotations, and scale. BDS-3 broadcast and precise ephemerides from December 2019 to 2022 are collected, and the characteristics of the transformation parameters as well as their effects on the signal in space error are analysed. The annual variation in the z-translation is obtained, and the similar amplitudes of 5.5 cm and phases of approximate 300 days are obtained for different years. When the rotation parameters are considered in the orbit comparison, the Root Mean Square (RMS) errors of the along- and cross-track orbital differences decrease from 29.1 to 12.5 cm and from 30.6 to 9.2 cm, respectively, because the three rotation parameters compensate for the majority of the errors in the BDS-3 broadcast ephemeris. Moreover, the high correlations in the obtained rotation parameters among the three orbital planes suggest that the orientation of the BDS-3 broadcast ephemeris is influenced by common model errors, i.e., uncertainty of Earth Rotation Parameters (ERPs). Further research is required because an offset of 1.5 × 10–9 for the scale parameter is observed. A degraded User Range Error (URE) for epochs of up to 84% is attained when the systematic pattern is considered, though the impact of the systematic pattern indicated by the z-translation and rotation parameters on the URE is less than 5.0 cm. With the refinement of the ERPs implemented in the new generation of broadcast ephemeris, we anticipate that the broadcast ephemeris performance of BDS-3 will be improved.

Real-Time LEO Satellite Orbits Based on Batch Least-Squares Orbit Determination with Short-Term Orbit Prediction

The augmentation of the Global Navigation Satellite System (GNSS) by Low Earth Orbit (LEO) satellites is proposed as an effective method to improve the precision and shorten the convergence time of Precise Point Positioning (PPP). Serving as navigation satellites in the future, LEO satellites need to be provided with their high-accuracy orbits in real-time. This would potentially enable the high-accuracy real-time LEO satellite clock determination, and eventually facilitate the high-accuracy ground-based positioning. Studies have been performed to achieve such real-time orbits using a Kalman filter in both the kinematic and reduced-dynamic modes. Batch Least-Squares (BLS) adjustment delivers more stable orbits in near-real-time, as it performs better phase screening. However, it suffers from longer delays compared to the Kalman filter. With the LEO satellite orbit prediction strategies improved over time, this latency can be bridged by short-term orbit prediction. In this study, using real-time GNSS satellite products, the real-time LEO satellite orbits are obtained based on the batch least-squares adjustment and short-term prediction. LEO ephemeris parameters are generated within specific prediction time windows. Using real data from the 500 km GRACE C satellite and 810 km Sentinel-3B satellite, the near-real-time BLS Precise Orbit Determination (POD) results exhibit good accuracy with an Orbital User Range Error (OURE) of 2–4 cm using different real-time GNSS products. A range of delays of the BLS POD processes are assumed, based on tests performed on different processing machines, leading to various prediction windows, from 3–8 min to 12–17 min that correspond to the real-time usage. The orbital prediction errors are shown to be highly correlated with the orbital height and the prediction time. The computational efficiency thus becomes essential to reduce the prediction errors for a certain LEO satellite. For advanced processing units leading to a prediction window shorter or equal to 6–11 min, one can expect a total real-time orbital error budget of 3–5 cm, provided that an appropriate prediction strategy is applied and high-quality GNSS products are used. For a given fitting interval, the ephemeris fitting errors are generally related to the number of ephemeris parameters and the orbital height. Compared with the prediction errors, the ephemeris fitting errors do not play a significant role in the total error budget when using 22 ephemeris parameters.

Quality monitoring of real-time GNSS precise positioning service system

ABSTRACT The Real-Time Global Navigation Satellite System (GNSS) Precise Positioning Service (RTPPS) is recognized as the most promising system by providing precise satellite orbit and clock corrections for users to achieve centimeter-level positioning with a stand-alone receiver in real-time. Although the products are available with high accuracy almost all the time, they may occasionally suffer from unexpected significant biases, which consequently degrades the positioning performance. Therefore, quality monitoring at the system-level has become more and more crucial for providing a reliable GNSS service. In this paper, we propose a method for the monitoring of real-time satellite orbit and clock products using a monitoring station network based on the Quality Control (QC) theory. The satellites with possible biases are first detected based on the outliers identified by Precise Point Positioning (PPP) in the monitoring station network. Then, the corresponding orbit and clock parameters with temporal constraints are introduced and estimated through the sequential Least Square (LS) estimator and the corresponding Instantaneous User Range Errors (IUREs) can be determined. A quality indicator is calculated based on the IUREs in the monitoring network and compared with a pre-defined threshold. The quality monitoring method is experimentally evaluated by monitoring the real-time orbit and clock products generated by GeoForschungsZentrum (GFZ), Potsdam. The results confirm that the problematic satellites can be detected accurately and effectively with missed detection rate and false alarm rate . Considering the quality alarms, the PPP results in terms of RMS of positioning differences with respect to the International GNSS Service (IGS) weekly solution in the north, east and up directions can be improved by 12%, 10% and 27%, respectively.

URE and URA for predicted LEO satellite orbits at different altitudes

In recent years, low Earth orbit (LEO) satellites have been frequently discussed for their benefits in positioning and navigation services as an augmentation to the global navigation satellite systems (GNSSs). Similar to the positioning concept based on ranging to GNSS satellites, precise positioning of single-receiver users needs high-accuracy orbits and clocks of LEO satellites as a pre-condition. For real-time users, high prediction accuracies of these orbits at different latencies are needed. Unlike the satellite clocks, the GNSS orbits can be typically predicted for hours with high accuracy. LEO satellites, however, face more complicated perturbing dynamic terms due to their low altitudes. Therefore, the prediction accuracy and integrity of their orbits need to be addressed. In this study, using real data of three test LEO satellites GRACE C, Sentinel-1A and Sentinel-3B of different altitudes, various reduced-dynamic prediction strategies are assessed, with the appropriate methods selected for different prediction times up to 6 h. The global-averaged orbital user range errors (OUREs) are shown to be altitude-related. For the 700–800 km Sentinel satellites and 500 km GRACE satellite, the RMS of the OUREs is at sub-dm and dm-level for the prediction time of 1 h, respectively, and around 0.2 m and 0.6 m at the prediction time of 6 h, respectively. For integrity purposes, the worst-location OURE are calculated for the predicted orbits using a proposed algorithm considering the Earth as an Ellipsoid, not a sphere as usually done for the GNSS satellites. The orbital user range accuracy (OURA) is then evaluated for different prediction periods, having a time-dependent model proposed to compute the overbounding OURA at any prediction time within 6 h. With an integrity risk of 10-5, using hourly quadratic polynomials as the time-dependent model, the overbounding OURA is around 0.1 m at the prediction of 1 h, and at the sub-meter level for the prediction of 6 h for the Sentinel satellites.

Impacts of Arc Length and ECOM Solar Radiation Pressure Models on BDS-3 Orbit Prediction

The BeiDou global navigation satellite system (BDS-3) has already provided worldwide navigation and positioning services for which the high-precision BDS-3-predicting orbit is the foundation. The arc length of the observed orbits and the solar radiation pressure (SRP) are two important factors for producing precise orbit predictions. The contribution studies the influences of these factors on BDS-3 orbit prediction. Three-month data from 1 July 2021 to 30 September 2021 are used to analyze optimal arc lengths and different ECOM SRP models for obtaining precise BDS-3 orbit predictions. The results show that the best-fitting arc length for the BDS-3 MEO/IGSO satellite is 42–48 h by comparing the final precise ephemeris and SLR validation. Furthermore, the ECOM9 SRP model shows improved orbit-prediction accuracy than that of the ECOM5 SRP model when the satellites move in and out of the eclipse season. As for the ECOM9 SRP model, the user range error (URE) accuracy of 6 h orbit predictions when satellites are in and outside of the eclipse season is 0.036 m and 0.030 m, respectively. In addition, the orbit prediction accuracy of the BDS-3 satellites does not decrease significantly since BDS-3 satellites apply the continuous yaw-steering (CYS) attitude mode during the eclipse season.

Emerging errors in the orientation of the constellation in GNSS autonomous orbit determination based on inter-satellite link measurements

The emergence of inter-satellite link (ISL) technology, which realizes the high-precision measurement of the inter-satellite distances and forms a spatial geometric constraint within the constellation, enables the high-precision autonomous orbit determination of the GNSS satellites. Firstly, according to the fact that ISL adjustment is singular to the satellite orbit state vector, a distributed autonomous orbit determination algorithm employing the long-term forecast ephemeris to constrain the constellation orientation is designed in this paper. Then, the autonomous orbit determination using 60-day onboard ISL observations of the whole constellation is carried out. Then, the resulting orbits accuracy is evaluated by comparing them with a precise orbit determination using a global reference network with an accuracy of 0.10 m. The results show that the mean root mean square (RMS) of the user range error (URE) over a 60-day period of the 24 BDS-3 satellites in the constellation is 3.22 m. The characteristics of orbit errors for individual satellite are very similar, which is mainly caused by the overall orientation errors of the constellation. After eliminating these orientation errors, the corresponding mean RMS of URE is reduced to 0.68 m. The prediction errors of the Earth rotation parameters and the determination errors of the parameters of the state vectors, which compose the orientation errors, are further investigated. The Earth rotation parameter prediction errors mainly cause errors in the estimates of the longitude of ascending node, of which the 60-day error can reach 2.5e-5°. The determination errors of the parameters of the state vectors -- the inclination and the right ascension of ascending node, can reach 2.4e-5° and 5.1e-5° rad, respectively.

Research on the Rotational Correction of Distributed Autonomous Orbit Determination in the Satellite Navigation Constellation

The autonomous orbit determination of the navigation constellation uses only bidirectional ranging data of the inter-satellite link for data processing. The lack of space-time benchmark information related to the Earth inevitably causes overall rotational uncertainty in the constellation, leading to a decrease in orbit accuracy and affecting user positioning accuracy. This study (1) introduces a method for rotation correction in distributed autonomous orbit determination based on inter-satellite bidirectional ranging; (2) conducts constellation autonomous orbit determination and time synchronization processing experiments based on inter-satellite ranging data for the 24 medium Earth orbit (MEO) satellites in the Beidou-3 global satellite navigation system (BDS-3); and (3) makes comparative analyses on the accuracy of autonomous orbit determination based on three rotation correction cases, including a no-rotation-correction case, independent satellite constraints case, and global satellite constraints case. The experimental results are described as follows. For the no-rotation-correction case, the prediction error of the orbital inclination angle (iot, i) for the entire constellation on the 30th day was 2.11 × 10−7/rad, the prediction error of the right ascension of the ascending point (Omega, Ω) was 2.25 × 10−7/rad, and the average root mean square (RMS) of the user range error (URE) for the entire constellation orbit was 1.41 m. In the autonomous orbit determination experiment with independent constraints on satellites, the prediction error of i for the entire constellation on the 30th day was 5.43 × 10−7/rad, the prediction error of Ω was 2.03 × 10−7/rad, and the average RMS of the orbital URE for the entire constellation was 1.09 m. In the autonomous orbit determination experiment with global satellite constraints, the prediction error of i for the entire constellation on the 30th day was 5.31 × 10−7/rad, the prediction error of Ω was 1.95 × 10−7/rad, and the RMS of the orbital URE for the entire constellation was 0.94 m. According to the analysis of the above experimental results, compared with the autonomous orbit determination under the no-rotation-correction case, the adoption of an algorithm for independent satellite constraints to correct the overall constellation rotation weakens the constellation rotation influence; however, it may destroy the overall constellation configuration, which affects the stability of autonomous orbit determination. Finally, the algorithm based on global satellite constraints both impairs the influence of constellation rotation and maintains the overall constellation configuration.

Multi-GNSS Combined Orbit and Clock Solutions at iGMAS.

Global navigation services from the quad-constellation of GPS, GLONASS, BDS, and Galileo are now available. The international GNSS monitoring and assessment system (iGMAS) aims to evaluate the navigation performance of the current quad systems under a unified framework. In order to assess impact of orbit and clock errors on the positioning accuracy, the user range error (URE) is always taken as a metric by comparison with the precise products. Compared with the solutions from a single analysis center, the combined solutions derived from multiple analysis centers are characterized with robustness and reliability and preferred to be used as references to assess the performance of broadcast ephemerides. In this paper, the combination method of iGMAS orbit and clock products is described, and the performance of the combined solutions is evaluated by various means. There are different internal precisions of the combined orbit and clock for different constellations, which indicates that consistent weights should be assigned for individual constellations and analysis centers included in the combination. For BDS-3, Galileo, and GLONASS combined orbits of iGMAS, the root-mean-square error (RMSE) of 5 cm is achieved by satellite laser ranging (SLR) observations. Meanwhile, the SLR residuals are characterized with a linear pattern with respect to the position of the sun, which indicates that the solar radiation pressure (SRP) model adopted in precise orbit determination needs further improvement. The consistency between combined orbit and clock of quad-constellation is validated by precise point positioning (PPP), and the accuracies of simulated kinematic tests are 1.4, 1.2, and 2.9 cm for east, north, and up components, respectively.

Satellite Availability and Service Performance Evaluation for Next-Generation GNSS, RNSS and LEO Augmentation Constellation

Positioning accuracy is affected by the combined effect of user range errors and the geometric distribution of satellites. Dilution of precision (DOP) is defined as the geometric strength of visible satellites. DOP is calculated based on the satellite broadcast or precise ephemerides. However, because the modernization program of next-generation navigation satellite systems is still under construction, there is a lack of real ephemerides to assess the performance of next-generation constellations. Without requiring real ephemerides, we describe a method to estimate satellite visibility and DOP. The improvement of four next-generation Global Navigation Satellite Systems (four-GNSS-NG), compared to the navigation constellations that are currently in operation (four-GNSS), is statistically analyzed. The augmentation of the full constellation the Quasi-Zenith Satellite System (7-QZSS) and the Navigation with Indian Constellation (11-NavIC) for regional users and the low Earth orbit (LEO) constellation enhancing four-GNSS performance are also analyzed based on this method. The results indicate that the average number visible satellites of the four-GNSS-NG will reach 44.86, and the average geometry DOP (GDOP) will be 1.19, which is an improvement of 17.3% and 7.8%, respectively. With the augmentation of the 120-satellite mixed-orbit LEO constellation, the multi-GNSS visible satellites will increase by 5 to 8 at all latitudes, while the GDOP will be reduced by 6.2% on average. Adding 7-QZSS and 11-NavIC to the four-GNSS-NG, 37.51 to 71.58 satellites are available on global scales. The average position DOP (PDOP), horizontal DOP (HDOP), vertical DOP (VDOP), and time DOP (TDOP) are reduced to 0.82, 0.46, 0.67 and 0.44, respectively.

Analysis of multi‐constellation GNSS receiver performance utilizing 1‐st side‐lobe signal on the use of SSV for KPS satellites

A numerical analysis is conducted for assessing the feasibility on the use of Global Navigation Satellite System (GNSS) receivers for Korea Positioning System (KPS) satellites in space service volume (SSV). KPS is planned to provide a navigation and timing service by constructing seven satellites over the Korean Peninsula, which will orbit above the GNSS constellation in SSV. The major problems caused by such orbital characteristics include reduced satellite visibility due to poor geometric diversity and weak signals, causing an increase in the user range error (URE). To address these constraints, this study considers multi-GNSS and 1-st side-lobe signal utilization scenarios. More specifically, the GNSS satellite visibility, geometric dilution of precision, carrier-to-noise ratio, URE, and navigation error for KPS satellites in SSV are analysed through a numerical simulation. A trade-off between visibility and received signal power as well as their effects on positioning accuracy is analysed to describe the utility of side-lobe signals. Finally, based on numerical analysis of the simulation results, this verifies the applicability of GNSS SSV for KPS satellites through multi-GNSS and side-lobe utilization scenarios.

BDS signal-in-space anomaly probability analysis over the last 6 years

Knowledge of the signal-in-space (SIS) anomaly probability is important for the integrity monitoring of satellite navigation. An efficient SIS anomaly detection method is indispensable for characterizing the probability of SIS anomalies with sufficient confidence. The traditional GPS anomaly detection method based on the zero-mean Gaussian distribution assumption of the instantaneous signal-in-space user range error (IURE) is not suitable for the emerging BeiDou navigation satellite system (BDS) because of the nonzero-mean, asymmetric distribution of the BDS IURE. By deliberately extracting the time series trend terms of the satellite orbit and clock errors, an SIS anomaly detection method with the worst user location protection principle is proposed based on 6 years of BDS data from March 2013 to March 2019. The detection results have shown that the probability of single-satellite SIS anomalies is at the 10−3 level and the probability of multiple-satellite SIS concurrent anomalies is at the 10−4 level. Meanwhile, the operational service performance provided by the BDS gradually improves over time.

Past, present and future of atomic clocks for GNSS

Global Navigation Satellite Systems (GNSS) are enabled by atomic clocks, which provide the timing precision and accuracy required for the ranging measurements. Significant investments have been made and will continue to be made, to improve GNSS atomic clock technology and reduce the signal-in-space user range error. After providing a baseline by reviewing current GNSS satellite atomic clock technology, we discuss how far, and in what directions, atomic clock technology should be pushed to provide maximum benefits to GNSS performance, reliability and cost.

Analysis of signal-in-space ranging error of GNSS navigation message

The signal-in-space ranging error (SISRE) is a major factor that affects the accuracy of positioning and timing. It describes the projection of the satellite-broadcast ephemeris error and clock difference error in the average direction from satellites to stations. In this study, the size and characteristics of the broadcast ephemeris user range error (URE), clock difference error, and SISRE are evaluated with respect to GPS, Galileo, and BDS-3. The results indicate that the SISREs of Galileo, GPS, and BDS-3 are 0.14, 0.49, and 0.35 m, respectively, the broadcast ephemeris UREs of Galileo, GPS, and BDS-3 are 0.14, 0.27, and 0.09 m, respectively, and the clock difference errors of Galileo, GPS, and BDS-3 are 0.14, 0.41, and 0.35 m, respectively. In case of Galileo, the radial orbit error and the clock difference error exhibit strong correlation. Both these errors cancel each other, and the SISRE associated with Galileo can be effectively reduced. Further, obvious differences can be observed with respect to the clock difference error and SISRE in case of different types of GPS satellites. The clock difference error and SISRE of GPS will gradually decrease with the upgradation of satellites. The SISRE of BDS-3 exhibits different characteristics when compared with those exhibited by the SISREs of GPS and Galileo. First, the radial error of BDS-3 is less correlated with the clock difference error, which exhibits poor self-consistency. Second, the BDS-3 satellite-broadcast ephemeris URE is small, whereas the clock difference error is large. Furthermore, the broadcast ephemeris URE associated with BDS-3 is lower than those associated with Galileo and GPS. However, the contribution of the clock difference error associated with BDS-3 to SISRE is considerably greater than those of the clock difference errors associated with GPS and Galileo to SISRE. In this study, the sizes and characteristics of the SISRE of BDS-3, Galileo, and GPS are compared, indicating that signal-in-space accuracy of BDS-3 can be improved by reducing the clock difference error.

Study on Optimal Broadcast Ephemeris Parameters for GEO/IGSO Navigation Satellites.

This paper proposes new sets of suitable broadcast ephemeris parameters for geosynchronous (GEO) and inclined geosynchronous (IGSO) navigation satellites (NSs). Despite the increasing number of GEO and IGSO NSs, global positioning system (GPS)-type ephemeris parameters are still widely used for them. In an effort to provide higher fit accuracy, we analyze a variety of broadcast ephemeris parameters for GEO and IGSO satellites along with their orbital characteristics and propose optimal sets of parameters. Nonsingular elements and orbital plane rotation are adopted for alleviating/avoiding the singularity issues of GEO satellites. On the basis of 16 parameters of GPS LNAV, we add one to four parameters out of 28 correction ones to determine optimal sets of ephemeris parameters providing higher accuracy. All possible parameter sets are tested with the least-square curve fit for four BeiDou GEOs and six BeiDou IGSOs. Their fit accuracies are compared to determine the optimal broadcast ephemeris parameters that provide minimum fit errors. The set of optimal ephemeris parameters depends on the type of orbit. User range error (URE) accuracies of the proposed optimal ephemeris parameters ensure results within 2.4 cm for IGSO and 3.8 cm for GEO NSs. Moreover, the experimental results present common parameter sets for both IGSO and GEO for compatibility and uniformity. Compared with four conventional/well-known sets of ephemeris parameters for BeiDou, our proposed parameters can enhance accuracies of up to 34.5% in terms of URE. We also apply the proposed optimal parameter sets to one GEO and three IGSO satellites of QZSS. The effects of fitting intervals, number of parameters, total bits, and orbit types on the fit accuracy are addressed in detail.

Analysis of BDS-3 distributed autonomous navigation based on BeiDou system simulation platform

Satellite autonomous navigation is an important function of the BeiDou-3 navigation System (BDS-3). Satellite autonomous navigation means that the navigation satellite uses long-term forecast ephemeris and Inter-Satellite Link (ISL) measurements to determinate its own spatial position and time reference without the support of the ground Operation and Control System (OCS) for a long time to ensure that the navigation system can normally maintain the time and space reference. This paper aims to analyze the feasibility of distributed autonomous navigation algorithms. For the first time, a ground parallel autonomous navigation test system (GPANTS) is built. The performance of distributed autonomous navigation is then analyzed using the two-way ISL ranging of BDS-3 satellites. First, the BDS simulation platform and the GPANTS are introduced. Then, the basic principles of distributed satellite autonomous orbit determination and time synchronization based on ISL measurements are summarized. Preliminary evaluation of the performance of the BDS-3 constellation autonomous navigation service under ideal conditions through simulation data. Then the performance of autonomous navigation for 22 BeiDou-3 satellites using ISL measurements is evaluated. The results show that when satellites operate autonomously for 50 days without the support of any ground station, the User Range Error (URE) of autonomous orbit determination is better than 3 m, and the time synchronization accuracy is better than 4 ns.

Proposed Orbital Products for Positioning Using Mega-Constellation LEO Satellites.

With thousands of low Earth orbit (LEO) satellites to be launched in the near future, LEO mega-constellations are supposed to significantly change the positioning and navigation service for ground users. The goal of this contribution is to suggest and discuss the feasibility of possible procedures to generate the LEO orbital products at two accuracy levels to facilitate different positioning methods—i.e., Level A orbits with meter-level accuracy as LEO-specific broadcast ephemeris, and Level B orbits with an accuracy of centimeters as polynomial corrections based on Level A orbits. Real data of the LEO satellite GRACE FO-1 are used for analyzing the error budgets. For the Level A products, compared to the orbital user range errors (OUREs) of a few centimeters introduced by the ephemeris fitting, it was found that the orbital prediction errors play the dominant role in the total error budget—i.e., at around 0.1, 0.2 and 1 m for prediction intervals of 1, 2 and 6 h, respectively. For the Level B products, the predicted orbits within a short period of up to 60 s have an OURE of a few centimeters, while the polynomial fitting OUREs can be reduced by a few millimeters when increasing the polynomial degree from one to two.

Optimal GPS Satellite Selection using Stochastic Optimization and Volumes of Tetrahedrons for High Precision Positioning

A possibility of utilizing the Global Positioning System (GPS) depends on the positioning accuracy. Two decisive factors of position accuracy are User Range Error (URE) value and dimensionless Dilution of Precision (DOP), related to number of visible satellites. Several error modeling and correction techniques are available to improve the accuracy by optimizing the errors. While finding the GDOP at every instant, satellite selection plays predominant role. Satellite geometry with more satellites gives the good GDOP. However, due to limited receiver tracking channels and smaller size memories and other problems, it may not be possible to use all satellites in view for positioning. In GPS navigation, position of user requires minimum of four visible satellites. The selection of four satellites has a considerable impact on the position accuracy and GDOP shows the order of this impact. By using the concept of relation between GDOP and volume of tetrahedron optimal four satellites are selected to improve the position accuracy. Genetic Algorithm is used to select best ten combinations based on GDOP. For experimental validation the data collected at Andhra University, Visakhapatnam, located at (706970.9093, 6035941.0226, 1930009.5821) (m) is used. It is observed that selected satellites which are arranged in tetrahedron by following the work done by M Kihara on satellite selection method and accuracy for the GPS, using GA gives the best position values.

GipsyX/RTGx, a new tool set for space geodetic operations and research

GipsyX/RTGx is the Jet Propulsion Laboratory’s (JPL) next generation software package for positioning, navigation, timing, and Earth science using measurements from three geodetic techniques: Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS); with Very Long Baseline Interferometry (VLBI) under development. The software facilitates combined estimation of geodetic and geophysical parameters using a Kalman filter approach on real or simulated data in both post-processing and in real-time. The estimated parameters include station coordinates and velocities, satellite orbits and clocks, Earth orientation, ionospheric and tropospheric delays. The software is also capable of full realization of a dynamic terrestrial reference through analysis and combination of time series of ground station coordinates.Applying lessons learned from its predecessors, GIPSY-OASIS and Real Time GIPSY (RTG), GipsyX/RTGx was re-designed from the ground up to offer improved precision, accuracy, usability, and operational flexibility. We present some key aspects of its new architecture, and describe some of its major applications, including Real-time orbit determination and ephemeris predictions in the U.S. Air Force Next Generation GPS Operational Control Segment (OCX), as well as in JPL’s Global Differential GPS (GDGPS) System, supporting User Range Error (URE) of <5 cm RMS; precision post-processing GNSS orbit determination, including JPL’s contributions to the International GNSS Service (IGS) with URE in the 2 cm RMS range; Precise point positioning (PPP) with ambiguity resolution, both statically and kinematically, for geodetic applications with 2 mm horizontal, and 6.5 mm vertical repeatability for static positioning; Operational orbit and clock determination for Low Earth Orbiting (LEO) satellites, such as NASA’s Gravity Recovery and Climate Experiment (GRACE) mission with GRACE relative clock alignment at the 20 ps level; calibration of radio occultation data from LEO satellites for weather forecasting and climate studies; Satellite Laser Ranging (SLR) to GNSS and LEO satellites, DORIS-based and multi-technique orbit determination for LEO; production of terrestrial reference frames and Earth rotation parameters in support of JPL’s contribution to the International Terrestrial Reference Frame (ITRF).