User Equivalent Range Error Research Articles

Calibration of Receiver-Dependent Pseudorange Bias and Its Impact on BDS Augmentation Positioning Accuracy

Pseudorange bias refers to the receiver-dependent and satellite-dependent constant bias in the pseudorange resulting from the nonideal characteristics of a signal. The impact of pseudorange bias on high-precision satellite navigation services has long been ignored. This paper proposes a pseudorange bias calibration method for two collocated receivers. Then, we calibrate pseudorange biases for two types of collocated receivers at a monitoring station within China and evaluate their impact on two high-precision services: BeiDou Navigation Satellite System 3 (BDS-3) dual-frequency pseudorange augmentation and precise point precision (PPP). Theoretical analysis reveals that the calibrated pseudorange biases contribute 17.2% and 7.7% to the user equivalent ranging error (UERE) of BDS-3 and Global Positioning System (GPS) dual-frequency pseudorange augmentation, respectively, and that the convergence time of the GPS static and kinematic PPP increases from 6 min and 26 min to 19 min and 58 min, respectively. The experimental results indicate that the calibrated pseudorange biases are consistent as the receiver location and time vary. The spatial distribution consistency is generally better than 0.1 m, and the temporal consistency is better than 0.15 m. The pseudorange biases for BDS-3 B1C and B2a are approximately 0.7 m and 0.1 m, respectively, whereas those for GPS L1C/A and L2P are both approximately 0.25 m. Furthermore, The results show that after correction of the pseudorange biases, the average convergence time for BDS-3/GPS static PPP decreases from 48.83/24.03 min to 38.54/21.12 min, respectively, a decrease of approximately 21%/12%. For BDS-3/GPS/BDS-3 + GPS kinematic PPP, the average convergence time decreases from 109.53/45.10/39.15 min to 62.99/40.83/22.94 min, respectively, a decrease of approximately 42%/41%/9%. Similarly, the three-dimensional positioning accuracy for BDS-3/GPS/BDS-3 + GPS dual-frequency pseudorange augmentation improves from 3.25/3.94/2.49 m to 2.65/3.69/2.16 m, respectively, increasing by approximately 6.3%, 18.5%, and 13.3%, respectively. The above analysis and experiments demonstrate that pseudorange bias is an important error source affecting both dual-frequency pseudorange augmentation and PPP services.

Performance analysis of the BDSBAS-B1C message in trial operation stage

BeiDou Satellite-based Augmentation System (BDSBAS) has come into the trial operation stage since July, 2020. To evaluate the characteristic of the augmentation message in BDSBAS-B1C signal, the effectiveness of the message content was firstly analyzed, and then the validity of the broadcasting strategy was estimated. Finally, the accuracy of the user equivalent ranging error (UERE) and the single frequency positioning error with different correction parameters in BDSBAS-B1C message was evaluated. Based on the above analysis, the effectiveness of the augmentation message was preliminarily verified with the results showing that: (1) the BDSBAS-B1C message type, information content and update interval have basically met the international standard; (2) the accuracy of the UERE obtained with the augmentation message had an obvious improvement in contrast to that of the UERE obtained with the usual navigation message of the GPS satellites, and the ionospheric delay was one of the important factors which affected the accuracy of the UERE; (3) the positioning accuracy obtained with the augmentation message was also improved, and the improvement was more obvious in the service areas with high availability of the ionospheric parameters.

A Study on Pseudorange Biases in BDS B1I/B3I Signals and the Impacts on Beidou Wide Area Differential Services

Due to satellite signal deformations, there are different constant biases in the same satellite signal that are measured by different technical types of receivers and different satellite signals that are measured by the same type of receiver, which are named pseudorange biases. These biases cannot be transmitted to users with existing navigation parameters, such as satellite time group delay (TGD) and receiver differential code biases (DCB). With the improvement of the signal-in-space accuracy of the Global Navigation Satellite System (GNSS), the pseudorange bias has become one of the primary error sources affecting the accuracy of GNSS services. To ensure the accuracy for users under the wide area differential services (WADS), we extracted the pseudorange biases of Beidou Satellite Navigation System (BDS) B1I, B3I and B1I/B3I signals and analyzed the impact of those biases on users under the WADS. Finally, we tried to eliminate this influence. The results show that the pseudorange biases of the B3I signal are smaller than those of the B1I signal at the centimeter level, but the pseudorange biases of the B1I/B3I signal can reach the meter level. Due to the large pseudorange bias of the B1I/B3I signal, the average user equivalent ranging error (UERE) under the WADS is 1.19 m, which is no better than the average UERE under open services (OS). Influenced by the pseudorange biases, the average positioning accuracies of the B1I/B3I signal are 4.17 m and 4.24 m under the WADS and the OS. When the pseudorange biases are deducted, these accuracies are 3.03 m and 3.50 m, respectively.

Time Transfer From GPS for Designing a SmallSat-Based Lunar Navigation Satellite System

<h3>Abstract</h3> For the future lunar navigation satellite system (LNSS), a GPS-like constellation for the Moon, NASA has expressed interest in using a smallsat platform. However, many design decisions have yet to be finalized, including the orbit, constellation, and onboard clock. Furthermore, designing a dedicated smallsat-based LNSS limits the payload capacity, thus restricting the size, weight, and power (SWaP) of the onboard clock. We propose an LNSS design with time transfer from intermittently available GPS signals wherein we design a Kalman filter to estimate timing corrections for a low-SWaP clock. Additionally, we devise a lunar User Equivalent Range Error (UERE) metric to characterize the ranging accuracy of signals transmitted by an LNSS satellite. We further validate our time-transfer technique with simulations of an LNSS satellite in an elliptical lunar frozen orbit (ELFO) with an onboard chip scale atomic clock (CSAC) while analyzing the visibility effects of GPS, timing errors, and lunar UERE across ELFOs.

Beidou wide-area augmentation system clock error correction and performance verification

On December 27, 2018, the Beidou-3 System (BDS-3) has completed the deployment of 18 Medium Earth Orbit (MEO) satellites combined as a space constellation. In addition to the augmentation information for the new system signals B1C and B2a, the BDS-3 is compatible with the three augmentation information broadcast by the BDS-2 system for B1I and B3I signals: equivalent clock error correction, User Differential Ranging Error (UDRE) and Grid Ionosphere Vertical Error (GIVE). In this paper, the observation data of Beidou monitoring network are used to analyze the pseudo-range observation quality of the smooth transition signals B1I and B3I of BDS-2 and BDS-3. At the same time, the relationship between the equivalent clock error correction and the prediction error of the satellite clock is analyzed by using the Two-Way Satellite Time and Frequency Transfer (TWSTFT) data. The results show that the correlation between the equivalent clock error correction and the monitored clock error by using the TWSTFT data is greater than 60%. We calculate the UDRE by using the equivalent clock error correction. The results show that the satellite equivalent clock error correction can improve the accuracy of User Equivalent Range Error (UERE) by about 50%. This paper also compares the positioning accuracy of the BDS-2 satellites with the BDS-2 satellites combined BDS-3 satellites. The results show that the three-dimensional positioning accuracy is improved by about 30% after the BDS-3 satellites are added.

Initial Assessment of the LEO Based Navigation Signal Augmentation System from Luojia-1A Satellite.

A low Earth orbiter (LEO)-based navigation signal augmentation system is considered as a complementary of current global navigation satellite systems (GNSS), which can accelerate precise positioning convergence, strengthen the signal power, and improve signal quality. Wuhan University is dedicated to LEO-based navigation signal augmentation research and launched one scientific experimental satellite named Luojia-1A. The satellite is capable of broadcasting dual-frequency band ranging signals over China. The initial performance of the Luojia-1A satellite navigation augmentation system is assessed in this study. The ground tests indicate that the phase noise of the oscillator is sufficiently low to support the intended applications. The field ranging tests achieve 2.6 m and 0.013 m ranging precision for the pseudorange and carrier phase measurements, respectively. The in-orbit test shows that the internal precision of the ephemeris is approximate 0.1 m and the clock stability is 3 × 10−10. The pseudorange and carrier phase measurement noise evaluated from the geometry-free combination is about 3.3 m and 1.8 cm. Overall, the Luojia-1A navigation augmentation system is capable of providing useable LEO navigation augmentation signals with the empirical user equivalent ranging error (UERE) no worse than 3.6 m, which can be integrated with existing GNSS to improve the real-time navigation performance.

Multi-GNSS signal-in-space range error assessment – Methodology and results

The positioning accuracy of global and regional navigation satellite systems (GNSS/RNSS) depends on a variety of influence factors. For constellation-specific performance analyses it has become common practice to separate a geometry-related quality factor (the dilution of precision, DOP) from the measurement and modeling errors of the individual ranging measurements (known as user equivalent range error, UERE). The latter is further divided into user equipment errors and contributions related to the space and control segment. The present study reviews the fundamental concepts and underlying assumptions of signal-in-space range error (SISRE) analyses and presents a harmonized framework for multi-GNSS performance monitoring based on the comparison of broadcast and precise ephemerides. The implications of inconsistent geometric reference points, non-common time systems, and signal-specific range biases are analyzed, and strategies for coping with these issues in the definition and computation of SIS range errors are developed. The presented concepts are, furthermore, applied to current navigation satellite systems, and representative results are presented along with a discussion of constellation-specific problems in their determination. Based on data for the January to December 2017 time frame, representative global average root-mean-square (RMS) SISRE values of 0.2 m, 0.6 m, 1 m, and 2 m are obtained for Galileo, GPS, BeiDou-2, and GLONASS, respectively. Roughly two times larger values apply for the corresponding 95th-percentile values. Overall, the study contributes to a better understanding and harmonization of multi-GNSS SISRE analyses and their use as key performance indicators for the various constellations.

Centralized autonomous orbit determination of Beidou navigation satellites with inter-satellite link measurements: preliminary results

Autonomous orbit determination is the process by which the orbit parameters of navigation satellites are estimated onboard using Inter-Satellite Link (ISL) measurements. In this contribution, autonomous orbit determination experiments using ISL measurements in a centralized mode of the new-generation Beidou navigation satellites are conducted. The mathematical formulation and the processing method of the dual one-way measurements are addressed as well as the main feathers of the ISL measurements are introduced. It is concluded that the ISL ranging data are high-precision measurements. The centralized autonomous orbit determination is processed in a batch mode. The average value of ISL measurements residuals is within 1.0 cm, standard deviation of ISL measurements residuals is within 10.0 cm and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The orbital accuracy is assessed by overlap comparison, User Equivalent Ranging Error and Satellite Laser Ranging (SLR) residuals. The radial overlap differences of the autonomous orbits are less than 6.0 cm and 24 h predicted orbital radial overlap differences less than 10.0 cm. The User Equivalent Ranging Error of 24 h predicted autonomous orbits is about 0.43 m and is better than the 24 h predicted L-band orbits at the 0.76 m level. The SLR residuals for the autonomous orbits are less than 10.0 cm. The ground anchor station which observes the constellation with ISL is important to maintain the Earth-Fixed-Frame and avoid the uncertainties of the entire constellation orientation. The influence of the ground station observation time span on autonomous orbit accuracy is also discussed. Even if the cutoff elevation of the ground anchor station is less than 60°, the radial accuracy of the autonomous orbits and 24 h predicted orbits is still better than 10.0 cm and three-dimensional orbit accuracy better than 1.5 m.

Improvement of orbit determination accuracy for Beidou Navigation Satellite System with Two-way Satellite Time Frequency Transfer

The Beidou Navigation Satellite System (BDS) manages to estimate simultaneously the orbits and clock offsets of navigation satellites, using code and carrier phase measurements of a regional network within China. The satellite clock offsets are also directly measured with Two-way Satellite Time Frequency Transfer (TWSTFT). Satellite laser ranging (SLR) residuals and comparisons with the precise ephemeris indicate that the radial error of GEO satellites is much larger than that of IGSO and MEO satellites and that the BDS orbit accuracy is worse than GPS. In order to improve the orbit determination accuracy for BDS, a new orbit determination strategy is proposed, in which the satellite clock measurements from TWSTFT are fixed as known values, and only the orbits of the satellites are solved. However, a constant systematic error at the nanosecond level can be found in the clock measurements, which is obtained and then corrected by differencing the clock measurements and the clock estimates from orbit determination. The effectiveness of the new strategy is verified by a GPS regional network orbit determination experiment. With the IGS final clock products fixed, the orbit determination and prediction accuracy for GPS satellites improve by more than 50% and the 12-h prediction User Range Error (URE) is better than 0.12m. By processing a 25-day of measurement from the BDS regional network, an optimal strategy for the satellite-clock-fixed orbit determination is identified. User Equivalent Ranging Error is reduced by 27.6% for GEO satellites, but no apparent reduction is found for IGSO/MEO satellites. The SLR residuals exhibit reductions by 59% and 32% for IGSO satellites but no reductions for GEO and MEO satellites.

GNSS Constellation Integrity Evaluation Based on Quality Control

In this paper, a composite integrity evaluation method of the Global Navigation Satellite Systems (GNSS) based on the constellation situation, observation conditions, measurement noise and application requirements is proposed. Two indicators are suggested, where Minimal Availability of Integrity (MAI) is used to assess the availability of integrity, and Minimal Detectable Effect Holes Ratio (MDEHR) is used to evaluate the proportion of faulty points which may not meet the necessary applications. The integrity performances of GPS, BeiDou, QZSS, IRNSS and their combined systems are assessed in three simulation scenarios based on different constellations, masking angles, User Equivalent Range Error (UERE), alert limit, spatial and temporal variations by the proposed method respectively. This proposed method has a wider serviceability to many GNSS applications related to navigation integrity. It is fit to evaluate the integrity of the whole GNSS constellation or combination systems.

A Run-Time Method Based on Observable Data for the Quality Assessment of GNSS Positioning Solutions

Several location-aware applications rely on the position estimated by means of Global Navigation Satellite Systems (GNSS), which are known to estimate an accurate position in an open environment. However, the quality of the estimated position is degraded in harsh environments in terms of accuracy and reliability. Liability-critical services, such as location-based charging, transportation, and road tolling, are threatened by the use of an unreliable position of the user, and the level of trust in the estimated position has to be considered to avoid a failure of the full service chain. Such an issue is faced by means of integrity monitoring methods in the field of GNSS. However, when dealing with harsh environments, integrity monitoring techniques designed for aeronautical applications would lead to very conservative results and to the rejection of all the positions obtained. Such conservative approach is based on the theoretical error models for the estimation of the pseudorange standard deviation in open sky. The purpose of this work is to propose an innovative method for estimating the pseudorange standard deviation extrapolating it from measurements of observable data, to assess the confidence level in the obtained positions in relation to the real environment surrounding the user. While measuring the pseudorange standard deviation taking into account environment conditions and receiver accuracy, the user is able to achieve better estimation of the user equivalent range error (UERE). Estimating the UERE from raw pseudorange measurements with the proposed run-time method and its subsequent use in the computation of protection levels using the receiver autonomous integrity monitoring (RAIM) algorithm shows significant improvement in navigation system availability by deriving tight protection levels.

Orbit determination and prediction for Beidou GEO satellites at the time of the spring/autumn equinox

Geostationary (GEO) satellites form an indispensable component of the constellation of Beidou navigation system (BDS). The ephemerides, or predicted orbits of these GEO satellites(GEOs), are broadcast to positioning, navigation, and timing users. User equivalent ranging error (UERE) based on broadcast message is better than 1.5 m (root formal errors: RMS) for GEO satellites. However, monitoring of UERE indicates that the orbital prediction precision is significantly degraded when the Sun is close to the Earth's equatorial plane (or near spring or autumn Equinox). Error source analysis shows that the complicated solar radiation pressure on satellite buses and the simple box-wing model maybe the major contributor to the deterioration of orbital precision. With the aid of BDS' two-way frequency and time transfer between the GEOs and Beidou time (BDT, that is maintained at the master control station), we propose a new orbit determination strategy, namely three-step approach of the multi-satellite precise orbit determination (MPOD). Pseudo-range (carrier phase) data are transformed to geometric range (biased geometric range) data without clock offsets; and reasonable empirical acceleration parameters are estimated along with orbital elements to account for the error in solar radiation pressure modeling. Experiments with Beidou data show that using the proposed approach, the GEOs' UERE when near the autumn Equinox of 2012 can be improved to 1.3 m from 2.5 m (RMS), and the probability of user equivalent range error (UERE)<2.0 m can be improved from 50% to above 85%.

Research on technique of orbit rapid recovery for GEO satellite of partial subsatellite point

Subsatellite point for geostationary satellite(GEO) needs to be retained based on the continual orbit maneuver, especially for GEO satellite of partial subsatellite point. How to recover orbit rapidly for GEO satellite based on short-arc tracking is the key factor to improve the service performance and usability of the navigation system. Due to its geostationary feature, GEO satellites orbit parameters are strongly correlated with the clock corrections parameters in precise orbit determination (POD) using L-band pseudorange data, which needs supports by the time synchronization technique. This paper presents an orbit rapid recovery method based on satellite clock offset and station clock offset. The satellite-ground time synchronization is realized by satellite-earth wireless two-way method, and the ground-ground time synchronization is realized by constellation combining orbit determination method. The precise orbit determination is realized based on pseudorange and phase data without clock offset. A new method of parameters decorrelation based on prior restriction and a short-arc orbit determination method based on the restriction by long-arc orbit determination are brought forward. The experiments based on ground data results indicate that the time of orbit recovery after maneuver is shortened from 24 h to 4 h. The 2-hour orbital prediction in radial component is better than 1 m, which is evaluated SLR data. User equivalent range error (UERE) is better than 1.5 m, and the precision is stable. The orbit recovery for GEO satellite of partial subsatellite point has come true.

Calculation and accuracy evaluation of TGD from IFB for BDS

With the development of new global navigation satellite system applications, the demand of high accurate positioning navigation timing (PNT) service becomes urgent. For precise PNT, the timing group delay (TGD) is regarded as an important parameter in the satellite navigation message. Instead of using the absolute receiver hardware delay, a method based on receiver inter-frequency bias (IFB, i.e., differential receiver hardware delay between different frequencies) calibration is presented to deal with the rank deficiency of a calculation matrix and to reduce jumps in TGD solutions in BDS. The double-differenced pseudorange obtained from a pair of zero baseline receivers is used to evaluate the IFB calibration accuracy. The estimated precision of TGD is evaluated and compared with GPS TGD provided by IGS. In order to ensure the quality of assessment, a method based on the difference of dual-frequency ionospheric delay is proposed to compare the accuracy of the estimated TGD and broadcast TGD. Finally, the effect of TGD on the user equivalent range error is analyzed. The analysis result shows that for BDS IGSO satellites, the precision of TGD1, which is the differential hardware delay between B1 (1561.098 MHz) and B3 (1268.52 MHz) frequencies, is better than 0.5 ns, and for GEO and MEO satellites the TGD1 is better than 1 and 2 ns, respectively. The precision of TGD2 of all satellites, which is the differential hardware delay between B2 (1207.14 MHz) and B3 frequencies, is better than 0.5 ns. The accuracy analysis result reveals that the proposed TGD estimation method can provide better results when compared with the broadcast data.

Global Positioning System (GPS) Positioning Errors During Ionospheric Scintillation Event

As technology advancement progresses throughout the years in this modern age, every technology has its part to play in that the world is moving towards a brighter future. GPS (Global Positioning System) has diverse application in current globalized world, its application has pervasive benefits not only to navigation and positioning, it is pivotal in industries like logistics, shipping, financial services and agriculture. Since the decision to shut down the Selectivity Availability (SA) by former U.S. President, Bill Clinton, ionospheric effect is now the primary concern of error contributing factors in GPS. Ionospheric scintillation induces rapid fluctuations in the phase and the amplitude of received Global Navigation Satellite System (GNSS) signals. These rapid fluctuations or scintillation potentially introduce cycle slips, degrade range measurements, and if severe enough lead to loss of lock in phase and code. Global Ionospheric Scintillation Model (GISM) was used to compute amplitude scintillation parameter for each GPS satellite visible from Melaka, Malaysia (Latitude 20 14’ N, Longitude 1020 16’ E) as its location has strong equatorial scintillation behavior. The output data from GISM was then used to calculate the positioning error where it is depends on the Dilution of Precision (DOP) and User Equivalent Range Error (UERE). There are two schemes that were used. First, the positioning error was calculated for all the visible satellites with better DOP but worse UERE due to scintillation event. Secondly, the positioning error was calculated for those satellites that have amplitude scintillation index, S4 &lt; 0.7 which leads to worse DOP with better UERE. Comparison of results from the both schemes was then made.

Estimation Of Global Positioning System Measurement Errors For GAGAN Applications

The Global Positioning System (GPS) has been in use for providing positioning, navigation and timing (PNT) services in many parts of the world. There are several errors that affect the positional accuracy of GPS. Prominent among them are ephemeris errors, satellite and receiver clock errors, multipath errors, signal propagation errors such as ionospheric delay, tropospheric delay, and instrumental biases of the satellite and receiver. In this paper, prominent estimation techniques to characterize various GPS measurement errors are reviewed. The GPS data in the Receiver INdependent EXchange (RINEX) format obtained from a Dual frequency GPS receiver is used in this analysis. Among all the errors, ionospheric delay is found to be the most dominant. However, these delay measurements are affected by the satellite and receiver instrumental biases. The instrumental biases exist as the signals at the two GPS frequencies experience different delays inside the satellite and receiver hardware. For estimation of the instrumental biases Extended Kalman filter(EKF) technique is adopted. The user equivalent range error (UERE) obtained due to all the error sources is of the order of few metres. After accounting for various errors, the estimation accuracy is significantly improved.The positional accuracy of the GPS Aided GEO Augmented Navigation (GAGAN) system is basically dependent on ranging errors and the satellite constellation geometry(1). The lineof-sight ionospheric measurements derived from the Global Positioning System (GPS) observables are corrupted by the instrumental biases present in both the GPS satellites and the receivers. The instrumental bias and Total Electron Content (TEC) results (Hyderabad GAGAN station (78.47°E, 17.45°N)) obtained using theExtended Kalman filter technique are presented in this paper. In this work the main focus is towards development of an improved error free approach for aircraft navigation. The existing navigation solutions are based on iterative algorithms and require an initial estimate of the receiver position for computing the navigation solution which is not possible in all conditions. Accurate, reliable and cost effective navigation solution algorithms that suit the Indian geographic area and area of application are proposed in this work. A non-iterative point solution approach algorithm computes the navigation solution based on the available satellite positions and pseudorange measurements(3). The improvement in GPS system has given a feasibility of automated operation of satellite based augmenting system in aircraft navigation can augment GAGAN and improves the positional accuracy of the user. In this paper a communication approach , high, accurate processing using EKF scheme is proposed for GPS aided geo augmented navigation (GAGAN) application. The effectiveness of the proposed approach for higher performance is evaluated under variable conditions.

A simulation system for GNSS multipath mitigation using spatial statistical methods

Multipath is one of the main causes of degraded position accuracy in the Global Navigation Satellite System (GNSS) because portions of the signals can be reflected by high buildings in dense urban areas. Multipath mitigation techniques based on hardware enhancement or signal processing help to improve GNSS accuracy for high-precision surveying. A Geographic Information System (GIS) is also used in the signal propagation model to predict multipath effects. In addition to these existing approaches, we found that spatial statistical methods are useful in multipath mitigation because the multipath produces a unique spatial distribution of user positions. In this paper, we present a spatial statistics-based simulation system for mitigating multipath and improving the accuracy in GNSS positioning. Multipath tends to be associated with spatial outliers in simulated user positions (SUPs) and contributes little to the spatial clustering of SUPs. Using these spatial characteristics, we developed a method called the “satellite participation ratio in outliers versus cluster” (SPROC) to identify multipath satellites. Once the identified multipath satellites are excluded, a user position is determined using a mean spatial center of the SUPs from the remaining satellites. The effects of such multipath mitigation were validated by examining whether the SPROC method correctly identified multipath satellites and by comparing the position errors with and without SPROC. We demonstrated the applicability of our system with a simulation experiment using a precise ephemeris for the Global Positioning System (GPS) and the orbital parameters for the proposed constellations of the GALILEO and the Quasi-Zenith Satellite System (QZSS). In our simulation of Shinjuku ward in Tokyo, the user-equivalent range error (UERE) other than multipath was virtually generated and added to the multipath delay. The pattern of position errors with and without SPROC showed that the improvements in accuracy were considerable at locations close to buildings.