Accuracy Of Single Point Positioning Research Articles

Improving BDS broadcast ephemeris accuracy using ground-satellite-link observations

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.

Navigation in GEO, HEO, and Lunar Trajectory Using Multi-GNSS Sidelobe Signals

Positioning of spacecraft (e.g., geostationary orbit (GEO), high elliptical orbit (HEO), and lunar trajectory) is crucial for mission completion. Instead of using ground control systems, global navigation satellite system (GNSS) can be an effective approach to provide positioning, navigation and timing service for spacecraft. In 2020, China finished the construction of the third generation of BeiDou navigation satellite system (BDS-3); this global coverage system will contribute better sidelobe signal visibility for spacecraft. Meanwhile, with more than 100 GNSS satellites, multi-GNSS navigation performance on the spacecraft is worth studying. In this paper, instead of using signal-in-space ranging errors, we simulate pseudorange observations with measurement noises varying with received signal powers. Navigation performances of BDS-3 and its combinations with other systems were conducted. Results showed that, owing to GEO and inclined geosynchronous orbit (IGSO) satellites, all three types (GEO, HEO, and lunar trajectory) of spacecraft received more signals from BDS-3 than from other navigation systems. Single point positioning (SPP) accuracy of the GEO and HEO spacecraft was 17.7 and 23.1 m, respectively, with BDS-3 data alone. Including the other three systems, i.e., GPS, Galileo, and GLONASS, improved the SPP accuracy by 36.2% and 19.9% for GEO and HEO, respectively. Navigation performance of the lunar probe was significantly improved when receiver sensitivity increased from 20 dB-Hz to 15 dB-Hz. Only dual- (BDS-3/GPS) or multi-GNSS (BDS-3, GPS, Galileo, GLONASS) could provide continuous navigation solutions with a receiver threshold of 15 dB-Hz.

Improved stochastic modeling of multi-GNSS single point positioning with additional BDS-3 observations

The accuracy of Global Navigation Satellite System (GNSS) observations is affected by many factors, such as different systems, frequencies, carriers and pseudoranges, all of which also vary with different situations. Therefore, it is challenging to establish an accurate stochastic model for multi-GNSS positioning in theory, particularly for the additional BeiDou-3 Global Navigation Satellite System (BDS-3). In practical applications, the real stochastic model needs to be estimated based on the characteristics of the observations themselves. We evaluated the influence of BDS-3 on the positioning results using 46 sites distributed around the world and proposed an improved stochastic model for multi-GNSS single point positioning (SPP) based on the least-squares variance component estimation (LS-VCE). The results show that when the BDS-3 observations are added, the positioning precision and accuracy are significantly improved. By using the improved LS-VCE method in GPS/BDS dual system positioning, the accuracy of E, N and U directions are 0.373, 0.498 and 1.044 m, respectively, when compared to the traditional method with 0.502, 0.533 and 1.333 m. The proposed stochastic model improves the multi-GNSS SPP accuracy without significantly increasing the calculation time. Furthermore, reliable results are obtained for all epochs with the improved LS-VCE model.

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.

Optimization Technique for Pseudorange Multipath Mitigation Using Different Signal Selection Methods

Abstract Nowadays, the use of multi-Global Navigation Satellite System (GNSS) has improved positioning accuracy in autonomous driving, navigation and tracking systems utilized by general users. However, signal quality in urban areas is degraded by poor satellite geometry and severe multipath errors, which may disturb up to a hundred-meter-ranging error as a consequence. In this study, the performance of several satellite selection methods in multipath mitigation was evaluated, based on the concept that better quality signals and more accurate solutions will be obtained, the more multipath signals can be excluded. Three methods were performed and compared: 1) azimuth-dependent elevation mask based on fisheye image technique, 2) receiver autonomous integrity monitoring (RAIM), and 3) signal-to-noise ratio (SNR) mask in the SPP method. To examine the effect of the satellite selection methods on multipath error, the static test (single-point positioning (SPP) in real-time 1 Hz test) was performed in a multipath environment. The preliminary results showed a possible impact on improving the horizontal positioning accuracy of SPP. Among the three techniques assessed in this study, the results indicated that the SNR mask set at 36 dB-Hz in every elevation showed the most promising result. The SNR mask method could improve positioning accuracy by up to 46.80% compared to the SPP method.

GNSS time offset monitoring based on the single difference among systems

Time offset monitoring of multiple Global Navigation Satellite Systems is important for compatibility and interoperability. Unlike conventional signal space approaches, such as single-point positioning (SPP) and precise point positioning, an approach based on the principle of single difference among systems, single-difference point positioning (SDPP), is proposed to omit the receiver clock parameter and reduce the influence of the common model errors during estimation. The proposed approach was validated on different datasets, and results shown that the estimated time offset among systems using SDPP has no significant difference with that using SPP. Moreover, SDPP retrieves the best time offset estimation when considering it as a random walk process, as it provides smooth estimation with low noise. Furthermore, considering constraints from station coordinates and tropospheric delay further improves time offset estimation. The time offset estimation over time remains within a reasonable range, exhibits some periodicity, and estimation from different stations is consistent if disregarding system biases. In addition, the estimated time offset can be used to improve the SPP accuracy.

A Quad-Constellation GNSS Navigation Algorithm with Colored Noise Mitigation.

The existence of colored noise in kinematic positioning will greatly degrade the accuracy of position solutions. This paper proposes a Kalman filter-based quad-constellation global navigation satellite system (GNSS) navigation algorithm with colored noise mitigation. In this algorithm, the observation colored noise and state colored noise models are established by utilizing their residuals in the past epochs, and then the colored noise is predicted using the models for mitigation in the current epoch in the integrated Global Positioning System (GPS)/GLObal NAvigation Satellite System (GLONASS)/BeiDou Navigation Satellite System (BDS)/Galileo navigation. Kinematic single point positioning (SPP) experiments under different satellite visibility conditions and road patterns are conducted to evaluate the effect of colored noise on the positioning accuracy for the quad-constellation combined navigation. Experiment results show that the colored noise model can fit the colored noise more effectively in the case of good satellite visibility. As a result, the positioning accuracy improvement is more significant after handling the colored noise. The three-dimensional positioning accuracy can be improved by 25.1%. Different satellite elevation cut-off angles of 10º, 20º and 30º are set to simulate different satellite visibility situations. Results indicate that the colored noise is decreased with the increment of the elevation cut-off angle. Consequently, the improvement of the SPP accuracy after handling the colored noise is gradually reduced from 27.3% to 16.6%. In the cases of straight and curved roads, the quad-constellation GNSS-SPP accuracy can be improved by 22.1% and 25.7% after taking the colored noise into account. The colored noise can be well-modeled and mitigated in both the straight and curved road conditions.

Initial assessment of BDS-3 preliminary system signal-in-space range error

The basic constellation of the BeiDou global satellite navigation system (BDS-3) had been successfully completed by the end of 2018. It included 18 medium earth orbit satellites and 1 geostationary orbit satellite. An initial assessment of BDS-3 broadcast orbit and clock accuracy based on 55 days of broadcast message data is presented in this contribution. Satellite positions and clock offsets derived from broadcast ephemeris are compared with precise orbit determination orbits and clock offsets. Furthermore, the corresponding signal-in-space range error (SISRE), which is of most interest to navigation users, is computed. Thanks to the new inter-satellite link payloads on BDS-3 satellites, the statistics of age-of-data-ephemeris and age-of-data-clock demonstrate that more than 98% of ephemerides and 93% of clock parameters are updated within only one hour. Experimental results show that the 3D root mean square (RMS) of broadcast orbit errors is less than 0.6 m for the overall constellation. The broadcast orbit is also assessed by satellite laser ranging measurements, giving an RMS of 7.3 cm. The orbit-only SISRE is about 0.1 m. With respect to clock errors, the timescale differences between two clock products are eliminated to assess the accuracy of broadcast clock offsets. The standard deviation value of 0.25 m shows a good performance, but the RMS value is regrettably nearly 0.5 m due to a nonzero mean bias. RMS of BDS-3 SISRE amounts to approximately 0.5 m, which is largely attributed to clock errors. Finally, a positioning experiment is conducted to analyze the accuracy of single point positioning (SPP). With 95% confidence level, the horizontal accuracy is less than 5 m, and the vertical accuracy is close to 6 m. Considering that the nonzero mean bias in clock errors may affect the performance of SPP, we correct the nonzero mean value by a satellite-specific constant to analyze the influence of clock bias on the SPP performance. The results show that improvement in the 3D position accuracy can be up to 11%, especially in the up direction.

Multistep weighted least squares estimation method for improving single-point positioning accuracy

The integration of multiple Global Navigation Satellite Systems (GNSSs), such as the Chinese BeiDou Navigation Satellite System (BDS) and the American Global Positioning System (GPS), makes it possible to improve the accuracy of single-point positioning (SPP). However, the current accuracy of GNSS SPP with code measurement is on the order of several meters. In order to further improve SPP accuracy, we develop a multistep weighted least squares (MWLS) estimation method based on the elevation-dependent weighted least squares (EWLS) method. In this approach, the weight of each visible satellite is determined by its elevation and azimuth, and the coordinate components are semi-independently and separately calculated by MWLS. We conduct open-sky and blocked static tests as well as a vehicle-based kinematic test using single-frequency receivers to assess the effectiveness of this approach. Comparing the positioning errors of GPS and GPS/BDS SPPs between the MWLS and EWLS methods shows that the former improved the positioning accuracy more than the customary latter. Specifically, MWLS achieves a horizontal accuracy of about 1 m and a positional accuracy of 2 to 3 m in clear observational environments, about 15% better than ELWS.

Initial Positioning Assessment of BDS New Satellites and New Signals

With the official announcement of open service since the end of 2018, the BeiDou navigation satellite system (BDS) has started to provide global positioning, navigation and timing (PNT) services. Thus, it is worth assessing the positioning service of new BDS satellites and signals. In this paper, we comprehensively assess the system status and the global positioning performance of BDS regarding single point positioning (SPP) and real-time kinematic (RTK) performance. Results show that the signal in space range error (SISRE) of BDS-3 satellites is superior to that of BDS-2 satellites, showing an overall accuracy of 0.71 m versus 0.97 m, which is competitive with GPS and Galileo. With the contribution of BDS-3, the number of global average visible satellites has increased from 5.1 to 10.7, which provides a mean global position dilution of precision (PDOP) value better than 6 at 99.88% and the mean availability of basic PNT performance is also improved from 35.25% to 98.84%. One week of statistical results from 54 globally distributed international GNSS service (IGS) stations show that the root mean square (RMS) of SPP accuracy is 1.1 m in horizontal and 2.2 m in vertical, which is at the same level of GPS. The new B1c and B2a signals show a smaller observation noise than B1I, and SPP performance of B1c is similar to that of B1I. However, the positioning precision is slightly worse at the B2a frequency, which may be due to the inaccurate BDS ionosphere correction. As for short baseline RTK, baseline accuracy is also improved due to the increased number of new BDS satellites.

Site-Specific Unmodeled Error Mitigation for GNSS Positioning in Urban Environments Using a Real-Time Adaptive Weighting Model

In Global Navigation Satellite System (GNSS) positioning, observation precisions are frequently impacted by the site-specific unmodeled errors, especially for the code observations that are widely used by smart phones and vehicles in urban environments. The site-specific unmodeled errors mainly refer to the multipath and other space loss caused by the signal propagation (e.g., non-line-of-sight reception). As usual, the observation precisions are estimated by the weighting function in a stochastic model. Only once the realistic weighting function is applied can we obtain the precise positioning results. Unfortunately, the existing weighting schemes do not fully take these site-specific unmodeled effects into account. Specifically, the traditional weighting models indirectly and partly reflect, or even simply ignore, these unmodeled effects. In this paper, we propose a real-time adaptive weighting model to mitigate the site-specific unmodeled errors of code observations. This unmodeled-error-weighted model takes full advantages of satellite elevation angle and carrier-to-noise power density ratio (C/N0). In detail, elevation is taken as a fundamental part of the proposed model, then C/N0 is applied to estimate the precision of site-specific unmodeled errors. The principle of the second part is that the measured C/N0 will deviate from the nominal values when the signal distortions are severe. Specifically, the template functions of C/N0 and its precision, which can estimate the nominal values, are applied to adaptively adjust the precision of site-specific unmodeled errors. The proposed method is tested in single-point positioning (SPP) and code real-time differenced (RTD) positioning by static and kinematic datasets. Results indicate that the adaptive model is superior to the equal-weight, elevation and C/N0 models. Compared with these traditional approaches, the accuracy of SPP and RTD solutions are improved by 35.1% and 17.6% on average in the dense high-rise building group, as well as 11.4% and 11.9% on average in the urban-forested area. This demonstrates the benefit to code-based positioning brought by a real-time adaptive weighting model as it can mitigate the impacts of site-specific unmodeled errors and improve the positioning accuracy.

The data processing and analysis for the CE-5T1 GNSS experiment

In this paper the performance of a high sensitivity GPS/GLONASS receiver mounted on CE-5T1 Service Module is studied and the data received on the first Earth-lunar transfer orbit is processed and analyzed. At least four GLONASS satellites are visible for 46% of the data span while for 98% of the data span at least four GPS satellites are visible. GLONASS serves as a necessary supplement to GPS in real time positioning whenever less than four GPS satellites are tracked, and helps to optimize the observation geometry by reducing the Position Dilution of Precision (PDOP) values by up to 77%. However, noisier GLONASS pseudorange data should be properly weighted in order not to deteriorate the positioning accuracy. Studies indicate that when the inverse square of the pseudorange measurement error of each satellite is applied as the weight value, single point positioning (SPP) accuracy improves from 57.7m (RMS) with GPS data alone to 44.6m (RMS) with the addition of GLONASS data. Transmitter antenna Equivalent Isotropic Radiated Power (EIRP)s of all the four blocks of GPS satellites as well as GLONASS satellites are derived from the received C/N0 data and show significant variance in sidelobe power patterns. In general, the EIRP patterns of GPS Block IIR-M and GLONASS satellite antennas have a comparatively flat power level of around 10dBW within the off-boresight angle range of 30–80° and roll off at the off-boresight angle of about 80°, offering deep space applications greater benefits than the other three blocks of GPS satellites. In addition, an interesting close encounter happens between CE-5T1 spacecraft and GLONASS satellite R06. Investigations indicate that the PDOP value increases up to 1.4 times and the SPP accuracy deteriorates by more than 142% if satellite R06 is excluded in the positioning computation.

An analysis on combined GPS/COMPASS data quality and its effect on single point positioning accuracy under different observing conditions

With the rapid development of the COMPASS system, it is currently capable of providing regional navigation services. In order to test its data quality and performance for single point positioning (SPP), experiments have been conducted under different observing conditions including open sky, under trees, nearby a glass wall, nearby a large area of water, under high-voltage lines and under a signal transmitting tower. To assess the COMPASS data quality, the code multipath, cycle slip occurrence rate and data availability were analyzed and compared to GPS data. The datasets obtained from the experiments have also been utilized to perform combined GPS/COMPASS SPP on an epoch-by-epoch basis using unsmoothed single-frequency code observations. The investigation on the regional navigation performance aims at low-accuracy applications and all tests are made in Changsha, China, using the “SOUTH S82-C” GPS/COMPASS receivers. The results show that adding COMPASS observations can significantly improve the positioning accuracy of single-frequency GPS-only SPP in environments with limited satellite visibility. Since the COMPASS system is still in an initial operational stage, all results are obtained based on a fairly limited amount of data.

Performance analysis of a 3D ionosphere tomographic model

A 3D high precision ionospheric model is developed based on tomography technique. This tomographic model employs GPS data observed by an operational network of dual-frequency GPS receivers. The methodology of developing a 3D ionospheric tomography model is briefly summarized. However emphasis is put on the analysis and evaluation of the accuracy variation of 3D ionosphere modeling with respect to the change of GPS data cutoff angle. Three typical cutoff angle values (15†, 20† and 25†) are tested. For each testing cutoff angle, the performances of the 3D ionospheric model constructed using tomography technique are assessed by calibrating the model predicted ionospheric TEC with the GPS measured TEC and by employing the model predicted TEC to a practical GPS positioning application—single point positioning (SPP). Test results indicate the 3D model predicted VTEC has about 0.4 TECU improvement in accuracy when cutoff angle rises from 15† to 20†. However, no apparent improvement is found from 20† to 25†. The model’s improvement is also validated by the better SPP accuracy of 3D model than its counterpart-dual frequency model in the 20† and 25† cases.

GPS SINGLE POINT POSITIONING WITH SA OFF: HOW ACCURATE CAN WE GET?

The announcement by U.S. President Bill Clinton to turn off ‘Selective Availability’ at midnight (Washington DC time) 1 May 2000 caught everyone by surprise. This decision to stop degrading the accuracy of the Global Positioning system's (GPS) Standard Positioning Service (SPS) will have a significant impact on users all over the world. One important outcome for the geomatics community is that the substantial improvement to GPS Single Point Positioning (SPP) results could make it an attractive alternative to the Differential GPS (DGPS) mode of positioning. In this paper some results from different SPP processing strategies are presented, and the accuracy improvement in the case of averaged static solutions is discussed. Finally, the paper speculates on the attainable SPP accuracy using single-frequency GPS receivers when the ionospheric activity is less intense in the future.