Carrier Phase Observations Research Articles

Improved high‐precision GNSS navigation with a passive hydrogen maser

<h3>Abstract</h3> Receiver clock modeling (RCM) based on code observations requires a chip-scale atomic clock to improve the PVT solution. When using carrier phase observations, a more stable oscillator like a passive hydrogen maser (PHM) is necessary. We applied a PHM in an automotive experiment of about 80 minutes in an urban environment recording 10 Hz multi-GNSS data. Modeling the clock process noise in a linearized Kalman filter according to the spectral behavior of the PHM (i.e., RCM), improves position and velocity regarding precision and accuracy by 15% and 57%, respectively, as well as reliability by 30%. In situations with sparse, geometrically unfavorable observations, RCM prevents large position drifts. The convergence time of the carrier phase ambiguities is not affected. Conclusively, precision, accuracy, and reliability in kinematic precise point positioning can be improved by using an oscillator like a PHM. Future advancements in clock technology should make this approach more feasible for ordinary use cases.

Precise Relative Orbit Determination for Chinese TH-2 Satellite Formation Using Onboard GPS and BDS2 Observations

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.

Using Multi-Antenna Trajectory Constraint to Analyze BeiDou Carrier-Phase Observation Error of Dynamic Receivers.

Appropriate cycle-slip and measurement-error models are essential for BeiDou carrier-phase-based integrity risk calculation. To establish the receiver’s measurement-error model, an accurate position reference of the GNSS antenna is fundamental for calculating the measurement error. However, it is still a challenge to acquire position references for dynamic BeiDou receivers, resulting in improper GNSS measurement-error models and unreliable integrity monitoring. This paper proposes an improved precise relative positioning scheme by adopting multi-antenna trajectory constraints for dynamic BeiDou receivers. The dynamic experiments show an obvious decline of 78.7%, at most, in the positioning failure rate of the proposed method, as compared with the traditional method. The position solutions obtained from the proposed approach are used as the reference to analyze the cycle-slip and measurement-error characteristics of the dynamic receiver. The field test results indicate that the cycle-slip rate decreases with the increase of signal-to-noise ratio (SNR), and cycle slipping obeys a positively skewed distribution that could be fitted by the Gaussian mixture model (GMM). On the other hand, the standard deviation of the carrier-phase measurement error is inversely proportional to SNR, and its distribution is characteristically fat-tailed, which could be fitted by the bi-normal model.

Observation of Ionospheric Gravity Waves Introduced by Thunderstorms in Low Latitudes China by GNSS

The disturbances of the ionosphere caused by thunderstorms or lightning events in the troposphere have an impact on global navigation satellite system (GNSS) signals. Gravity waves (GWs) triggered by thunderstorms are one of the main factors that drive short-period Travelling Ionospheric Disturbances (TIDs). At mid-latitudes, ionospheric GWs can be detected by GNSS signals. However, at low latitudes, the multi-variability of the ionosphere leads to difficulties in identifying GWs induced by thunderstorms through GNSS data. Though disturbances of the ionosphere during low-latitude thunderstorms have been investigated, the explicit GW observation by GNSS and its propagation pattern are still unclear. In this paper, GWs with periods from 6 to 20 min are extracted from band-pass filtered GNSS carrier phase observations without cycle-slips, and 0.2–0.8 Total Electron Content Unit (TECU) magnitude perturbations are observed when the trajectories of ionospheric pierce points fall into the perturbed region. The propagation speed of 102.6–141.3 m/s and the direction of the propagation indicate that the GWs are propagating upward from a certain thunderstorm at lower atmosphere. The composite results of disturbance magnitude, period, and propagation velocity indicate that GWs initiated by thunderstorms and propagated from the troposphere to the ionosphere are observed by GNSS for the first time in the low-latitude region.

Carrier Phase-Based Precise Heading and Pitch Estimation Using a Low-Cost GNSS Receiver

Attitude and heading estimation methods using the global navigation satellite system (GNSS) are generally based on multi-antenna deployment, where the installation space and system cost increase with the increase in the number of antennas. Since the single-antenna receiver is still the major choice of the mass market, we focus on precise and reliable heading and pitch estimation using a low-cost GNSS receiver. Carrier phase observations are precise but have an ambiguity problem. A single difference between consecutive epochs can eliminate ambiguity and reduce the measurement errors. In this work, a measurement model based on the time-differenced carrier phases (TDCPs) is utilized to estimate the precise delta position of the antenna between two consecutive epochs. Then, considering the motion constraint, the heading and pitch angles of a moving land vehicle can be determined by the components of the estimated receiver delta position. A threshold on the length of the delta position is selected to avoid large errors in static periods. To improve the reliability of the algorithm, the Doppler-aided cycle slip detection method is applied to exclude carrier phases with possible cycle slips. A real vehicular dynamic experiment using a low-cost, single-frequency GNSS receiver is conducted to evaluate the proposed algorithm. The experimental results show that the proposed algorithm is capable of providing precise vehicular heading and pitch estimates, with both the root mean square errors being better than 1.5°. This also indicates that the cycle slip exclusion is indispensable to avoid unexpected large errors.

A new real‐time cycle slip detection and repair approach based on BDS dual‐frequency carrier phase and Doppler observations

The Global Navigation Satellite System (GNSS) traditional dual-frequency cycle slip detection and repair methods such as the TurboEdit algorithm are restricted by the availability and accuracy of pseudorange observations. Doppler observations represent the instantaneous variation of the carrier phase during the integration time, which are immune to cycle slips. They are less affected by multipath effects compared with the pseudorange observations. Hence, a real-time cycle slip detection and repair approach for the BeiDou Navigation Satellite System (BDS) dual-frequency signals is proposed by combining the carrier phase and Doppler observations. The proposed method adopts the phase-Doppler combination and the geometry-free combination to detect cycle slips, and uses the simple rounding method or the dual-frequency least-square ambiguity decorrelation adjustment (LAMBDA) method to repair cycle slips. The validity of the proposed method is verified by the static and kinematic observation data under 1 s sampling interval and steady ionosphere. The results show that the new method can successfully detect all the small, insensitive, and large cycle slips. Moreover, the fixing rates of the simple rounding method under static and kinematic conditions are above 94% and 83%, respectively, while those of the dual-frequency LAMBDA method are both 100%.

Estimation and Analysis of the Observable-Specific Code Biases Estimated Using Multi-GNSS Observations and Global Ionospheric Maps

Observable-specific bias (OSB) parameterization allows observation biases belonging to various signal types to be flexibly addressed in the estimation of ionosphere and global navigation satellite system (GNSS) clock products. In this contribution, multi-GNSS OSBs are generated by two different methods. With regard to the first method, geometry-free (GF) linear combinations of the pseudorange and carrier-phase observations of a global multi-GNSS receiver network are formed for the extraction of OSB observables, and global ionospheric maps (GIMs) are employed to correct ionospheric path delays. Concerning the second method, satellite and receiver OSBs are converted directly from external differential code bias (DCB) products. Two assumptions are employed in the two methods to distinguish satellite- and receiver-specific OSB parameters. The first assumption is a zero-mean condition for each satellite OSB type and GNSS signal. The second assumption involves ionosphere-free (IF) linear combination signal constraints for satellites and receivers between two signals, which are compatible with the International GNSS Service (IGS) clock product. Agreement between the multi-GNSS satellite OSBs estimated by the two methods and those from the Chinese Academy of Sciences (CAS) is shown at levels of 0.15 ns and 0.1 ns, respectively. The results from observations spanning 6 months show that the multi-GNSS OSB estimates for signals in the same frequency bands may have very similar code bias characteristics, and the receiver OSB estimates present larger standard deviations (STDs) than the satellite OSB estimates. Additionally, the variations in the receiver OSB estimates are shown to be related to the types of receivers and antennas and the firmware version. The results also indicate that the root mean square (RMS) of the differences between the OSBs estimated based on the CAS- and German Aerospace Center (DLR)-provided DCB products are 0.32 ns for the global positioning system (GPS), 0.45 ns for the BeiDou navigation satellite system (BDS), 0.39 ns for GLONASS and 0.22 ns for Galileo.

Multipath Error Fusion Modeling Methods for Multi-GNSS

The multipath error is considered to be the most limiting factor for high precision positioning applications. The sidereal filtering (SF) method can be used to mitigate the multipath error in the observation domain, and it has been successfully applied in the multipath mitigation in global positioning systems (GPS) and regional BeiDou navigation satellite systems (BDS2). However, there are few reports on the SF method in other systems. The performance of the SF method relies on the explicit orbit repeat periods of satellites in diverse systems or even different types of constellations. It is therefore inconvenient to utilize the SF method for multi-GNSS multipath error mitigation. Alternatively, a space domain multipath error reduction method, which establishes the multi-point hemispherical grid model (MHGM) using the residuals of the double-differenced carrier phase observations in the ambiguity-fixed period, has been modified. It is an integrated model for multi-GNSS, without considering the diversity of different systems and constellations. To compare the performance of MHGM and SF from a multi-GNSS point of view, the determination method of orbit repeat periods via the broadcast ephemerides is summarized, and the SF method is extended to the global BeiDou navigation satellite system (BDS3) and Galileo navigation satellite system. Further test results show that the performance of MHGM and SF are comparable from the perspective of root mean squares (RMS) and the power spectrum analysis of double-differenced residuals, as well as the static positioning results. This implies that the space domain MHGM can obtain similar correction effects as the SF method in the observation domain, but the former is more flexible for modeling with various systems’ data. In addition, the established MHGM using the data of multi orbit periods demonstrates a better performance compared with that of only one orbit period, and an average improvement of 13.1% in the RMS of the double-differenced residuals can be achieved.

Precision-Aided Partial Ambiguity Resolution Scheme for Instantaneous RTK Positioning

The use of carrier phase data is the main driver for high-precision Global Navigation Satellite Systems (GNSS) positioning solutions, such as Real-Time Kinematic (RTK). However, carrier phase observations are ambiguous by an unknown number of cycles, and their use in RTK relies on the process of mapping real-valued ambiguities to integer ones, so-called Integer Ambiguity Resolution (IAR). The main goal of IAR is to enhance the position solution by virtue of its correlation with the estimated integer ambiguities. With the deployment of new GNSS constellations and frequencies, a large number of observations is available. While this is generally positive, positioning in medium and long baselines is challenging due to the atmospheric residuals. In this context, the process of solving the complete set of ambiguities, so-called Full Ambiguity Resolution (FAR), is limiting and may lead to a decreased availability of precise positioning. Alternatively, Partial Ambiguity Resolution (PAR) relaxes the condition of estimating the complete vector of ambiguities and, instead, finds a subset of them to maximize the availability. This article reviews the state-of-the-art PAR schemes, addresses the analytical performance of a PAR estimator following a generalization of the Cramér–Rao Bound (CRB) for the RTK problem, and introduces Precision-Driven PAR (PD-PAR). The latter constitutes a new PAR scheme which employs the formal precision of the (potentially fixed) positioning solution as selection criteria for the subset of ambiguities to fix. Numerical simulations are used to showcase the performance of conventional FAR and FAR approaches, and the proposed PD-PAR against the generalized CRB associated with PAR problems. Real-data experimental analysis for a medium baseline complements the synthetic scenario. The results demonstrate that (i) the generalization for the RTK CRB constitutes a valid lower bound to assess the asymptotic behavior of PAR estimators, and (ii) the proposed PD-PAR technique outperforms existing FAR and PAR solutions as a non-recursive estimator for medium and long baselines.

The CODE ambiguity-fixed clock and phase bias analysis products: generation, properties, and performance

The generation and use of GNSS analysis products that allow—particularly for the needs of single-receiver applications—precise point positioning with ambiguity resolution (PPP-AR) are becoming more and more popular. A general uncertainty concerns the question on how the necessary phase bias information should be provided to the PPP-AR user. Until now, each AR-enabling clock/bias representation method had its own practice to provide the necessary bias information. We have generalized the observable-specific signal bias (OSB) representation, as introduced in Villiger (J Geod 93:1487–1500, 2019) originally exclusively for pseudorange measurements, to carrier phase measurements. The existing common clock (CC) approach has been extended in a way that OSBs allowing for flexible signal and frequency handling between multiple GNSS become possible. Advantages of the proposed OSB-based PPP-AR approach are: GNSS biases can be provided in a consistent way for phase and code measurements and it is capable of multi-GNSS and suitable for standardization. This new, extended PPP-AR approach has been implemented by the Center for Orbit Determination in Europe (CODE). CODE clock products that adhere to the integer-cycle property have been submitted to the International GNSS Service (IGS) since mid of 2018 for three analysis lines: Rapid, Final, and MGEX (Multi-GNSS Extension). Ambiguity fixing is performed not only for GPS but also for Galileo. The integer-cycle property of between-satellite clock differences is of fundamental importance when comparing satellite clock estimates among various analysis lines, or at day boundaries. Both kinds of comparisons could be exploited at a very high level of consistency. Any retrieved comparison essentially indicated a standard deviation for between-satellite clocks from CODE of the order of 5 ps (1.5 mm in range). Finally, the integer-cycle property that may be recovered between the CODE Final clock and the accompanying bias product of consecutive daily sessions (using clock estimates additionally provided for the second midnight epoch) allows us to deduce GPS satellite clock and phase bias information that is consistent and continuous with respect to carrier phase observation data over two, three, or, in principle, yet more days. Phase-based clock densification from initially estimated integer-cycle-conform clock corrections at intervals of 300 s to 30 s (5 s in case of our Final clock product) is a matter of particular interest. Based on direct product comparisons and GRACE K-band ranging (KBR) data analysis, the quality of accordingly densified clock corrections could be confirmed to be on a level similar to that of “anchor” (300 s) clock corrections.

Functional model modification of precise point positioning considering the time-varying code biases of a receiver

Precise Point Positioning (PPP), initially developed for the analysis of the Global Positing System (GPS) data from a large geodetic network, gradually becomes an effective tool for positioning, timing, remote sensing of atmospheric water vapor, and monitoring of Earth’s ionospheric Total Electron Content (TEC). The previous studies implicitly assumed that the receiver code biases stay constant over time in formulating the functional model of PPP. In this contribution, it is shown this assumption is not always valid and can lead to the degradation of PPP performance, especially for Slant TEC (STEC) retrieval and timing. For this reason, the PPP functional model is modified by taking into account the time-varying receiver code biases of the two frequencies. It is different from the Modified Carrier-to-Code Leveling (MCCL) method which can only obtain the variations of Receiver Differential Code Biases (RDCBs), i.e., the difference between the two frequencies’ code biases. In the Modified PPP (MPPP) model, the temporal variations of the receiver code biases become estimable and their adverse impacts on PPP parameters, such as ambiguity parameters, receiver clock offsets, and ionospheric delays, are mitigated. This is confirmed by undertaking numerical tests based on the real dual-frequency GPS data from a set of global continuously operating reference stations. The results imply that the variations of receiver code biases exhibit a correlation with the ambient temperature. With the modified functional model, an improvement by 42% to 96% is achieved in the Differences of STEC (DSTEC) compared to the original PPP model with regard to the reference values of those derived from the Geometry-Free (GF) carrier phase observations. The medium and long term (1 × 104 to 1.5 × 104 s) frequency stability of receiver clocks are also significantly improved.

Raw GNSS observations from Android smartphones: characteristics and short-baseline RTK positioning performance

The release of raw global navigation satellite system (GNSS) observations by Google Android makes high-precision positioning possible with low-cost smart devices. This study contributes to this research trend by constructing a stochastic model based on raw GNSS observation characteristics from Android smartphones and verifying the feasibility of smartphone-based ambiguity fixing in the short-baseline real-time kinematic (RTK) case. This study uses the raw observation standard deviations (ROSTDs) delivered by the Android application programming interface (API) as a stochastic model and takes advantage of the multipath index from the API to rule out unusable observations. As well as these, the ambiguity integer property is investigated by analyzing the residuals of double-differenced carrier-phase observations associated with one smartphone and one geodetic-grade receiver. Furthermore, we note that the carrier-phase observations collected by tested smartphones do not have the integer property but for the Huawei P30 and Xiaomi 8 devices, such an integer property can be successfully recovered by means of detrending. With the use of ROSTD-dependent weighting, we first perform single-point positioning (SPP) and real-time differentition (RTD) using pseudorange observations delivered by the Huawei P30 and Xiaomi 8 devices. The results show that the stochastic model is applicable to the Xiaomi 8. Moreover, the three-dimensional root-mean-square (3D-RMS) errors of the two smartphones for SPP are 1.28 m and 1.96 m, and the 3D-RMS errors for RTD are 0.79 m and 1.64 m, respectively. We next test the RTK positioning performance based on a short-baseline of 882 m using carrier-phase observations with recovered integer ambiguities. For the Huawei P30, the positioning errors achieved were 7.8, 2.4, 1.1 mm for the east, north, and up (ENU) components at the time of first fix while for the Xiaomi 8, the positioning errors achieved were 4.3, 4.2, 4.2 mm for the ENU components at the time of first fix.

A Novel Method to Mitigate the Multipath Error for BDS-2 Dam Deformation Monitoring

The multipath effect on carrier-phase observations is related to the observational environment of the station, and cannot be eliminated or attenuated by the differential method. In the actual dam environment of deformation monitoring, multipath is very complicated. It is the main error source of BDS-2 for high precision data processing. In this paper, a new method called the multi-point hemispherical grid model (MHGM) is studied and evaluated. This method uses the hemispheric grid model to attenuate the influence of multipath errors. The effectiveness and improvement of the new method with respect to the popular sidereal filter (SF) method were assessed and verified by the actual dam monitoring data with only the BDS-2. The MHGM and SF approach calculates the multipath corrections from multi-days historical data, and then corrects the multipath error from the observations on the day of interest. Compared with the SF method, the MHGM can also effectively provide a graphical display of multipath error interference around the stations, which matches the surrounding observation environment. The results show that the double-differenced (DD) residuals of the MHGM for GEO/IGSO and MEO satellites are slightly better than those of SF, but the RMS of MHGM for GEO/IGSO+MEO DD residuals is improved by about 17.0%. The performance of the MHGM method for different satellite constellations is consistent and not affected by the different orbital repeat times, which could solve the “zero mean” assumption problem of the SF method. Meanwhile, the RMS of static with a 2 h interval and kinematic positioning errors of the MHGM method in the horizontal and vertical direction can be up to 1.7, 3.6 and 2.4, 8.1 mm, respectively. The MHGM model could avoid the multipath reference problem caused by different orbital repetition periods, making it more suitable for the combined multipath modeling of BDS-2 and BDS-3.

Bandwidth correction of Swarm GPS carrier phase observations for improved orbit and gravity field determination

Gravity fields derived from GPS tracking of the three Swarm satellites have shown artifacts near the geomagnetic equator, where the carrier phase tracking on the L2 frequency is unable to follow rapid ionospheric path delay changes due to a limited tracking loop bandwidth of only 0.25 Hz in the early years of the mission. Based on the knowledge of the loop filter design, an analytical approach is developed to recover the original L2 signal from the observed carrier phase through inversion of the loop transfer function. Precise orbit determination and gravity field solutions are used to assess the quality of the correction. We show that the a posteriori RMS of the ionosphere-free GPS phase observations for a reduced-dynamic orbit determination can be reduced from 3 to 2 mm while keeping up to 7% more data in the outlier screening compared to uncorrected observations. We also show that artifacts in the kinematic orbit and gravity field solution near the geomagnetic equator can be substantially reduced. The analytical correction is able to mitigate the equatorial artifacts. However, the analytical correction is not as successful compared to the down-weighting of problematic GPS data used in earlier studies. In contrast to the weighting approaches, up to 9–10% more kinematic positions can be retained for the heavily disturbed month March 2015 and also stronger signals for gravity field estimation in the equatorial regions are obtained, as can be seen in the reduced error degree variances of the gravity field estimation. The presented approach may also be applied to other low earth orbit missions, provided that the GPS receivers offer a sufficiently high data rate compared to the tracking loop bandwidth, and provided that the basic loop-filter parameters are known.

An In-Depth Assessment of the New BDS-3 B1C and B2a Signals

An in-depth and comprehensive assessment of new observations from BDS-3 satellites is presented, with the main focus on the Carrier-to-Noise density ratio (C/N0), the quality of code and carrier phase observations for B1C and B2a signal. The signal characteristics of geosynchronous earth orbit (GEO), inclined geosynchronous satellite orbit (IGSO) and medium earth orbit (MEO) satellites of BDS-3 were grouped and compared, respectively. The evaluation results of the new B1C and B2a signals of BDS-3 were compared with the previously B1I/B2I/B3I signals and the interoperable signals of GPS, Galileo and quasi-zenith satellite system (QZSS) were compared simultaneously. As expected, the results clearly show that B1C and B2a have better signal strength and higher accuracy, including code and carrier phase observations. The C/N0 of the B2a signal is about 3 dB higher than other signals. One exception is the code observation accuracy of B3I, which value is less than 0.15 m. The carrier precision of B1C and B2a is better than that of B1I/B2I/B3I. Despite difference-in-difference (DD) observation quantity or zero-base line evaluation is adopted, while B1C is about 0.3 mm higher carrier precision than B2a. The BDS-3 MEO satellite and GPS, Galileo, and QZSS satellites have the same level of signal strength, code and phase observation accuracy at the interoperable frequency, namely 1575.42 MHz and 1176.45 MHz which are very suitable for the co-position application.

Higher order ionospheric error correction in BDS precise orbit determination

The ionospheric error affects the accuracy of the Global Navigation Satellite Systems observation and precise orbit determination. Usually, only the first order ionospheric error is considered, which can be eliminated by the ionospheric-free linear combination observation. But the remaining higher order ionospheric error will affect the accuracy of observations and their applications. In this paper, the influence of the higher order ionospheric error have been studied by using the International Geomagnetic Reference Field 13 and the Global Ionosphere Maps model produced by the Center for Orbit Determination in Europe. Focus on ionospheric error, the experiment of paper at doy 302 in 2019, which show that the second order ionospheric error impacting BeiDou Navigation Satellite System (BDS) B1I and B3I observation is 6.3569 mm and 11.8484 mm, respectively. Whereas, the third order ionospheric error impacting BDS B1I and B3I observation is 0.1734 mm and 0.3977 mm, respectively. Due to the current measurement accuracy of BDS carrier-phase observation can reach 2 mm, the influence of high order ionospheric error on observation should be considered. For BDS precise orbit determination, the orbit overlapping results are indicated that its orbit accuracy can be improved approximately 5 mm with the higher order ionospheric error correction, which is also in agreement with the results of Satellite Laser Ranging in this work.

Preliminary analysis of the quality and positioning performance of BDS-3 global interoperable signal B1C&B2a

BeiDou-3 Navigation Satellite System (BDS-3) satellites are equipped with the new generation GNSS signals B1C and B2a, which support the interoperability with GPS and Galileo systems. In this study, the pseudo-range multipath error and carrier phase observation noise of the BDS-3 B1C and B2a signals were evaluated based on zero baseline measurements from the day of year (DOY) 113 to 116, 2020. Further, the precision and performance of the single point positioning (SPP) and precise point positioning (PPP) are assessed at 9 stations. This assessment manifests that the standard deviations (STDs) of the pseudo-range multipath error are about 0.09 ~ 0.22 m, while STDs of the carrier phase observation noise are about 0.075 mm. For the single-frequency SPP, its positioning precision is about 2.03 ~ 4.85 m and 3.29 ~ 10.73 m at the 99.99% confidence level in horizontal and vertical directions, respectively, while the dual-frequency SPP precision is about 1.92 ~ 8.02 m and 4.81 ~ 12.77 m in horizontal and vertical directions, respectively. For the daily static PPP, the convergence time is about 20 ~ 30 min, while the daily positioning precision can reach 1.38 ~ 4.42 cm and -1.31 ~ 4.34 cm in horizontal and vertical directions, respectively. In general, the quality and the SPP and PPP performance of the BDS-3 B1C&B2a signals are comparable to the GPS and Galileo.

Robust Filtering Techniques for RTK Positioning in Harsh Propagation Environments.

Global navigation satellite systems (GNSSs) play a key role in intelligent transportation systems such as autonomous driving or unmanned systems navigation. In such applications, it is fundamental to ensure a reliable precise positioning solution able to operate in harsh propagation conditions such as urban environments and under multipath and other disturbances. Exploiting carrier phase observations allows for precise positioning solutions at the complexity cost of resolving integer phase ambiguities, a procedure that is particularly affected by non-nominal conditions. This limits the applicability of conventional filtering techniques in challenging scenarios, and new robust solutions must be accounted for. This contribution deals with real-time kinematic (RTK) positioning and the design of robust filtering solutions for the associated mixed integer- and real-valued estimation problem. Families of Kalman filter (KF) approaches based on robust statistics and variational inference are explored, such as the generalized M-based KF or the variational-based KF, aiming to mitigate the impact of outliers or non-nominal measurement behaviors. The performance assessment under harsh propagation conditions is realized using a simulated scenario and real data from a measurement campaign. The proposed robust filtering solutions are shown to offer excellent resilience against outlying observations, with the variational-based KF showcasing the overall best performance in terms of Gaussian efficiency and robustness.

Multi-frequency multi-GNSS receiver antenna calibration at IfE: Concept - calibration results - validation

Multi-frequency and multi-constellation GNSS have the potential to boost the overall performance of GNSS-based positioning, navigation and timing. This has an impact on the realisation of global reference frames, geophysical monitoring applications as well as enabling new applications. To this end, all error sources should be adequately corrected for. However, currently multi-frequency multi-GNSS receiver antenna calibration values are still missing. In this paper, the newly developed multi-frequency multi-GNSS calibration process at Institut für Erdmessung (IfE), Leibniz University Hannover, is presented. The basic concept and the assumptions for the antenna calibration are described. Resulting phase centre corrections (PCC) for GPS and Galileo for typical antennas are presented. We show that the repeatability of the estimated patterns are almost better than 2 mm in terms of maximum deviation and that the used tracking strategies by the receivers have marginal impact on the patterns, at maximum 1.2 mm for the studied receiver-antenna combinations. Furthermore, applying phase centre corrections for multi-frequency multi-GNSS carrier phase observations reduces significantly (up to 37%) the antenna related biases as validated on short baselines. Moreover, a validation in the coordinate domain shows that with IfE PCC a short baseline can be computed with high accuracy: the topocentric coordinate differences to the known baseline are in most cases smaller than 1 mm for the horizontal components and smaller than 2.2 mm in vertical.

Multi-GNSS real-time precise clock estimation considering the correction of inter-satellite code biases

For reasons mostly related to chip shape distortions, global navigation satellite system (GNSS) observations are corrupted by receiver-dependent biases. These are often stable in the long term, though numerically different depending on the signal frequency, satellite system and receiver manufacturer. Based on the mixed-differenced model combining undifferenced pseudorange with epoch-differenced carrier phase observations, we present a multi-GNSS real-time precise clock estimation model considering correction of inter-satellite code biases (ISCBs). Pre-estimated receiver-dependent ISCB corrections are introduced to correct the inter-receiver, inter-satellite and inter-system biases largely. Then the number of estimated parameters is reduced to a manageable level for real-time estimation. Comparisons with post-processed data show that compared to undifferenced, epoch-differenced and non-bias-corrected mixed-differenced models, the proposed bias-corrected model can greatly reduce the precise clock offset systematic biases, especially for GLONASS and BeiDou. The test results show the root mean square data reductions are improved by up to 96% for GLONASS, 78% for BeiDou and 40% for GPS and Galileo.