Carrier Phase Ambiguity Resolution Research Articles

An improved GNSS ambiguity best integer equivariant estimation method with Laplacian distribution for urban low-cost RTK positioning

The integer least squares (ILS) estimation is commonly used for carrier phase ambiguity resolution (AR). More recently, the best integer equivariant (BIE) estimation has also attracted an attention for complex application scenarios, which exhibits higher reliability by a weighted fusion of integer candidates. However, traditional BIE estimation with Gaussian distribution (GBIE) faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning, mainly due to the presence of outliers and unmodeled errors. To this end, an improved BIE estimation method with Laplacian distribution (LBIE) is proposed, and several key issues are discussed, including the weight function of LBIE, determination of the candidates included based on the OIA test, and derivation of the variance of LBIE solutions for reliability evaluation. The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution (TBIE), and significantly outperforms the ILS-PAR and GBIE methods. In an urban expressway test with a Huawei Mate40 smartphone, the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50% improvements compared to the ILS-PAR and GBIE methods. In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics, the positioning accuracy of LBIE in three directions is 0.112 m, 0.107 m, and 0.252 m, respectively, with improvements of 17.6%, 27.2%, and 26.1% compared to GBIE, and 23.3%, 28.2%, and 30.6% compared to ILS-PAR. Moreover, its computational time increases by 30–40% compared to ILS-PAR and is approximately half of that using TBIE.

Evaluation of C/N0 raw observation positioning by smartphone based on indoor asynchronous pseudolite

With the rapid development of the economy and information services, there is an increasing demand for indoor positioning. However, Global Navigation Satellite System (GNSS) signals face difficulties in penetrating buildings, making indoor positioning challenging. As a complementary solution to outdoor GNSS signals, pseudolites have shown promising results in various scenarios, and have become one of the research hotspots in the field of indoor positioning. Previous studies on indoor positioning with pseudolites have focused on issues such as initial position determination and carrier phase ambiguity resolution. However, most of these studies have remained in the research stage due to data post-processing and complex calculations. To overcome the limitations associated with the aforementioned factors, this paper proposes a real-time indoor positioning method that utilizes only a smartphone equipped with a built-in GNSS chip. By effectively obtaining pseudolite signal information, the smartphone establishes a simple model based on the distance and received power between the pseudolite and the smartphone. Kalman filtering is employed to mitigate the effects of multipath and occlusion. This simple and low-complexity model enables fast estimation of the user's distance from the pseudolite, thereby facilitating indoor positioning services. In this paper, the effectiveness and low complexity of the method are verified through data collection and experiments in the actual scene of the underground garage. The valuation results show that the root mean square error (RMSE) of its navigation and positioning is better than 3 m, which can meet the needs of daily life applications.

A Novel Factor Graph Framework for Tightly Coupled GNSS/INS Integration With Carrier-Phase Ambiguity Resolution

A Novel Factor Graph Framework for Tightly Coupled GNSS/INS Integration With Carrier-Phase Ambiguity Resolution

Performance Analysis of Real-Time GPS/Galileo Precise Point Positioning Integrated with Inertial Navigation System

The integration of global navigation satellite system (GNSS) precise point positioning (PPP) and inertial navigation system (INS) is widely used in navigation for its robustness and resilience, especially in case of GNSS signal blockage. With GNSS modernization, a variety of PPP models have been developed and studied, which has also led to various PPP/INS integration methods. In this study, we investigated the performance of a real-time GPS/Galileo zero-difference ionosphere-free (IF) PPP/INS integration with the application of uncombined bias products. This uncombined bias correction was independent of PPP modeling on the user side and also enabled carrier phase ambiguity resolution (AR). CNES (Centre National d'Etudes Spatiales) real-time orbit, clock, and uncombined bias products were used. Six positioning modes were evaluated, including PPP, PPP/INS loosely coupled integration (LCI), PPP/INS tightly coupled integration (TCI), and three of these with uncombined bias correction through a train positioning test in an open sky environment and two van positioning tests at a complex road and city center. All of the tests used a tactical-grade inertial measurement unit (IMU). In the train test, we found that ambiguity-float PPP had almost identical performance with LCI and TCI, which reached an accuracy of 8.5, 5.7, and 4.9 cm in the north (N), east (E) and up (U) direction, respectively. After AR, significant improvements on the east error component were achieved, which were 47%, 40%, and 38% for PPP-AR, PPP-AR/INS LCI, and PPP-AR/INS TCI, respectively. In the van tests, frequent signal interruptions due to bridges, vegetation, and city canyons make the IF AR difficult. TCI achieved the highest accuracies, which were 32, 29, and 41 cm for the N/E/U component, respectively, and also effectively eliminated the solution re-convergence in PPP.

Instantaneous Best Integer Equivariant Position Estimation Using Google Pixel 4 Smartphones for Single- and Dual-Frequency, Multi-GNSS Short-Baseline RTK.

High-precision global navigation satellite system (GNSS) positioning and navigation can be achieved with carrier-phase ambiguity resolution when the integer least squares (ILS) success rate (SR) is high. The users typically prefer the float solution under the scenario of having a low SR, and the ILS solution when the SR is high. The best integer equivariant (BIE) estimator is an alternative solution since it minimizes the mean squared errors (MSEs); hence, it will always be superior to both its float and ILS counterparts. There has been a recent development of GNSSs consisting of the Global Positioning System (GPS), Galileo, Quasi-Zenith Satellite System (QZSS), and the BeiDou Navigation Satellite System (BDS), which has made precise positioning with Android smartphones possible. Since smartphone tracking of GNSS signals is generally of poorer quality than with geodetic grade receivers and antennas, the ILS SR is typically less than one, resulting in the BIE estimator being the preferred carrier phase ambiguity resolution option. Therefore, in this contribution, we compare, for the first time, the BIE estimator to the ILS and float contenders while using GNSS data collected by Google Pixel 4 (GP4) smartphones for short-baseline real-time kinematic (RTK) positioning. It is demonstrated that the BIE estimator will always give a better RTK positioning performance than that of the ILS and float solutions while using both single- and dual-frequency smartphone GNSS observations. Lastly, with the same smartphone data, we show that BIE will always be superior to the float and ILS solutions in terms of the MSEs, regardless of whether the SR is at high, medium, or low levels.

OPTIMAL LINEAR COMBINATIONS SELECTION BASED ON FUZZY CLUSTERING ANALYSIS FOR MULTI-FREQUENCY GNSS

Abstract. Currently, satellite navigation and positioning systems, such as BDS, GPS, and Galileo, can broadcast 3 or more navigation signals. In theory, multi-frequency signals can form more high-quality carrier-phase linear combinations, which is conducive to improving the performance of multi-frequency carrier ambiguity resolution (MCAR). In this paper, focusing on the selection of the optimal combinations in the multi-frequency GNSS carrier phase ambiguity resolution, according to the long wavelength of the combinations, the influence of weak ionospheric delay, and low noise, the fuzzy clustering analysis method is used to realize objective selection of multi-frequency optimal linear combinations (e.g., GPS, BDS-2, BDS-3, Galileo) and introduced the total noise level (TNL) for the analysis of the combinations characteristics under different baseline length scenarios. In order to verify the ambiguity resolution performance of the extra-wide lane combinations selected by the fuzzy clustering analysis method, the GF_MCAR model was used to solve the BDS-2, BDS-3 triple-frequency combination ambiguities and the BDS-3 five-frequency combination ambiguities of the baseline JNFG and WUH2. The results manifest that the number of high-quality linear combinations of multi-frequency GNSS increases sharply with the increase of the frequencies number, which is conducive to the formation of combinations with a lower total noise level, and the experiments show that the difference between adjacent epochs of the combination ambiguities of the extra-wide lane obtained by GF_MCAR is basically less than ±0.5 cycles, and the single epoch rounding can be used to directly fix the ambiguity of the extra-wide lane.

Performance Analysis of Zero-Difference GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 Point Positioning Using CNES Uncombined Bias Products

The modernization of Global Navigation Satellite System (GNSS) including the transmission of signals on multiple frequencies has greatly promoted the development of the popular PPP (Precise Point Positioning) technique. A key issue of multi-frequency PPP is the handling of the observable-specific signal biases in order to allow for carrier-phase ambiguity resolution (AR). As a result, PPP modeling at a user side in the multi-frequency case varies depending on the definition of the applied phase bias products. In this study, we investigate the positioning performance of GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 undifferenced ionosphere-float model in the conventional PPP mode and the single-epoch mode using the uncombined code and phase bias products generated at the French CNES (Centre National D’Etudes Spatiales). A series of widelane ambiguities are configured in our multi-frequency PPP functional model instead of forming the classical Melbourne–Wübbena (MW) combination. The best integer equivariant (BIE) estimator is used for the ambiguity resolution in a conventional cascading scheme according to the wavelength of the combined ambiguities for each constellation. Real data collected at IGS stations with a 30-s sampling interval is applied to evaluate the above models. For the conventional kinematic PPP configuration, a significant accuracy improvement of 63% on the east component of the fixed solution is obtained with respect to the ambiguity-float solution. The PPP convergence is accelerated by 17% after the AR. Regarding the single-epoch positioning, an accuracy of 32 and 31 cm for north and east components can be achieved, respectively, (68th percentile) with the instantaneous widelane-ambiguity resolution, which is improved by 13% and 16% compared to multi-frequency code-based or float solution.

Reduced-Dynamic Precise Orbit Determination of Haiyang-2B Altimetry Satellite Using a Refined Empirical Acceleration Model

The Haiyang 2B (HY-2B) satellite requires precise orbit determination (POD) products for geodetic remote sensing techniques. An improved set of reduced-dynamic (RD) orbit solutions was generated from the onboard Global Positioning System (GPS) measurements over a 14-month period using refined strategies and processing techniques. The key POD strategies include a refined empirical acceleration model, in-flight calibration of the GPS antenna, and the resolution of single-receiver carrier-phase ambiguities. In this study, the potential periodicity of empirical acceleration in the HY-2B POD was identified by spectral analysis. In the along-track direction, a noticeable signal with four cycles per revolution (CPR) was significant. A mixed spectrum was observed for the cross-track direction. To better understand the real in-flight environment, a refined empirical acceleration model was used to cope with the time variability of empirical accelerations in HY-2B POD. Three POD strategies were used for the reprocessing for superior orbit quality. Validation using over one year of satellite laser ranging (SLR) measurements demonstrated a 5.2% improvement in the orbit solution of the refined model. Reliable correction for the GPS antenna phase center was obtained from an over-420-day dataset, and a trend in radial offset change was observed. After application of the in-flight calibration of the GPS antenna, a 26% reduction in the RMS SLR residuals was achieved for the RD orbit solution, and the carrier phase residuals were clearly reduced. The integer ambiguity resolution of HY-2B led to strong geometric constraints for the estimated parameters, and a 15% improvement in the SLR residuals could be inferred compared with the float solution.

Empirical Stochastic Model of Multi-GNSS Measurements.

The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

Baseline length constraint approaches for enhancing GNSS ambiguity resolution: comparative study

Reliable and correct carrier phase ambiguity resolution is the key to global navigation satellite system (GNSS) high-precision navigation and positioning applications. For kinematic situations, such as moving-baseline-based positioning and attitude determination, the baseline length between two antennas is constant; such a priori information could contribute to integer ambiguity resolution, especially when only a few satellites are viewed. In this research, three different approaches using baseline information—the linearized joint adjustment method, validation method, and constrained LAMBDA (CLAMBDA) method—are comprehensively evaluated through theoretical and experimental analyses. The performance of each method is assessed in terms of the ambiguity success rate and baseline solution accuracy with static and kinematic GPS/BDS datasets. The additional baseline length constraint improves the precision of the float solution and the ambiguity fixed success rate (compared to the standard LAMBDA method), but there are differences in the performance of the three methods. Specifically, the performance of the linearized joint adjustment method primarily depends on baseline length and improves as the baseline length increases; however, caution should be exercised for short baselines. The validation method and CLAMBDA method both consider the quadratic form of ambiguity residuals and baseline length constraint for selecting the ambiguity solution. However, the validation method directly judges the ambiguity to obtain a locally optimal solution, whereas the CLAMBDA method constructs a rigorous mathematical formula to obtain a globally optimal solution. Moreover, because the linearized joint adjustment method and CLAMBDA method primarily contribute to the float and fixed solution, respectively, we fused the two methods to improve the ambiguity resolution success rate. The results confirm that the combined algorithm achieves better performance that exceeds that of either individual method for a baseline length of tens of meters.

Kinematic ME-MAFA for Pseudolite Carrier-Phase Ambiguity Resolution in Precise Single-Point Positioning.

Precise single-point positioning using carrier-phase measurements can be provided by the synchronized pseudolite system. The primary task of carrier phase positioning is ambiguity resolution (AR) with rapidity and reliability. As the pseudolite system is usually operated in the dense multipath environment, cycle slips may lead the conventional least-squares ambiguity decorrelation adjustment (LAMBDA) method to incorrect AR. A new AR method based on the idea of the modified ambiguity function approach (MAFA), which is insensitive to the cycle slips, is studied in this paper. To improve the model strength of the MAFA and to eliminate the influence of constant multipath biases on the time-average model in static mode, the kinematic multi-epoch MAFA (kinematic ME-MAFA) algorithm is proposed. A heuristic method for predicting the ‘float position’ corresponding to every Voronoi cell of the next epoch, making use of Doppler-based velocity information, is implemented to improve the computational efficiency. If the success rate is very close to 1, it is possible to guarantee reliable centimeter-level accuracy positioning without further ambiguity validation. Therefore, a computing method of the success rate for the kinematic ME-MAFA is proposed. Both the numerical simulations and the kinematic experiment demonstrate the feasibility of the new AR algorithm according to its accuracy and reliability. The accuracy of the horizontal positioning solution is better than 1.7 centimeters in our pseudolite system.

Dynamic GPS-based LEO orbit determination with 1 cm precision using the Bernese GNSS Software

The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20% improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

Best integer equivariant estimation for elliptically contoured distributions

This contribution extends the theory of integer equivariant estimation (Teunissen in J Geodesy 77:402–410, 2003) by developing the principle of best integer equivariant (BIE) estimation for the class of elliptically contoured distributions. The presented theory provides new minimum mean squared error solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Next to the BIE estimator for the multivariate normal distribution, special attention is given to the BIE estimators for the contaminated normal and the multivariate t-distribution, both of which have heavier tails than the normal. Their computational formulae are presented and discussed in relation to that of the normal distribution.

The ADOP and PDOP: Two Complementary Diagnostics for GNSS Positioning

Ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP) are two popular scalar-diagnostics used in Global Navigation Satellite System (GNSS) positioning. Where the ADOP is a predictor for carrier-phase ambiguity resolution performance, the PDOP is meant to predict the receiver-satellite geometry’s capability for precise positioning. We will show, however, that although the PDOP works well for code-based positioning, one has to exercise great care in using the PDOP for real-time kinematic (RTK) positioning. We show that the ADOP and PDOP have distinct behaviors, an important consequence of which is that one can have time periods with small PDOPs, and thus seemingly good geometry for precise positioning, but at the same time large ADOPs, thus showing that successful ambiguity resolution and therefore precise positioning will not be possible. Also, the reverse situation may occur, i.e., having large PDOPs with small ADOPs. In such a situation, the large PDOPs should not automatically lead to the conclusion of poor position performance, because the large gain that ambiguity resolution brings will often still make precise positioning possible. We will analyze and explain this complementary behavior of the PDOP and ADOP and demonstrate this both analytically and empirically. For this analysis we use real Global Positioning System (GPS) single- and multifrequency signals and GPS/Quasi-Zenith Satellite System (QZSS), GPS/Navigation with Indian Constellation (NAVIC) L5 signals of two baselines located in Perth, Australia.

A Triple Checked Partial Ambiguity Resolution for GPS/BDS RTK Positioning.

Reliable and accurate carrier phase ambiguity resolution is the key to high-precision Global Navigation Satellite System (GNSS) positioning and application. With the fast development of modern GNSS, the increased number of satellites and ambiguities makes it hard to fix all ambiguities completely and correctly. The partial ambiguity fixing technique, which selects a suitable subset of high-dimensional ambiguities to fix, is beneficial for improving the fixed success rate and reliability of ambiguity resolution. In this contribution, the bootstrapping success rate, bounded fixed-failure ratio test, and the new defined baseline precision defect are used for the selection of the ambiguity subset. Then a model and data dual-driven partial ambiguity resolution method is proposed with the above three checks imposed on it, which is named the Triple Checked Partial Ambiguity Resolution (TC-PAR). The comprehensive performance of TC-PAR compared to the full-fixed LAMBDA method is also analyzed based on several criteria including the fixed rate, the fixed success rate and correct fixed rate of ambiguity as well as the precision defect and RMS of the baseline solution. The results show that TC-PAR could significantly improve the fixed success rate of ambiguity, and it has a comparable baseline precision to the LAMBDA method, both of which are at centimeter level after ambiguities are fixed.

Real-time clock comparison and monitoring with multi-GNSS precise point positioning: GPS, GLONASS and Galileo

The precise point positioning (PPP) technique is widely used in time and frequency applications. Because of the real-time service (RTS) project of the International GNSS Service, we can use the PPP technique for real-time clock comparison and monitoring. As a participant in the RTS, the Centre National d’Etudes Spatiales (CNES) implements the PPPWIZARD (Precise Point Positioning with Integer and Zero-difference Ambiguity Resolution Demonstrator) project to validate carrier phase ambiguity resolution. Unlike the Integer-PPP (IPPP) of the CNES, fixing ambiguities in the post-processing mode, the PPPWIZARD operates in the real-time mode, which is also called real-time IPPP (RT-IPPP). This paper focuses on applying the RT-IPPP for real-time clock comparison and monitoring. We review the principle of real-time clock comparison and monitoring, and introduce the methodology of the RT-IPPP technique. The observations of GPS, GLONASS and Galileo were processed for the experiments. Five processing modes were provided in the experiment to analyze the benefits of ambiguity resolution and multi-GNSS. In the clock comparison experiment, the average reduction ratios of standard deviations with respect to the G PPP mode range from 9.7% to 35.0%. In the clock monitoring experiment, G PPP mode can detect clock jumps whose magnitudes are larger than 0.9 ns. The RT-IPPP technique with GRE PPP AR (G) mode allows for the detection of any clock jumps larger than 0.6 ns. For frequency monitoring, G PPP mode allows detection of frequency changes larger than 1.1 × 10−14. When the RT-IPPP technique is applied, monitoring with GRE PPP AR (G) mode can detect frequency changes larger than 6.1 × 10−15.

BDS Triple-frequency Medium and Long Baseline Ambiguity Resolution by Taking into Account of The Innospheric Delay Residuals

In order to solve the shortcomings of the classic geometry-free TCAR algorithm in the process of the medium-long baseline ambiguity resolution, this paper puts forward the expression of the combined ambiguity standard deviation by considering the ionospheric delay residuals, tropospheric delay residuals, satellite orbital residuals and observation noise. It also comes up with the total noise level(TNL) of many optimal extra-wide lane(EWL), wide lane(WL) and narrow lane(NL) combinations based on the existing empirical value of each residual item under the condition of 100km, 100-200km and greater than 200km baseline length. Moreover, it proves that ionospheric delay residuals are the most dominant error source in the medium-long baseline carrier phase ambiguity resolution by analyzing the correlation between the total noise level(TNL) of each combination and its corresponding ionospheric delay residuals. Finally, it presents an ionospheric delay correction algorithm and then carries out experimental verification and feasibility analysis of the algorithm based on the beidou triple-frequency measured data. Results show that the fluctuation range of the NL float ambiguity can be reduced from 10 cycle to less than 1 cycle.

A MEMS-IMU Assisted BDS Triple-Frequency Ambiguity Resolution Method in Complex Environments

Emerging technologies such as smart cities and unmanned vehicles all need Global Navigation Satellite Systems (GNSS) to provide high-precision positioning and navigation services. Fast and reliable carrier phase ambiguity resolution (AR) is a prerequisite for high-precision positioning. The poor satellite geometry and severe multipath effect caused by Beidou Navigation Satellite System (BDS) signal occlusion and reflection in complex environments will degrade the AR performance. In this contribution, a fast triple-frequency AR method combining Microelectromechanical System-Inertial Measurement Unit (MEMS-IMU) and BDS is proposed. First, the Extra-Wide Lane (EWL) ambiguity is fixed with the positioning parameters of MEMS-IMU instead of the pseudorange. Then, the phase noise variance of Narrow Lane (NL) observation is obtained from ambiguity-fixed EWL observation to reduce the total noise level of NL observation, and the NL ambiguity can be reliably fixed, and the BDS positioning result is obtained. Finally, the BDS positioning result is used as the posterior measurement of the extended Kalman filter to update the MEMS-IMU positioning parameters to form the coupling loop of MEMS-IMU and BDS. The data of urban road vehicle experiments were collected to verify the feasibility and effectiveness of the proposed algorithm. Results show that MEMS-IMU can speed up AR, and reduction of total noise level can significantly improve the reliability of AR.

Network-based triple-frequency carrier phase ambiguity resolution between reference stations using BDS data for long baselines

Network-based ambiguity resolution (AR) between reference stations is the prerequisite to realize a precise real-time kinematic positioning service. With the help of BDS triple-frequency signals, we can efficiently deal with the ionospheric delay and tropospheric delay, and achieve rapid and reliable AR. To overcome the inaccurate ionospheric delay estimated by the geometry-free three carrier ambiguity resolution (GF TCAR) technique, which leads to failure in the original ambiguity resolution, we propose an ionospheric-free (IF) TCAR method to resolve the ambiguity between the reference stations over long baselines. Taking full advantage of the known positions of the reference stations, the easily resolved extra-wide-lane (EWL) ambiguity, and the IF phase combinations, we can reliably fix the wide-lane (WL) ambiguity. A Kalman filter is applied to estimate precise IF ambiguities and the original ambiguity is resolved with the fixed WL ambiguity. A numerical analysis with triple-frequency BDS data from three long baselines of a CORS network is provided to compare the AR performance of GF TCAR with that of IF TCAR. The results show that both methods can reliably resolve the WL ambiguity with a remarkable correctly-fixed rate of higher than 99%, and the reliably-fixed rates of the IF TCAR slightly increase from 92.19, 94.67 and 94.61–98.26, 99.54 and 97.51% for the three baselines. Herein “correctly-fixed” and “reliably-fixed” mean the difference between the float ambiguity and the true one are less than ± 0.5 and ± 0.25 cycles, respectively. On the other hand, the AR performance of the original signals with the IF TCAR method is much better than that with the GF TCAR method attaining a 100% correctly-fixed rate, while the GF TCAR method can hardly fix the original ambiguity with the largest bias being as much as 4 cycles because of the amplified systematic bias.

Low‐cost positioning with rotating antenna in constrained environment for global navigation satellite systems

In high-precision relative positioning applications of global navigation satellite systems, multipath and phase centre offset/variation remain as the major coupled error sources, as they cannot be eliminated by the differential operation. A circular rotating low-cost antenna is introduced for the rover station in a constrained environment. The spatial diversity of multipath is explored by circular motion to aid the carrier-phase ambiguity resolution and error elimination. The multipath and phase centre offset are separated and estimated. Field tests demonstrate that the proposed method with low-cost antenna is able to achieve the survey-grade precision.