Extra-wide-lane Research Articles

Fast and Reliable Network RTK Positioning Based on Multi-Frequency Sequential Ambiguity Resolution under Significant Atmospheric Biases

The positioning performance of the Global Navigation Satellite System (GNSS) network real-time kinematic (NRTK) depends on regional atmospheric error modeling. Under normal atmospheric conditions, NRTK positioning provides high accuracy and rapid initialization. However, fluctuations in atmospheric conditions can lead to poor atmospheric error modeling, resulting in significant atmospheric biases that affect the positioning accuracy, initialization speed, and reliability of NRTK positioning. Consequently, this decreases the efficiency of NRTK operations. In response to these challenges, this paper proposes a fast and reliable NRTK positioning method based on sequential ambiguity resolution (SAR) of multi-frequency combined observations. This method processes observations from extra-wide-lane (EWL), wide-lane (WL), and narrow-lane (NL) measurements; performs sequential AR using the LAMBDA algorithm; and subsequently constrains other parameters using fixed ambiguities. Ultimately, this method achieves high precision, rapid initialization, and reliable positioning. Experimental analysis was conducted using Continuous Operating Reference Station (CORS) data, with baseline lengths ranging from 88 km to 110 km. The results showed that the proposed algorithm offers positioning accuracy comparable to conventional algorithms in conventional NRTK positioning and has higher fixed rate and positioning accuracy in single-epoch positioning. On two datasets, the proposed algorithm demonstrated over 30% improvement in time to first fix (TTFF) compared to conventional algorithms. It provides higher precision in suboptimal positioning solutions when conventional NRTK algorithms fail to achieve fixed solutions during the initialization phase. These experiments highlight the advantages of the proposed algorithm in terms of initialization speed and positioning reliability.

A hierarchical combination algorithm for real-time cycle slip detection and repair in low satellite elevation and high ionospheric activity conditions

To enhance the accuracy and robustness of cycle slip detection and repair for triple-frequency data while minimizing the adverse effects of low satellite elevation and high ionospheric activity, a hierarchical combination algorithm for real-time cycle slip detection and repair is proposed. This algorithm begins by prioritizing the reduction of noise and ionospheric delay coefficients. It determines the optimal coefficients for the combination of observations from the BeiDou Navigation Satellite System’s (BDS) Extra-Wide Lane (EWL), Wide Lane (WL), and Narrow Lane (NL). Leveraging the longer wavelength characteristics of the EWL combination, it simultaneously conducts cycle slip detection on the EWL combination alongside the pseudorange combination. Following this, based on the detection outcomes from the EWL combination, cycle slip detection is carried out on the WL combination. Finally, using the detection findings from the WL combination, cycle slip detection is executed on the NL combination. Given the NL combination’s shorter wavelength and higher susceptibility to ionospheric delay, a dynamic ionospheric prediction model is applied to the NL combination to further mitigate the impact of ionospheric disturbances. After completing the cycle slip detection process, the results from the EWL, WL, and NL combinations are integrated and solved. Experimental results clearly demonstrate that, even in scenarios characterized by low satellite elevation and active ionospheric conditions, this algorithm consistently delivers outstanding detection performance for cycle slip instances, particularly for small cycle slip (less then two cycles). Remarkably, this performance is achieved without the need for intricate searches during cycle slip repair.

BDS-3/Galileo multi-frequency phase-only model for long baseline with best integer equivariant estimation

Currently, long baselines generally adopt phase-code models that include both phase and pseudorange observations, such as dual-frequency ionosphere-free (PC-DFIF) and multi-frequency uncombined (PC-MFUC) models. The more significant unmodeled errors in pseudorange are likely to reduce ambiguity resolution (AR) performance, and the phase-only model with only phase observations involved is expected to avoid this problem. In view of the fact that existing phase-only research is mainly focuses on GPS/BDS-2 triple-frequency signals, a BDS-3/Galileo multi-frequency phase-only (MFPO) model is proposed in this paper. Four linearly independent extra-wide-lane (EWL) phase ranges (i.e. IR1, IR2, EWL3 and EWL4) are determined stepwise with a sliding window, among which the first two belong to ionosphere-reduced (IR) combination. In the determination of EWL3/EWL4, in addition to theoretical precision, the amplified phase multipath is also considered. The aforementioned four EWL phase ranges are then equivalently transformed to wide-lane (WL) combinations with smaller coefficients, and further incorporated with narrow-lane (NL) equation to construct MFPO model. Meanwhile, the best integer equivariant (BIE) is introduced to improve AR performance. The MFPO model is evaluated with real-tracked long baseline data. The performance of EWL phase ranges can be significantly improved after phase multipath is considered. The float solution, fixed solution and BIE solution of MFPO model all achieve centimeter-level accuracy. However, during convergence stage, incorrect fixing might exist in fixed solution, while BIE solution can improve this situation. The MFPO model is further compared with commonly used PC-DFIF and PC-MFUC models. The accuracy of the three models after convergence is basically the same, while the MFPO model has higher accuracy during convergence stage.

Analysis of Multifrequency GNSS Signals and an Improved Single-Epoch RTK Method for Medium-Long Baseline

In recent years, the quantity of visible satellites has increased significantly due to multiple satellite systems that leaped forward. The BeiDou Navigation Satellite System (BDS) and Galileo satellite navigation system (Galileo) broadcast triple-frequency signals and above to users, thus enhancing the reliability, continuity, and availability of the single-epoch real-time kinematic (RTK) positioning. In this study, an improved single-epoch multifrequency multisystem RTK method is successfully developed for the medium-long baseline. First, the Galileo and BDS extra-wide-lane (EWL) ambiguities are fixed at a high success rate, and the Galileo and BDS wide-lane (WL) ambiguity is achieved via the transformation process. Second, the fixed WL ambiguities of Galileo and BDS are exploited to elevate the fixed rate of GPS WL ambiguity. Third, the parametric strategies for ionospheric delay are carried out to upregulate the narrow-lane (NL) ambiguity-fixed rate of GPS. Further, the real-time data are adopted for verifying the feasibility of the method developed in this study. The experimental results demonstrate the optimal carrier-to-noise density ratio (C/N0) of full operational capability (FOC) E5a/E5b at all frequencies, followed by IIR-M L1, and IIR-A/B L2 exhibits the worst performance. Generally, the multipath combination (MPC) of Galileo signals shows root mean square (RMS) values within 0.4 m, ordered as follows: E 1 > E 5 b > E 5 a . For the BDS-2, the B3 signal exhibits optimal performance, while the B1 signal is the worst. The RMS of MPC errors of L1 signals is smaller than the L2 signals for the GPS. Furthermore, under the 50 km baseline, the GPS NL ambiguity-fixed rate using the ionosphere-free (IF) combination reaches only 47.74% at the ratio threshold of 2. Finally, compared to the ionosphere-free combination method, the GPS NL ambiguity-fixed rate is increased by 45.52% with the presented method. The proposed approach broadens the future application of deformation monitoring in medium-long baseline scenarios.

Research on single-epoch ambiguity resolution method based on BDS-3 ionosphere-reduced combinations

In conventional ambiguity resolution method for single-epoch, narrow-lane (NL) observations are often inaccurately fixed due to improper treatment of error sources such as ionospheric and tropospheric delays. Therefore, based on the multi-frequency observation data of the BeiDou Global Navigation Satellite System (BDS-3), this paper adopts a single-epoch resolution method based on the ionosphere-reduced combinations. Firstly, select the appropriate combination observations of extra wide-lane (EWL) and wide-lane (WL) and get its fixed ambiguity. Then the ambiguity of the WL combination with high observation accuracy is obtained by linear combination, which goes to constrain the fixation of NL ambiguity. Secondly, different from the conventional method, the ionosphere-reduced combinations observations were selected as NL, thus significantly weakening the influence of first-order ionospheric delay error on the fixation of narrow-lane ambiguity. The experimental results show that compared with the conventional methods, the method adopted in this paper can significantly improve the fixing success rate of the wide-lane ambiguity. In the NL ambiguity resolution part, using the ionosphere-reduced combinations as NL for solving improved the average fixing success rate from 68.6%/44.4%/35.7%/27.6% to 97.4%/95.4%/95.6%/87.3% compared to the conventional method of using the base frequency as NL for solving. Furthermore, the N/E/U positioning accuracy improved by an average of 63.05%/64.37%/52.27%. To sum up, this method effectively improves the success rate of NL ambiguity fixing and positioning accuracy.

Single-Epoch Decimeter-Level Precise Point Positioning with a Galileo Five-Frequency Ionosphere-Reduced Combination

Currently, there are two main methods for single-epoch decimeter-level precise point positioning (PPP); one is a model based on ambiguity-fixed ionosphere-free (AFIF) observations, and the other is based on uncombined (UC) PPP. The implementation of these two models requires both extra-wide-lane (EWL) and wide-lane (WL) ambiguity fixing. Different from the existing methods, this paper proposes a multi-frequency ionosphere-reduced (IR) PPP model suitable for single-epoch decimeter-level positioning. Based on Galileo five-frequency data, the optimal selection strategy of IR combinations is first studied with ionosphere, noise level and wavelength factors considered. Then, based on the selected IR combination, two IR PPP models, namely IR(EST) and IR(IGN), are established according to whether ionosphere parameters are estimated or ignored. Finally, the proposed models are verified with real tracked data from globally distributed stations, and further compared with the existing AFIF/UC models in terms of positioning performance and time consumption. The relationship between the ionosphere equivalent ranging error and satellite elevation in the IR models is analyzed. The lower the elevation is, the larger the residual ranging error is, and its impact on positioning is weakened by downweighting its observations and adjusting the cut-off elevation during the partial ambiguity fixing (PAF) process. The results show that the performance of the two IR models is basically the same, and both can achieve horizontal and vertical accuracies better than 20 cm and 40 cm, respectively. Compared with the existing AFIF/UC models, the proposed IR models can achieve similar decimeter-level accuracy with only one step of EWL ambiguity fixing, and at the same time, the IR models have varying degrees of improvement in time consumption: 38% shorter than the AFIF model and 97% shorter than the UC model.

Continuous Decimeter-Level Positioning in Urban Environments Using Multi-Frequency GPS/BDS/Galileo PPP/INS Tightly Coupled Integration

Time- and precision-critical applications, such as autonomous driving, have extremely rigorous standards for continuous high-precision positioning. The importance of precise point positioning (PPP) technology for self-navigation equipment is self-evident by delivering decimeter-/centimeter-level absolute position accuracy in a global coordinate framework. Nevertheless, the prolonged initialization period renders PPP almost too difficult to be widely used for time-critical applications in real transportation scenarios, for example, in city canyons and overpasses. We proposed a method to accomplish continuous decimeter-level positioning by leveraging triple-frequency GNSS observations with an Inertial Navigation System (INS) aiding in urban environments. In the proposed method, the inertial measurements and the original tri-frequency pseudorange and carrier phase measurements are tightly fused in an extended Kalman filter to obtain the optimal state estimate. Afterwards, with precise extra-wide-lane (EWL) and wide-lane (WL) Uncalibrated Phase Delay (UPD) products, the EWL and WL ambiguities can be resolved sequentially to implement instantaneous decimeter-level positioning. Exploiting the short-term high-precision characteristic of the INS, the continuity of the PPP solution can be ameliorated noticeably, and the ability of decimeter-level positioning can be maintained effortlessly throughout the navigation process. With land vehicle data collected, several experiments are undertaken to comprehensively assess the capability of the proposed system in urban scenarios, taking the solution obtained by a commercial post-processing software as the reference. The single-epoch decimeter-level position estimation can be captured instantaneously for WL ambiguity-fixed PPP solutions. Furthermore, for WL ambiguity-fixed PPP/INS-integrated solutions, the position estimation is better than 0.2 m for horizontal components and improved by 40–90% compared with that of the WL ambiguity-fixed PPP solutions. More importantly, the availability rate of positioning accuracy is better than 0.3 m in the horizontal direction and 0.5 m in the up direction reaching 93.91%, whereas it is only 53.78% for WL ambiguity-fixed PPP solutions. Overall, the WL ambiguity-fixed PPP/INS-integrated solutions have the favorable performance to maintain continuous decimeter-level positioning for self-navigation equipment, even if full GNSS outages are encountered.

Assessment of Galileo FOC + IOV Signals and Geometry-Based Single-Epoch Resolution of Quad-Frequency Carrier Ambiguities

Galileo can independently provide navigation and positioning services globally. Galileo satellites transmit quad-frequency E1, E5a, E5b, and E5 signals, which can benefit the integer ambiguity rapid resolution. Firstly, the qualities of Galileo signals from Carrier-to-Noise (C/N0), Multipath Combination (MPC), and pseudo-range and phase noise using the ultra-short baseline were evaluated. The experimental results indicated that the Galileo E5 signal has the highest C/N0, while the C/N0 of other signals is lower and almost equal. In terms of MPC, the Galileo E1 was the most severe followed by E5a and E5b, and the MPC of E5 is less severe. As for the precision of un-differenced observations, the carrier phase and pseudo-range observations of Galileo E5 had higher accuracy than those of Galileo E5a, E5b, and E1. Secondly, the quad-frequency observations allowed for various linear combinations of different frequencies, which provides some feasibility for improving the performance of ambiguity resolution. Assuming that the phase noise σ∇ΔΦ = 0.01 m and the first-order ionosphere σ∇ΔI1 = 1 m, the total noise of the Extra-Wide-Lane (EWL) combination observation ((0, 0, 1, −1) and (0, −1, 1, 0)) and Very-Wide-Lane (VWL) combination observation ((0, −2, 1, 1), (0, −3, 2, 1)) are still less than 0.5 cycles. Finally, a geometry-based quad-frequency carrier ambiguities (GB-QCAR) method was developed, and all different options of linear combinations were investigated systematically from the ambiguity-fixed rate with two baselines. Experimental results demonstrated that, the ambiguity fixed rate of combination observation (0, −1, 1, 0), (0, −3, 5, −2), (1, −1, 0, 0) and (0, 0, 0, 1) is the highest and the positioning accuracy of VWL combination observation (0, −3, 5, −2) is equivalent to that of the EWL combination observation (0, −1, 1, 0). The positioning accuracies of WL combination observation (1, −1, 0, 0) are preferable to 3 cm and 10 cm in the horizontal and vertical, respectively. The positioning accuracy of NL combination observation E5 in the horizontal direction is about 1 cm, and is better than 4 cm in the vertical direction. Therefore, we can use Galileo observations to realize high-precise navigation services utilizing the proposed GB-QCAR method.

Toward BDS/Galileo/GPS/QZSS triple-frequency PPP instantaneous integer ambiguity resolutions without atmosphere corrections

Multi-frequency precise point positioning (PPP) has drawn attention along with the modernization of the Global Navigation Satellite Systems. There are now nearly 90 satellites providing multi-frequency signals. This contribution aims to achieve fast convergence of a few seconds for BDS/Galileo/GPS/QZSS integrated triple-frequency PPP with integer ambiguity resolution (IAR) without atmosphere corrections. A unified model of an uncombined and undifferenced manner for PPP-IAR with dual- and triple-frequency observations is presented. The uncalibrated phase delays (UPD) of extra wide-lane (EWL), wide-lane (WL), and N1 ambiguities for triple-frequency PPP are estimated with standard deviations of 0.02, 0.05, and 0.10 cycles achieved, respectively. The PPP-IAR validation based on 20 stations evenly distributed in China is conducted using UPD products generated from a regional network covering a large part of China. The EWL, WL, and N1 ambiguities are sequentially fixed utilizing the least-squares ambiguity decorrelation adjustment (LAMBDA) technique. In terms of convergence time, PPP instantaneous IAR is achievable without using atmosphere corrections, thanks to the contribution of the multi-frequency and multi-constellation observations. This has been proved by performing PPP-IAR restart every 10-min over 2520 times in our case study. For PPP-IAR solutions produced with BDS/Galileo/GPS/QZSS triple-frequency observations with an interval of 1 s, the convergence is fulfilled within 1 s for the horizontal components with an accuracy of better than 5 cm, while 2 s for the vertical component with better than 10 cm accuracy, and both are at 95% confidence level.

Single-Epoch Ambiguity Resolution of a Large-Scale CORS Network with Multi-Frequency and Multi-Constellation GNSS

Ambiguity resolution at Continuously Operating Reference Station (CORS) network sites is the key step in the whole processing chain of Network Real Time Kinematic (NRTK). An appropriate ambiguity-resolution speed is important, and single-epoch ambiguity resolution has not been realized yet, especially for large-scale CORS. We attempt to realize single-epoch ambiguity resolution for a large-scale CORS network by neglecting tropospheric delay through forming difference between satellites with close mapping functions whether they belong to the same or different GNSSs. As only two frequency bands are shared among GPS, Galileo and BeiDou, the biggest challenge is how to get this single-epoch ambiguity solution for wide-lane combinations of L1 and L5 when the difference is formed between satellites of different GNSSs. The proposed method includes five steps for ambiguity resolution for different combinations: extra wide-lane, wide-lane, inter-GNSS wide-lane, subset narrow-lane and narrow-lane. The single-epoch ambiguity-resolution performance is assessed based on GNSS observations from two long-distance baselines formed with IGS stations, BRUX-REDU and BAUT-LEIJ, separated by distances of approximately 104 km and 151 km, respectively. The numerical results show that the fixing rate of the single-epoch ambiguity resolution can reach more than 90%, so for a large-scale CORS network, single-epoch ambiguity resolution is feasible and can be realized in the future.

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.

Principle and performance of multi-frequency and multi-GNSS PPP-RTK

PPP-RTK which takes full advantages of both Real-Time Kinematic (RTK) and Precise Point Positioning (PPP), is able to provide centimeter-level positioning accuracy with rapid integer Ambiguity Resolution (AR). In recent years, with the development of BeiDou Navigation Satellite System (BDS) and Galileo navigation satellite system (Galileo) as well as the modernization of Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS), more than 140 Global Navigation Satellite System (GNSS) satellites are available. Particularly, the new-generation GNSS satellites are capable of transmitting signals on three or more frequencies. Multi-GNSS and multi-frequency observations become available and can be used to enhance the performance of PPP-RTK. In this contribution, we develop a multi-GNSS and multi-frequency PPP-RTK model, which uses all the available GNSS observations, and comprehensively evaluate its performance in urban environments from the perspectives of positioning accuracy, convergence and fixing percentage. In this method, the precise atmospheric corrections are derived from the multi-frequency and multi-GNSS observations of a regional network, and then disseminated to users to achieve PPP rapid AR. Furthermore, a cascade ambiguity fixing strategy using Extra‐Wide‐Lane (EWL), Wide-Lane (WL) and L1 ambiguities is employed to improve the performance of ambiguity fixing in the urban environments. Vehicle experiments in different scenarios such as suburbs, overpasses, and tunnels are conducted to validate the proposed method. In suburbs, an accuracy of within 2 cm in the horizontal direction and 4 cm in the vertical direction, with the fixing percentage of 93.7% can be achieved. Compared to the GPS-only solution, the positioning accuracy is improved by 87.6%. In urban environments where signals are interrupted frequently, a fast ambiguity re-fixing can be achieved within 5 s. Moreover, multi-frequency GNSS signals can further improve the positioning performance of PPP-RTK, particularly in the case of small amount of observations. These results demonstrate that the multi-frequency and multi-GNSS PPP-RTK is a promising tool for supporting precise vehicle navigation.

Multi-GNSS Fast Precise Point Positioning with Multi-Frequency Uncombined Model and Cascading Ambiguity Resolution

Conventional ambiguity resolution (AR) strategy of directly fixing all raw frequency ambiguities for uncombined precise point positioning (PPP) generally requires a long initial time to ensure fixing reliability. The rich signals from multi-frequency GNSS can provide new opportunities for rapid PPP AR. In this paper, based on a unified multi-frequency uncombined PPP model, the raw frequency ambiguities are linearly transformed to the between-satellite-single-differenced extra-wide-lane (EWL), wide-lane (WL), and narrow-lane (NL) ambiguities, and a cascading ambiguity resolution (CAR) method of fixing EWL/WL/NL ambiguities sequentially is proposed. Meanwhile, a partial ambiguity fixing (PAF) strategy with ambiguity subset adaptively selected based on the successively increased elevations is also adopted in each step to improve the fixing rate. Further, experiments with globally distributed stations are carried out to verify the algorithm. With the constraints of EWL/WL AR, the precision of NL ambiguity and its variance-covariance matrix can be effectively optimized, so the time to first fix (TTFF) is significantly shortened, and the ratio value is also improved to varying degrees. As for BDS-only solution, the average TTFF is shortened from 23.7 min to 10.9 min, with an improvement over 50%; for GPS/BDS, GPS/Galileo, and GPS/Galileo/BDS combined solutions, the TTFF is shortened from 14.3 min, 9.4 min, and 6.7 min to 8.1 min, 2.6 min, and 1.8 min, which are, respectively, shortened by 43.4%, 72.3%, and 73.1%. In general, the proposed CAR strategy can shorten the TTFF of multi-GNSS multi-frequency PPP to about 2 min. The performance of EWL/WL/NL ambiguity-fixed solutions is also analyzed. The NL solution is generally at centimeter-level accuracy over the entire period; however, limited by the atmosphere errors during the convergence stage, the EWL/WL solutions can only obtain decimeter-level accuracy, and the difference between them and NL solution gradually decreases with the continuous improvement of atmosphere accuracy.

Performance of Single-Epoch EWL/WL/NL Ambiguity-Fixed Precise Point Positioning with Regional Atmosphere Modelling

Precise point positioning (PPP) with ambiguity resolution (AR) can improve positioning accuracy and reliability. The narrow-lane (NL) AR solution can reach centimeter-level accuracy but there is a certain initialization time. In contrast, extra-wide-lane (EWL) or wide-lane (WL) ambiguity can be fixed instantaneously. However, due to the limited correction accuracy of the empirical atmospheric model, the positioning accuracy is only a few decimeters. In order to further improve the real-time performance of PPP while ensuring accuracy, we developed a multi-system multi-frequency uncombined PPP single-epoch EWL/WL/NL AR method with regional atmosphere modelling. In the proposed method, the precise atmosphere, including zenith wet-troposphere delay (ZWD) and the slant ionosphere, is extracted through multi-frequency stepwise AR, which then is both interpolated and broadcast to users. By adding regional atmosphere constraints, users can achieve single-epoch PPP AR with centimeter-level accuracy. To verify the algorithm, four sets of reference networks with different inter-station distances are used for experiments. With atmosphere constraints, the accuracy of the single-epoch WL solution can be improved from the decimeter level to a few centimeters, with an improvement of more than 90%, and the epoch fix rate can also be improved to varying degrees, especially for the dual-frequency case. Due to the enlarged noise of the EWL combination, its accuracy is at the decimeter level, while the accuracy of the WL/NL solution can reach several centimeters. However, reliable NL ambiguity-fixing tightly relies on atmosphere constraints with sufficiently high accuracy. When the modelling of the atmosphere correction is not accurate enough, the NL AR performance is degraded, although this situation can be improved to a certain extent through the multi-GNSS combination. In contrast, in this case, the WL ambiguity can be successfully fixed and can support the precise positioning with an accuracy of several centimeters.

Estimating the Fractional Cycle Biases for GPS Triple-Frequency Precise Point Positioning with Ambiguity Resolution Based on IGS Ultra-Rapid Predicted Orbits

We investigate the estimation of the fractional cycle biases (FCBs) for GPS triple-frequency uncombined precise point positioning (PPP) with ambiguity resolution (AR) based on the IGS ultra-rapid predicted (IGU) orbits. The impact of the IGU orbit errors on the performance of GPS triple-frequency PPP AR is also assessed. The extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL) FCBs are generated with the single difference (SD) between satellites model using the global reference stations based on the IGU orbits. For comparison purposes, the EWL, WL and NL FCBs based on the IGS final precise (IGF) orbits are estimated. Each of the EWL, WL and NL FCBs based on IGF and IGU orbits are converted to the uncombined FCBs to implement the static and kinematic triple-frequency PPP AR. Due to the short wavelengths of NL ambiguities, the IGU orbit errors significantly impact the precision and stability of NL FCBs. An average STD of 0.033 cycles is achieved for the NL FCBs based on IGF orbits, while the value of the NL FCBs based on IGU orbits is 0.133 cycles. In contrast, the EWL and WL FCBs generated based on IGU orbits have comparable precision and stability to those generated based on IGF orbits. The use of IGU orbits results in an increased time-to-first-fix (TTFF) and lower fixing rates compared to the use of IGF orbits. Average TTFFs of 23.3 min (static) and 31.1 min (kinematic) and fixing rates of 98.1% (static) and 97.4% (kinematic) are achieved for the triple-frequency PPP AR based on IGF orbits. The average TTFFs increase to 27.0 min (static) and 37.9 min (kinematic) with fixing rates of 97.0% (static) and 96.3% (kinematic) based on the IGU orbits. The convergence times and positioning accuracy of PPP and PPP AR based on IGU orbits are slightly worse than those based on IGF orbits. Additionally, limited by the number of satellites transmitting three frequency signals, the introduction of the third frequency, L5, has a marginal impact on the performance of PPP and PPP AR. The GPS triple-frequency PPP AR performance is expected to improve with the deployment of new-generation satellites capable of transmitting the L5 signal.

Using Galileo and BDS-3 Quad-Frequency Signals for Long-Baseline Instantaneous Decimeter-Level Positioning

As the signals of Galileo and the global BDS-3 navigation satellite system have been accessible, positioning users can use quad-frequency even five-frequency signals nowadays. With multifrequency signals, one can form some useful combinations to improve the positioning performance, e.g., the widely used extra-wide-lane (EWL)/wide-lane (WL) in triple-frequency cases. For quad-frequency or five-frequency cases, better positioning performance can be expected since additional frequencies are introduced. In this study, we systematically analyse the benefits of Galileo and BDS-3 quad-frequency signals on long-baseline instantaneous positioning. First, the theoretical analysis of EWL/WL ambiguity resolution (AR) and satellite-station range estimation with a single-satellite geometry-free and ionosphere-free model is studied, along with the comparison with triple-frequency cases. Second, using the quad-frequency advantages, an instantaneous decimeter-level positioning model is proposed, where the geometry-free model is adopted for the first two EWL AR and the geometry-based model is adopted for the third WL AR. In the end, the AR and positioning performance are evaluated using real long-baseline date containing Galileo and BDS-3 quad-frequency observations. The results indicate that, with quad-frequency observations, both Galileo and BDS-3 EWL/WL ambiguities can be fixed reliably with a single epoch. Contributed by the resolved EWL/WL ambiguities, instantaneous decimeter-level positioning can be obtained, with the accuracies of 0.116 m/0.126 m/0.351 m in north, east, and up directions, respectively.

Assessment of Quad-Frequency Long-Baseline Positioning with BeiDou-3 and Galileo Observations

Quad-frequency signals have thus far been available for all satellites of BeiDou-3 and Galileo systems. The major benefit of quad-frequency signals is that more extra-wide-lane (EWL) combinations can be formed with quad-frequency than with triple- or dual-frequency, of which the ambiguities can be fixed instantaneously in medium and long baselines. In this paper, the long-baseline positioning algorithm based on optimal triple-frequency EWL/wide-lane (WL) combinations of BeiDou-3 and Galileo is proposed. First, the theoretical precision of multi-frequency combinations of BeiDou-3 and Galileo is studied, and EWL/WL combinations with a small noise amplitude factor and a small ionospheric scalar factor are selected. Then, geometry-free methods are used to estimate the a priori precision of EWL/second EWL/WL signals for different combination schemes. Second, the double-differenced (DD) geometry-based function models of quad-frequency configurations and three different triple-frequency configurations are given, and the DD ionospheric delays are estimated as unknown parameters. In the end, the real BeiDou-3 and Galileo data are used to evaluate the positioning preference. The results show that, when using fixed EWL observations to constrain WL ambiguities, the proposed triple-frequency EWL/WL signals composed of (B1I,B3I,B2a) of BeiDou-3 and (E1,E5a,E6) of Galileo can achieve the same precision as the quad-frequency signals. Therefore, the method proposed in this article can realize long-baseline instantaneous decimeter-level positioning while reducing the dimension of matrix and improving calculation efficiency.

A Comparative Study of BDS Triple-Frequency Ambiguity Fixing Approaches for RTK Positioning.

Concerning the triple-frequency ambiguity resolution, in principle there are three different realizations. The first one is to fix all the ambiguities of the original frequencies together. However, it is also believed that fixing the combined integer ambiguities with longer wavelength, such as extra-wide-lane (EWL), wide-lane (WL), should be advantageous. Also, it is demonstrated that fixing sequentially EWL, WL and one type of original ambiguities provides better results, as the previously fixed ambiguities increase parameters’ precision for later fixings. In this paper, we undertake a comparative study of the three fixing approaches by means of experimental validation. In order to realize the three fixing approaches from the same information in terms of adjustment, we developed a processing strategy to provide fully consistent normal equations. We first generate the normal equation with the original undifferentiated carrier phase ambiguities, then map it into that with the combined and double-differenced ambiguities required by the individual approach for fixing. Four baselines of 258 m, 22 km, 47 km and 53 km are selected and processed in both static and kinematic mode using the three ambiguity-fixing approaches. Indicators including time of first fixed solution (TFFS), the correct fixing rate, positioning accuracy and RATIO are used to evaluate and investigate results. We also made a preliminary theoretical explanation of the results by looking into the decorrelation procedure of the ambiguity searching algorithm and the intermediate results. As conclusions, integrated searching of original ambiguities or combined ambiguities has almost the same fixing performance, whereas the sequential fixing of EWL, WL and B1 ambiguities overperforms the integrated searching. By the way, the third-frequency data can shorten the TFFS significantly but can hardly improve the positioning.

GREAT-UPD: An open-source software for uncalibrated phase delay estimation based on multi-GNSS and multi-frequency observations

To meet the demands of precise orbit and clock determination, high-precision positioning, and navigation applications, a software called GREAT (GNSS + Research, Application and Teaching) was designed and developed at Wuhan University. As one important module in the GREAT software, GREAT-UPD was developed for multi-GNSS and multi-frequency uncalibrated phase delay (UPD) estimation. It can provide extra-wide-lane (EWL), wide-lane (WL), and narrow-lane (NL) UPDs for GPS, GLONASS, Galileo and BDS (GREC) satellites for precise point positioning (PPP) ambiguity resolution (AR) in a multi-GNSS and multi-frequency environment. The open-source GREAT-UPD software is written in C + + 11 language following object-oriented principles and can be compiled and run on several popular operating systems, such as Windows, Linux, and Macintosh. Observations from 222 stations spanning days from DOY 091 to 120 were used to conduct multi-GNSS and multi-frequency UPD estimation and PPP AR. Results indicate that GREAT-UPD can generate stable and reliable UPD products with multi-GNSS and multi-frequency observations. After applying the UPD corrections, the multi-frequency GREC PPP AR was achieved with the averaged time to first fix of 9.0 min. The software package can be obtained at https://geodesy.noaa.gov/gps-toolbox , including the source code, user manual, batch processing scripts, example data, and some auxiliary tools.

A Tightly Coupled BDS/INS Integrated Positioning Algorithm Based on Triple-Frequency Single-Epoch Observations

Vehicular dynamic positioning based on tightly coupled (TC) Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integration in urban areas is due to either low accuracy of pseudorange or poor continuity of carrier phase, resulting in insufficient positioning performance. To enhance the stability while ensuring positioning accuracy, this paper proposed a tightly coupled Beidou Navigation Satellite System (BDS)/INS integration scheme by improving measurement modelling with triple-frequency observations: first, a stepwise single-epoch ambiguity resolution of extra-wide-lane (EWL)/wide-lane (WL) combined observations and then modelling the measurement equation with fixed WL observation instead of conventional pseudorange or carrier phase. Experiments were carried out for verification with data collected in real traffic by a measurement vehicle. The proposed method achieved single-epoch output with an RMS statistical accuracy of decimetre level of 0.152 m horizontally and 0.196 m vertically. The signal outage experiment verified that the proposed algorithm is restoring high-accuracy positioning output in single-epoch once the signal is recaptured. The proposed method obtained a positioning accuracy improvement of 43.6% horizontally and 6.2% vertically in signal outage sections compared to the conventional method. This avoids the multiepoch ambiguity searching to fix with conventional carrier-phase processing, thereby improving the positioning stability.