Ambiguity Resolution Success Rate Research Articles

Precise positioning in complex environments with GNSS-RTK and weighted linear regression UWB observations

ABSTRACT In complex urban, port, and factory environments, GNSS and UWB encounter significant challenges from signal blockage and multipath effects. This study proposes a GNSS-RTK/WLR-UWB tight integration positioning method, utilizing Weighted Linear Regression to fit missing UWB epochs and introducing dynamic weight adjustment. The track cart and pedestrian experiment demonstrates that the single-epoch positioning accuracy is improved by 53.47%, 65.94%, and 28.03% in E, N and U compared to RTK. The filtering positioning achieves accuracy better than 1 cm in E and N, with a high ambiguity resolution success rate exceeding 99.40%, and reduces time-to-first-fix from 6-13 s to 3 s.

Distortion‐less carrier phase tracking space‐time adaptive processor based on power inversion criterion for GNSS anti‐jamming receiver

AbstractSpace‐time adaptive processor (STAP) has been widely used for global navigation satellite system (GNSS) anti‐jamming receiver due to its good anti‐jamming performance. When direction of satellite is unknown, STAP can be implemented based on power inversion (PI) criterion. However, existing space‐time PI algorithm will introduce tens to hundreds of degrees biases into carrier phase, and sometimes will even cause cycle slips, which will reduce the success rate of ambiguity resolution, ultimately deteriorating positioning accuracy. A distortion‐less carrier phase tracking space‐time PI algorithm is proposed. The main novelty is that the proposed algorithm keeps the coefficients of the temporal taps as real values by imposing constraints on the weights of the antenna array. Several experiments are implemented to verify the effectiveness of the proposed algorithm. For comparison, the results of PI algorithm and minimum variance distortion‐less response (MVDR) algorithm are shown. Results show that when the number, style, and direction of interferences and the direction of GNSS signal vary, different degrees of biases are introduced into carrier phases for the PI and the MVDR algorithm. However, no bias is introduced into the proposed algorithm. As a result, the effectiveness of the proposed algorithm is verified.

An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm

In 2020, the BeiDou-3 global navigation satellite system (BDS-3) was officially completed and put into service. Currently, network real-time kinematic (RTK) technology is considered the main means through which to improve the positioning accuracy of the BeiDou navigation satellite system (BDS). This paper proposes a long-range undifferenced network RTK (URTK) algorithm, based on multi-frequency observation data of the BDS. First, the multi-frequency phase integer ambiguity resolution (AR) model considering atmospheric error parameters is designed, and the multi-frequency phase integer ambiguity of the long-range BDS reference station is determined. Then, the undifferenced integer ambiguity of each reference station is obtained, using linear variation based on the accurately determined phase integer ambiguity between reference stations, and the undifferenced observation error of each reference station is calculated. Considering the weakening spatial correlation of the observation errors between long-range stations, undifferenced classification error corrections of a reference station network are separated, according to different error characteristics. Finally, the inverse distance weighting method is employed to calculate the classification undifferenced error correction of the rover station. The rover station corrects the observation error through applying the undifferenced error correction to achieve high-precision positioning. The measured data of a long-range continuous operation reference station (CORS) network are selected for an experiment. The results show that the proposed algorithm can quickly and accurately realize the resolution of the BDS integer ambiguity of a reference station network and establish an undifferenced area error correction model in order to achieve accurate classification of undifferenced error correction values for a rover station. In China, the BDS-3 is superior to the global positioning system (GPS) in terms of the satellite number, position dilution of precision (PDOP) value, AR success rate, stability, and convergence time. The results show that the AR success rate, stability, and convergence time increase with the operational frequency, and the BDS-3 can achieve centimeter-level positioning of single-system rover stations without relying on the GPS.

Assessing the influence of differential code bias and satellite geometry on GNSS ambiguity resolution through MANS-PPP software package

Abstract Ambiguity resolution (AR) is essential for quick and accurate Global Navigation Satellite System GNSS location and navigation. In addition to location parameters, there are various additional GNSS characteristics that are relevant for a wide range of applications such as instrumental calibrations, atmospheric sounding, and time transfer. We offer differential code bias and satellite geometry for the GNSS estimable parameters using MANS-PPP software backage. In this research, we used the MANS-PPP software package to execute the processing method and generate the PPP GNSS solution. We demonstrated how differential code bias and satellite geometry can effectively enhance initial time and positioning error for multi-GNSS satellites. PPP Processing observation data in static mode was used by the different DCB files the Chinese Academy of Sciences (CAS), the German Aerospace Centre (DLR), and the Centre for Orbit Determination in Europe (CODE), for the 12 stations from IGS, and we analyzed the impact of errors from the satellite geometry. The results illustration that the correction of DCB significantly improves the PPP ambiguity resolution success rate and quality, which have higher DCB values. The satellite geometry also has a substantial influence on the PPP ambiguity resolution, with a better geometry leading to a higher success rate and quality. Furthermore, the use of multiple GNSS constellations and the optimization of the satellite selection and weighting algorithms can further improve the PPP ambiguity resolution and the resulting positioning accuracy.

Stochastic modeling with robust Kalman filter for real-time kinematic GPS single-frequency positioning

The centimeter-level positioning accuracy of real-time kinematic (RTK) depends on correctly resolving integer carrier-phase ambiguities. To improve the success rate of ambiguity resolution and obtain reliable positioning results, an enhanced Kalman filtering procedure has been developed. Based on a posteriori residuals of measurements and state predictions, the measurement noise variance–covariance matrix for double-differenced measurements is adaptively estimated, rather than approximated by an empirical function which uses satellite elevation angle as input. Since, in real-world situations, unexpected outliers and carrier-phase outages can degrade the filter performance, a stochastic model based on robust Kalman filtering is proposed, for which the double-differenced measurement noise variance–covariance matrix is computed empirically with a modified version of the IGG (Institute of Geodesy and Geophysics) III method in order to detect and identify outliers. The performance of the proposed method is assessed by two tests, one with simulated data and one with real data. In addition, the performance of F-ratio and W-ratio tests as proxies for the success of ambiguity fixing is investigated. Experimental results reveal that the proposed method can improve the reliability and robustness of relative kinematic positioning for simulation scenarios as well as in a real urban test.

Improved undifferenced ambiguity resolution for LEO precise orbit determination

Ambiguity resolution (AR) is critical for enhancing the orbit accuracy in precise orbit determination (POD) for low earth orbit (LEO) satellites. While orbit estimation using single-difference (SD) AR has been widely researched, the investigation of orbit estimation using undifferenced (UD) AR for LEO satellites is limited due to time-varying hardware biases at the LEO receiver end. To address this deficiency, we propose an improved UD AR method for LEO satellite orbit determination. The method employs the optimal integer datum ambiguity for a 1-day observation arc, and the random-walk clock model is utilized to transfer the integer ambiguity datum to the other epochs, which enables the arc-wise ambiguities to regain the integer property within the time frame. To validate the effectiveness of our improved method, numerical experiments are conducted. Moreover, we assess the performance of the random-walk clock model for a spaceborne ultra-stable oscillator (USO). The high frequency stability of the USO establishes the satisfactory requirements for this study. Both in the kinematic and dynamic modes, the AR success rates of our improved method are ∼ 2% higher than that of the current SD AR method, and the orbit results indicate a slight improvement. The 3-Dimensional (3D) root-mean-squares (RMS) of the orbit differences between JPL precise science orbits (PSO) and our orbits are reduced by up to 4% and 5% for kinematic and dynamic orbits, respectively. The subtle benefit is also proven by K-band ranging (KBR) system validations. In the case of the Gravity Recovery and Climate Experiment Follow-on (GFO) satellites, the results indicate that the effect of our improved UD AR can be equivalent to that of SD AR. Our improved UD AR method can be a good alternative for its superior ability to generate hardware delay at the LEO receiver end.

Modeling, refinement and evaluation of multipath mitigation based on the hemispherical map in BDS2/BDS3 relative precise positioning

Multipath is one of the critical constraints in millimeter-level BeiDou navigation satellite system (BDS) positioning. Since multipath hemispherical map (MHM) can be conducted in relatively real-time and kinematic scenarios, it has great potential in real BDS applications. However, limited studies focus on the mitigation performance and efficiency problem based on MHM with the second-generation regional system (BDS2) and third-generation global system (BDS3). In this paper, the MHM is systematically studied in BDS2/BDS3 relative precise positioning, including the issues of MHM about the modeling, refinement, and evaluation. Specifically, at first, a rigorous modeling procedure of MHM with quality control is given, where the high-precision and high-reliability multipath corrections can be obtained. Second, based on a consecutive eleven-day designed experiment, different MHM models considering the systems, satellites, and frequencies are formed and compared comprehensively. Third, the MHM models are systematically evaluated on the positioning performance, including ambiguity resolution, float solution, and fixed solution. The results show that in MHM models, the multipath corrections for low elevation angles are more significant, and the multipath effects are usually different in different directions due to the obstacles. The behaviors of MHM models are dependent on the system, satellite, and frequency types. Besides, the MHM models are relatively stable over seven consecutive days. After applying the MHM models, the success rate of ambiguity resolution can be improved in millimeter-level positioning. Approximately 7 cm improvements can be obtained for the float solution in the 3D direction. The MHM models can improve the positioning accuracy by approximately 13% for the fixed solution especially in locations where the multipath is more severe. Moreover, the unified MHM method of the previous day with quality control can replace the refined MHM method when considering the balance between accuracy and efficiency.

Position and Attitude Determination in Urban Canyon with Tightly Coupled Sensor Fusion and a Prediction-Based GNSS Cycle Slip Detection Using Low-Cost Instruments.

We present a position and attitude estimation algorithm of moving platforms based on the tightly coupled sensor fusion of low-cost multi baseline GNSS, inertial, magnetic and barometric observations obtained by low-cost sensors and affordable dual-frequency GNSS receivers. The sensor fusion algorithm is realized by an Extended Kalman Filter and estimates the states including GNSS receiver inter-channel biases, integer ambiguities and non-GNSS receiver biases. Tightly coupled sensor fusion increases the reliability of the position and attitude solution in challenging environments such as urban canyons by utilizing the inertial observations in case of GNSS outage. Moreover, GNSS observations can be efficiently used to mitigate IMU sensor drifts. Standard GNSS cycle slips detection methods, such as the application of triple differences or linear combinations such as Melbourne-Wübbena combination and the phase ionospheric residual extended TurboEdit method. However, these techniques are not well suited for the localization in quickly changing environments such as urban canyons. We present a new method of tightly coupled sensor fusion supported by a prediction based cycle slip detection technique, applied to a GNSS setup using three antennas leading to multiple moving baselines on the platform. Thus, not only the GNSS signal properties but also the dynamics of the moving platform are considered in the cycle slip detection. The developed algorithm is tested in an open-sky validation measurement and two sets of measurement in an urban canyon area. The sensor fusion algorithm processes the data sets using the proposed prediction-based cycle slip method, the loss-of-lock indicator-based, and for comparison, the Melbourne-Wübbena and the TurboEdit cycle slip detection methods are also included. The obtained position and attitude estimation results are compared to the internal solution of raw data source GNSS receivers and to the observations of a high-accuracy GNSS/INS unit including a fiber optic gyro. The validation test confirms the proper cycle slip detection in an ideal environment. The more challenging urban canyon test results show the reliability and the accuracy of the proposed method. In the case of the second urban canyon test, the proposed method improved the integer ambiguity resolution success rate by 19% and these results show the lowest horizontal and vertical coordinate distortion in comparison of the linear combination and the loss-of-lock-based cycle slip methods.

PROPOSED STRATEGY TO OBTAIN OPTIMUM INTER-STATION DISTANCE FOR GPS CORS DEVELOPMENT SCENARIO

Abstract. The critical part in the development of GPS CORS network is known as the inter-station distance between the CORS or baseline length. Due to the diversity of baseline length can be implemented for the CORS network, this paper presents an alternative strategy to obtain the optimum inter-station distance between the CORS. The optimum inter-station distance between the CORS can be achieved by analysing the quality of GPS baseline data and applying GPS CORS Optimal Prediction Number Calculator (ONPC). Three baselines have been designed with appropriate range of baseline length which short (0–30km), medium (30–70km) and long (70–180km) baselines in order to examine the quality of GPS data and GPS CORS ONPC. The GPS baseline data quality analysis presents the performance of short, medium, and long baselines in term of percentage of ambiguity resolution (AR) and separated medium of GPS distance-dependent errors. The GPS CORS ONPC shows the distribution of CORS network using the length of short, medium, and long baselines within the frame and the total cost required for the establishment of the CORS network. From the result, it is found that the short and medium baselines have superior performances in term of GPS data quality which has stated higher success rate of AR (more than 50 percent) and less than 1cm standard deviation for dispersive and non-dispersive medium of GPS distance-dependent errors compared to long baseline. However, in term of cost, the longer baseline stated the cheapest, followed by medium baseline and short baseline which is 12 times and 182 times greater than longer baselines respectively. Therefore, the medium baseline is chosen as optimum inter-station distance in the development of CORS network due to better coverage and satisfied quality of GPS data with acceptable cost.

GNSS RTK/UWB/DBA Fusion Positioning Method and Its Performance Evaluation

As a significant space–time infrastructure, the Global Navigation Satellite System (GNSS) provides high-precision positioning, navigation, and timing (PNT) information to users all over the world. However, GNSS real-time kinematic (RTK) mobile receiver signal attenuation is obvious in complex environments such as under trees, urban canyons, and indoors, among others, and it is incapable of meeting the demand of multi-level mass users for indoor and outdoor seamless positioning applications. The goal of this study was to address the limitations and vulnerabilities of the GNSS RTK positioning above-mentioned. First, we propose a GNSS RTK/UWB/DBA fusion positioning model and provide detailed algorithm steps for various types of observations. The performance of the GNSS RTK/UWB/DBA fusion positioning under various occlusion environments is then thoroughly evaluated using static and dynamic cart experiments. The experiment results show that as the elevation mask angle increases, the number of available GNSS satellites decreases and the ambiguity resolution success rate decreases; in comparison to GNSS RTK, the proposed GNSS RTK/UWB/DBA fusion positioning model can significantly improve the spatial geometry distribution of observations, reduce the position dilution of precision (PDOP) value, and improve the ambiguity resolution success rate. At an elevation mask angle of 50 degrees, GNSS RTK/UWB/DBA combination positioning can improve the ambiguity resolution success rate by 20% to 60%, and a positioning error less than 5 cm by 20% to 50%. It also indicates that the GNSS RTK/UWB/DBA fusion positioning model has higher positioning accuracy and can effectively improve the availability and reliability of GNSS RTK in a local harsh environment.

Attitude Determination with GPS L1/Galileo E1 Observations from Common-Clock Receiver: A Comparison of Four Different Models

The development of the commercial multi global navigation satellite system (GNSS) dual (multi)-antenna common-clock receiver that uses time-synchronization technology has brought new opportunities for high-precision GNSS-based attitude determination. In this article, for the first time, we present a performance comparison of global positioning system (GPS) L1/Galileo navigation satellite system (Galileo) E1 attitude determination with a common-clock receiver using four different models, i.e., the loosely combined single-differenced (SD-LC) model, the tightly combined single-differenced (SD-TC) model, the loosely combined double-differenced (DD-LC) model, and the tightly combined double-differenced (DD-TC) model. We first introduce the SD-LC, SD-TC, DD-LC, and DD-TC relative positioning models with GPS L1/Galileo E1 observations from a common-clock receiver. Then, we present a performance comparison of the four models in both single-epoch and multi-epoch modes using static data collected with a Trimble BD992 common-clock receiver in terms of the ambiguity dilution of precision (ADOP), the ambiguity resolution (AR) success and failure rates, and the positioning and attitude determination accuracy. In the case of the single-epoch mode, the experimental results revealed that the results of the single-differenced (SD) models were identical to those of double-differenced (DD) models, i.e., the results of SD-LC and SD-TC models were identical to DD-LC and DD-TC models, respectively. Moreover, compared with the loosely combined model (SD-LC/DD-LC), the tightly combined model (SD-TC/DD-TC) delivered a much higher AR success rate and a lower AR failure rate, especially under a high elevation cutoff angle. The AR success rate increased by approximately 35.1% under a 40° elevation cutoff angle, while the AR failure rate decreased by approximately 4.3%. In the case of the multi-epoch mode, the experimental results confirmed the advantages of the tightly combined model over the loosely combined model as well as the SD model over the DD model. Compared with the DD-LC and SD-LC models, the AR success rates of the DD-TC and SD-TC models were improved by approximately 16.7% and 0.6% under a 45° elevation cutoff angle, respectively. The AR failure rates were reduced by approximately 12.4% and 0.3%, respectively. Moreover, compared with the DD-LC and DD-TC models, the AR success rates of the SD-LC and SD-TC models under a 45° elevation cutoff angle were improved by approximately 24.0% and 7.9%, respectively, and the AR failure rates were reduced by approximately 19.9% and 7.8%, respectively. Meanwhile, compared with the DD model, the SD model delivered comparable yaw accuracy and remarkably better pitch accuracy. The pitch accuracy was improved by approximately 65.2–75.0%.

AGAR: Array-Geometry-Aided Ambiguity Resolution for Baseline Growing With Global Navigation Satellite Systems

Ambiguity resolution (AR) is a fundamental problem for carrier phase based signal processing tasks to leverage the superhigh precision of wavelength-level range and velocity measurements. With the elaborately designed waveform and coordinated running of the space-based satellite system, the antenna-array observations of global navigation satellite system (GNSS) signals feature a phase measurement model. In this article, the AR of baseline estimation with GNSS carrier phase measurements only in the AR step is examined from an array signal processing perspective. The array-geometry-aided ambiguity resolution approach, coined as AGAR, is proposed for growing the baseline estimation provided by a search-free algorithm to the accuracy of the aperture level in an effective way. First, the single-epoch and search-free $2q$-order AR method is further investigated in size and statistical independence. Second, the conventional phase beampattern is defined to characterize the similarity of carrier phase measurement vector of signals from different directions. Third, a simple and effective ambiguity-lookup-table approach after the conventional phase beampattern is proposed which fulfills the goal of baseline growing to the array aperture level. Fourth, the identifiability, success rate, Cramér–Rao bound (CRB), and computation complexity are analyzed. As a result, the phase-based and complex-based processings are distinguished, resulting in an alternative analytical prediction of outlier probability that well approximates AR’s success rate. The relationship between the success rate of AR and CRB is also clarified. Numerical simulations are carried out to verify the proposed analytical prediction and AR approach. The AR success rate increased from 10% to 93% at a relatively large measurement error of 0.05 cycle.

A novel ambiguity resolution model of BeiDou navigation satellite system/inertial navigation system tightly coupled for kinematic-to-kinematic precise relative positioning

The carrier-based kinematic-to-kinematic relative positioning can obtain the precise baseline between two moving stations, which greatly expands the application field of dynamic relative positioning. However, the relative positioning performance is degraded greatly with low fixation rate of ambiguity with low-cost receivers. Especially, in the complex dynamic environment, ambiguity resolution effect is influenced by the satellite signal blocked, multipath outlier, and abnormal state prediction. Aiming at the problems, a novel inertial navigation system–aided robust adaptive filtering ambiguity resolution model is proposed. In addition, a hierarchical filtering strategy is developed to eliminate ambiguity parameters in BeiDou navigation satellite system/inertial navigation system tightly coupled integrated system. Finally, the precise relative position can be calculated with the “best” ambiguity solution. Both experiments with static data and field vehicle test were carried out to evaluate the algorithm efficiency in different data configurations. The results indicate that IRAFAR-TCRP method can effectively suppress the influence of observation outliers and model prediction abnormalities, which improves the success rate of ambiguity resolution, raises the accuracy as well as the continuity of relative positioning. The success rate of ambiguity resolution with single-frequency BeiDou navigation satellite system can reach 90% in the gross error and abnormal disturbance environments and centimeter-level accuracy can be achieved.

A TCAR method for common clock source single difference carrier phase observation ambiguity fixing

The ambiguity resolution is the key issue for global navigation satellite system (GNSS) high precision position. As the traditional three carrier ambiguity resolution (TCAR) method has shortcoming when solving the carrier ambiguity of single difference carrier phase measurement. A single difference carrier phase (SDCP) three carrier ambiguity resolution method was proposed by using the estimation of the relative position between two receiving antennas. It is illustrated by the test experiments that the success rate of SDCP ambiguity resolution with using the proposed algorithm is more than 98%; and the three-dimension(3D) position accuracy based on the ambiguity free SDCP measurements is about 58% higher than the position accuracy that using double differences carrier phase (DDCP) measurements.

Model comparison and performance analysis of multi-frequency precise positioning with the joint BDS-2 and BDS-3 system

The global BeiDou Navigation Satellite System (BDS-3) has been formally operated together with the regional system (BDS-2) for more than one year. However, the different frequency numbers between BDS-2 and BDS-3 makes their integration a troublesome problem, especially when all available frequencies are taken into account. To make a comprehensive analysis of multi-frequency precise positioning models in BDS-2 and BDS-3, the popular real-time kinematic positioning is taken as an example for data processing. Since in general the reliable, successful and rapid ambiguity resolution is the key of an appropriate multi-frequency positioning model, the framework of multi-frequency ambiguity resolution (AR) is summarized first. The usual loose combined model for the joint BDS-2 and BDS-3 system is described. To make full use of the common frequencies B1I and B3I in BDS-2 and BDS-3, an improved combined model is proposed where both the loose combined mode and tightly combined mode are applied. The performance of ambiguity resolution (AR) and positioning precision are obtained from four short baselines with different lengths in the above two models and with different elevation masks. The comparison results show that: (1) Both the combined model and improved combined model can achieve nearly 100% AR success rate and correctly-fixed rate, as well as consistent centimeter level’s fixed solution; (2) The improved combined model can obtain higher AR fixed rate and shorter time to first fix (TTFF) compared with the usual combined model, and the improvements can be up to 15% for the fixed rate and 37% for TTFF; (3) To achieve the largest AR fixed rate while keep reliable AR and precise positioning, a relative large elevation mask such as 30° is highly recommended for a joint BDS-2 and BDS-3 system with sufficient observed satellites.

A Novel Two-Stage Adaptive Filtering Model-Based GNSS/INS Tightly Coupled Precise Relative Navigation Algorithm for Autonomous Aerial Refueling

Autonomous aerial refueling (AAR) has generated great interest in recent years. However, much research has focused on the vision-based close docking stage; few studies have been conducted on the navigation algorithm for the rendezvous and following stages. High-precision relative navigation in following stage can provide favourable conditions for successful docking. Aiming at precise relative navigation in the complex high dynamic environment of aerial refueling rendezvous and following stages, a two-stage adaptive filtering architecture is exploited in this paper. An adaptive main Kalman filter (AKF) is realized for ambiguity eliminated GNSS/INS tightly coupled integrated system, and a robust adaptive subfilter is developed for GNSS individually. Particularly, aiming at the influence of pseudorange observation multipath outliers and state abnormal disturbances in unmanned air vehicle- (UAV-) tanker proximity, an INS-aided bifactor robust and classified factor adaptive filtering (IBRCAF) algorithm for single-frequency ambiguity resolution is proposed. Finally, the effectiveness of the algorithm is verified by the simulation experiments for UAV-tanker. The results indicate that the IBRCAF algorithm can efficiently suppress the influence of pseudorange multipath gross errors and abnormal state disturbances and greatly raise the success rate of ambiguity resolution, and the two-stage adaptive filtering algorithm of IBRCAF-AKF can significantly improve relative navigation performance and achieve centimeter-level accuracy.

Single Epoch Ambiguity Resolution of Small-Scale CORS with Multi-Frequency GNSS

The network real-time kinematic (RTK) technique uses continuously operating reference stations (CORS) within a geographic area to model the distance dependent errors, allowing users in the area to solve ambiguities. A key step in network RTK is to fix ambiguities between multiple reference stations. When a new satellite rises or when maintenance happens, many unknown parameters are involved in the mathematical model, and traditional methods take some time to estimate the integer ambiguities reliably. The purpose of this study is the single-epoch ambiguity resolution on small-scale CORS network with inter-station distance of around 50 km. A new differencing scheme is developed to explore the full potential of multi-frequency Global Navigation Satellite System (GNSS). In this scheme, a differencing operation is formed between satellites with the closest mapping functions. With the new differencing scheme, tropospheric error can be mostly neglected after the correction, as well as the double-differencing operation. Numerical tests based on two baselines of 49 km and 35 km show that the success rate of ambiguity resolution can reach more than 90%. The single-epoch ambiguity resolution for reference stations brings many benefits to the network RTK service, for example, the instantaneous recovery after maintenance or when a new satellite rises.

Research on Tightly Coupled Multi-Antenna GNSS/MEMS Single-Frequency Single-Epoch Attitude Determination in Urban Environment

GNSS-only attitude determination is difficult to perform well in poor-satellite-tracking environments such as urban areas with high and dense buildings or trees. In addition, it is harder to resolve integer ambiguity in the case of single-frequency single-epoch process mode. In this contribution, a low-cost MEMS gyroscope is integrated with multi-antenna GNSS to improve the performance of the attitude determination. A new tightly coupled (TC) model is proposed, which uses a single filter to achieve the optimal estimation of attitude drift, gyro biases and ambiguities. In addition, a MEMS-Attitude-aided Quality-Control method (MAQC) for GNSS observations is designed to eliminate both the carrier multipath errors and half-cycle slips disturbing ambiguity resolution. Vehicle experiments show that in GNSS-friendly scenarios, the Ambiguity Resolution (AR) success rate of the proposed model with MAQC can reach 100%, and the accuracy of attitudes are (0.12, 0.2, 0.2) degrees for heading, pitch and roll angles, respectively. Even in harsh scenarios, the AR success rate increases from about 67% for the GNSS only case to above 90% after coupling GNSS tightly with MEMS, and it is further improved to about 98% with MAQC. Meanwhile, the accuracy and continuity of attitude determination are effectively guaranteed.

GPS-BDS-Galileo double-differenced stochastic model refinement based on least-squares variance component estimation

AbstractStochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively.

An Improved Multipath Mitigation Method and Its Application in Real-Time Bridge Deformation Monitoring

A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to the influence of observation noise and the multipath differences between different satellites. Aiming at the insufficiency of MHM in dealing with the adverse impact of observation noise, we proposed the MHM_V model, based on Variational Mode Decomposition (VMD) and the MHM algorithm. Utilizing the VMD algorithm to extract the multipath from single-difference (SD) residuals, and according to the principle of the closest elevation and azimuth, the original observation of carrier phase in the few days following the implementation are corrected to mitigate the influence of the multipath. The MHM_V model proposed in this paper is verified and compared with the traditional MHM algorithm by using the observed data of the Forth Road Bridge with a seven day and 10 s sampling rate. The results show that the correlation coefficient of the multipath on two adjacent days was increased by about 10% after residual denoising with the VMD algorithm; the standard deviations of residual error in the L1/L2 frequencies were improved by 37.8% and 40.7%, respectively, which were better than the scores of 26.1% and 31.0% for the MHM algorithm. Taking a ratio equal to three as the threshold value, the fixed success rates of ambiguity were 88.0% without multipath mitigation and 99.4% after mitigating the multipath with MHM_V. The MHM_V algorithm can effectively improve the success rate, reliability, and convergence rate of ambiguity resolution in a bridge multipath environment and perform better than the MHM algorithm.