Carrier Phase Observations Research Articles

A model to obtain timing solution with un-differenced observations suitable for single-station/multi-station, a case study of BDS data

This study proposes a model for a BeiDou Satellite Navigation System (BDS) precise timing solution with un-differenced carrier phase observations, and it is suitable for both single-station and multi-station. With this model, not only can users employ high-precision carrier phase observations to improve the uncertainty of the timing service for single station, but they can also directly use the un-differenced model and augmentation correction which collected from the reference stations to get the timing service, which is more efficient than the traditional single-differenced model for multi-stations. The validation showed that the carrier phase observations can improve the uncertainty from 0.49 to 0.10 ns, and the mean stability improved 70 times. In addition, whether for the single-station and multi-station solution or for the single-differenced model and un-differenced model, the final uncertainty and stability were nearly the same, thus it allows for the realisation of a seamless timing solution for the single-station model and multi-station model.

BDS RTK High-precision Positioning Algorithm for Deformation Solution

In view of the increasing scope, scale and quantity of landslide, debris flow and other geological disasters and without achieving long-term stable high-precision monitoring in the exist, a solution algorithm on RTK high-precision differential positioning deformation is presented in this paper. The algorithm uses high-precision board receiver as the satellite positioning reference station, the u-blox receiver as the monitoring station. The carrier phase double difference relative positioning model is based on the carrier phase observation and pseudo range observation, combined with the RTK unscented Kalman filter model and smooth filtering algorithm, and then more accurate position results are obtained. This method can be used to calculate the position of deformation monitoring body with high precision, which is simple, easy to realize and practical. The positioning accuracy of deformation monitoring is higher. After smoothing, the horizontal precision can reach 3mm, and the elevation precision can reach 5mm.

Cycle slip detection and repair for BeiDou-3 triple-frequency signals

When carrier phase observations are applied to high-precision positioning, how to handle the cycle slip is an unavoidable problem. For cycle slip correction, detection combination noise and the ionospheric delay are two crucial factors. Specifically, the drastic changes in the ionosphere and the increased noise of code observations will increase the failure probability of cycle slip detection. To reduce the influence of code observation noise and ionospheric bias, a novel cycle slip detection method for BDS-3 satellites is proposed. Considering that code measurement noise is closely related to the satellite elevation angle, an elevation-based model is built to evaluate the code measurement noise. Firstly, two modified code-phase combinations are selected optimally based on 1% missed detection rate and 99% success detection rate to minimize the effects of code measurement noise. However, the second modified code-phase combination is more affected by ionospheric delay bias, so ionospheric bias of current epoch needs to be corrected. To reduce the influence of ionospheric bias, two moving windows of time-differenced ionospheric delay are introduced to correct the ionospheric bias of the second code-phase combination. Experiments with BeiDou-3 data are implemented in three different scenarios. To verify the effectiveness of the algorithm in the environment of high code observations noise, Gaussian noise is added to the code observations in the first scenario, and the results demonstrate that the success rate of cycle slip detection and repair is still greater than 95% when the standard deviation of Gaussian noise is 0.8 m. The second scenario is carried out under low ionospheric activity, and results indicate that the proposed method significantly reduces the times of failed detection and repair. Moreover, in the third scenario, BeiDou-3 data with cycle slips of different types under high ionospheric activity are tested, and all cycle slips can be correctly detected and corrected.

The research of key technology and approach for time and frequency transfer based on GNSS carrier phase observation

The research of key technology and approach for time and frequency transfer based on GNSS carrier phase observation

A highly adaptable method for GNSS cycle slip detection and repair based on Kalman filter

The cycle slip detection and repair are crucial steps in the preprocessing of GNSS carrier phase observation. Currently, however, there are few cycle slip detection and repair methods that can meet the data processing needs for diverse situations. To solve this problem, a highly adaptable cycle slip detection and repair method is proposed. First, a cycle slip detection equation is established using the pseudo-range and carrier double-differenced (DD) observations; the state equation is developed based on the satellite-ground distance. Then, a Kalman filter estimation model is established by joining the two equations. Subsequently, the cycle slip can be detected and repaired. Finally, the state parameters are refined in accordance with the conditional distribution. According to the results of the example, all the simulated cycle slips are detected and repaired by the method proposed. It shows that the method can meet the data processing needs for multiple situations.

Feasibility of Consumer Grade GNSS Receivers for the Integration in Multi-Sensor-Systems.

Various GNSS applications require low-cost, small-scale, lightweight and power-saving GNSS devices and require high precision in terms of low noise for carrier phase and code observations. Applications vary from navigation approaches to positioning in geo-monitoring units up to integration in multi-sensor-systems. For highest precision, only GNSS receivers are suitable that provide access to raw data such as carrier phase, code ranges, Doppler and signal strength. A system integration is only possible if the overall noise level is known and quantified at the level of the original observations. A benchmark analysis based on a zero baseline is proposed to quantify the stochastic properties. The performance of the consumer grade GNSS receiver is determined and evaluated against geodetic GNSS receivers to better understand the utilization of consumer grade receivers. Results indicate high similarity to the geodetic receiver, even though technical limitations are present. Various stochastic techniques report normally distributed carrier-phase noise of 2 mm and code-range noise of 0.5–0.8 m. This is confirmed by studying the modified Allan standard deviation and code-minus-carrier combinations. Derived parameters serve as important indicators for the integration of GNSS receivers into multi-sensor-systems.

GNSS code and carrier phase observations of a Huawei P30 smartphone: quality assessment and centimeter-accurate positioning

In 2016, an application programming interface was added to the Android operating systems, which enables the access of GNSS raw observations. Since then, an in-depth evaluation of the performance of smartphone GNSS chips is very much simplified. We analyzed the quality of the GNSS observations, especially the carrier phase observations, of the dual-frequency GNSS chip Kirin 980 built into Huawei P30 and other smartphones. More than 80 h of static observations were collected at several locations. The code and carrier phase observations were processed in baseline mode with reference to observations of geodetic-grade equipment. We were able to fix carrier phase ambiguities for GPS L1 observations. Furthermore, we performed an antenna calibration for this frequency, which revealed that the horizontal phase center offsets from the central vertical axis of the smartphone and also the phase center variations do not exceed 1–2 cm. After successful ambiguity fixing, the 3D position errors (standard deviations) are smaller 4 cm after 5 min of static observation session and 2 cm for long observation session.

Characteristics Analysis of Raw Multi-GNSS Measurement from Xiaomi Mi 8 and Positioning Performance Improvement with L5/E5 Frequency in an Urban Environment

Achieving continuous and high-precision positioning services via smartphone under a Global Navigation Satellite System (GNSS)-degraded environment is urgently demanded by the mass market. In 2018, Xiaomi launched the world’s first dual-frequency GNSS smartphone, Xiaomi Mi 8. The newly added L5/E5 signals are more precise and less prone to distortions from multipath reflections. This paper discusses the characteristics of raw dual-frequency GNSS observations from Xiaomi Mi 8 in urban environments; they are characterized by high pseudorange noise and frequent signal interruption. The traditional dual-frequency ionosphere-free combination is not suitable for Xiaomi Mi 8 raw GNSS data processing, since the noise of the combined measurements is much larger than the influence of the ionospheric delay. Therefore, in order to reasonably utilize the high precision carrier phase observations, a time differenced positioning filter is presented in this paper to deliver continuous and smooth navigation results in urban environments. The filter first estimates the inter-epoch position variation (IEPV) with time differenced uncombined L1/E1 and L5/E5 carrier phase observations and constructs the state equation with IEPV to accurately describe the user’s movement. Secondly, the observation equations are formed with uncombined L1/E1 and L5/E5 pseudorange observations. Then, kinematic experiments in open-sky and GNSS-degraded environments are carried out, and the proposed filter is assessed in terms of the positioning accuracy and solution availability. The result in an open-sky environment shows that, assisted with L5/E5 observations, the root mean square (RMS) of the stand-alone horizontal and vertical positioning errors are about 1.22 m and 1.94 m, respectively, with a 97.8% navigation availability. Encouragingly, even in a GNSS-degraded environment, smooth navigation services with accuracies of 1.61 m and 2.16 m in the horizontal and vertical directions are obtained by using multi-GNSS and L5/E5 observations.

A Holistic Approach to Guarantee the Reliability of Positioning Based on Carrier Phase for Indoor Pseudolite

The integrity monitoring algorithm based on pseudorange observations has been widely used outdoors and plays an important role in ensuring the reliability of positioning. However, pseudorange observations are greatly affected by the error sources such as multipath, clock drift, and noise in indoor pseudolite system, thus the pseudorange observations cannot be applied to high-precision indoor positioning. In general, double differenced (DD) carrier phase observations are used to obtain a high-precision indoor positioning result. What’s more, the carrier phase-based integrity monitoring (CRAIM) algorithm is applied to identify and exclude potential faults of the pseudolites. In this article, a holistic method is proposed to ensure the accuracy and reliability of positioning results. Firstly, if the reference pseudolite operates normally, extended Kalman filter is used for parameter estimation on the premise that the number of common pseudolites meets positioning requirements. Secondly, the innovation sequence in the Kalman filter is applied to construct test statistics and the corresponding threshold is determined from the Chi distribution with a given probability of false alert. The pseudolitehorizontal protection level (HPL) is calculated by the threshold and a prior probability of missed detection. Finally, compared the test statistics with the threshold to exclude the faultypseudolite for the reliability of positioning. The experiment results show that the proposed method improves the accuracy and stability of the results through faults detection and exclusion. This method ensures accuracies at the centimeter level for dynamic experiments and millimeter levels for static ones.

Integrity monitoring of carrier phase-based ephemeris fault detection

Ephemeris faults must be monitored when integrity is provided for safety–critical applications. The ground facility consisting of multiple short-baseline reference receivers is used to detect the ephemeris faults. The test statistic for the ephemeris fault monitoring is constructed by the double-differenced carrier phase observation. The false alarm and missed detection errors of the proposed ephemeris fault monitoring method are constrained by accounting for the effect of ephemeris fault and geometry-free ambiguity resolution failure simultaneously. Real BDS data with simulated ephemeris fault are utilized to test the proposed method. The experimental results have shown that the ephemeris fault can be detected by satisfying the required false alarm and missed detection probabilities. The detection power loss of the proposed method can be constrained at less than 0.1%. It has been proven that the real-time protection of the proposed method is achievable against Type A and Type B ephemeris faults.

Performance of Galileo precise time and frequency transfer models using quad-frequency carrier phase observations

GNSSs, such as Galileo and modernized GPS, BeiDou and GLONASS systems, offer new potential and challenges in precise time and frequency transfer using multi-frequency observations. We focus on the performance of Galileo time and frequency transfer using the E1, E5a, E5b and E5 observations. Dual-frequency, triple-frequency and quad-frequency models for precise time and frequency transfer with different Galileo observations are proposed. Four time and transfer links between international time laboratories are used to assess the performances of different models in terms of time link noise level and frequency stability indicators. The average RMS values of the smoothed residuals of the clock difference series are 0.033 ns, 0.033 ns and 0.034 ns for the dual-frequency, triple-frequency and quad-frequency models with four time links, respectively. With respect to frequency stability, the average stability values at 15,360 s are 9.51 × 10−15, 9.46 × 10−15 and 9.37 × 10−15 for the dual-frequency, triple-frequency and quad-frequency models with four time links, respectively. Moreover, although biases among different models and receiver the inter-frequency exist, their characteristics are relatively stable. Generally, the dual-/triple-/quad-frequency models show similar performance for those time links, and the quad-frequency models can provide significant potential for switching among and unifying the three multi-frequency solutions, as well as further enhancing the redundancy and reliability compared to the current dual-frequency time transfer method.

Using GPS Time-Differenced Carrier Phase Observations to Calibrate LDV/INS Integrated Navigation Systems

A laser Doppler velocimeter (LDV) is usually integrated with an inertial navigation system (INS) to autonomously acquire a vehicle’s position, velocity and attitude. The calibration process is trying to determine the scale factor of the LDV and the installation angles between LDV and INS. As a dead-reckoning system, the calibration accuracy affects the navigation performance of the LDV/INS integrated navigation system. This paper presents how to use time-differenced carrier phase (TDCP) observations instead of differenced GPS (DGPS) or precise point positioning (PPP) techniques to complete the calibration process. Differencing carrier phase observations between two GPS epochs can save the effort in ambiguity fixing and achieve centimeter relative positioning after outlier and cycle slip detection, which is suitable for LDV calibration. In order to finish the calibration within several minutes, an iteration scheme is implemented into the calibration for rapid convergence. The navigation experiment indicates that the horizontal position error of the LDV/INS integrated navigation system can achieve 26.6m/25.5km.

Complementary Kalman Filter as a Baseline Vector Estimator for GPS-based Attitude Determination

The Global Positioning System (GPS) offers the interferometer for attitude determination by processing the carrier phase observables. By using carrier phase observables, the relative positioning is obtained in centimeter ... | Find, read and cite all the research you need on Tech Science Press

Cycle Slips Detection for Triple-Frequency Signals of BDS by Combining Carrier Phase and Doppler Measurements

A new model is presented to resolve cycle slips detection for triple-frequency observations of BeiDou navigation satellite system (BDS) in this article when pseudorange observations are missing or insufficiently accurate under harsh or special situations. Based on the first-order time-difference geometry-free (GF) pseudorange-phase combination model, the new cycle slips detection and correction method based on the triple-frequency carrier phase and Doppler observations is proposed. With analyses on the two common sampling intervals (30 s and 1 s), it can be concluded that the optimal combination coefficients of the proposed model relate to sampling intervals. Combinations [4, −2, −3], [−1, −5,6], and [−3,6, −2] are selected to detect and correct cycle slips for 30 s sampling interval, while combinations [0, −1,1], [1,0, −1], and [−3,2,2] are selected for 1 s sampling interval. The validity of the phase-Doppler combination model under the static condition and the steady ionosphere with 30 s sampling interval and 1 s sampling interval is verified by two static experiments. Results show that the phase-Doppler combination model can achieve the same performance as the pseudorange-phase combination model. All the small, insensitive, and large cycle slips added to the three types of BDS satellites which separately belong to Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) are detected and corrected successfully by the proposed model.

A Novel Dual-Domain Filtering Method to Improve GNSS Performance Based on a Dynamic Model Constructed by TDCP

To overcome the strikes from the tremendous noise of pseudorange and the integer ambiguity of carrier phase observation, we developed a novel dual-domain filtering method that integrates the traditional observation- and an innovative position- domain filtering method. The novel method employed the conventional Hatch's smoother to improve the precision of pseudorange at the observation-domain filtering part. At the position- domain filtering part, the proposed method constructs an accurate dynamical model for KF (Kalman filter) or ARKF (adaptive-robust KF) that relies on the TDCP (time differential carrier phase) velocity measurement technology. To assess the effectiveness of the novel method, we compared it with other methods under various system integration by measured data from IGS (International GNSS Service) MGEX (Multi-GNSS Experiment) and dynamic data collected at CUMT (China University of Mining and Technology). The static numerical experiments obtained from IGS datasets show that the ARKF improves the precision of 60/84 and 55/84 situations' directions compared with the LS method based on OP (original pseudorange) and SP (smoothed pseudorange), respectively, and Hatch's smother improves the precision of all situations' directions. The experiment results prove that both types of observation- and position- domain filtering methods can improve positioning precision. Also, the novel dual-domain filtering improved the precision of 80/84 situations' directions compared with the LS method. Moreover, the dynamic experiment shows that the novel method can improve all of the situations' directions except the N (North) direction provided by KF base on SP under GC and U (Upon) direction provided by LS base on SP under GR. The average of improved accuracy is 0.212m, 0.346m, and 0.588m at the E (East), N, U direction and its corresponding average percentage of improved accuracy is 30.2%, 60.2%, and 26.7%, respectively, which proves the novel dual-domain filtering method provided the best performance among the tested algorithms.

Analysis of Tiangong-2 orbit determination and prediction using onboard dual-frequency GNSS data

Tiangong-2 is the first Chinese real space laboratory, launched into earth orbit with an altitude of approximately 393 km on September 15, 2016. Precise orbit determination (POD) is one of the essential conditions for conducting onboard scientific research. The precise orbit of Tiangong-2 is mainly determined by the reduced-dynamic method using space-borne global navigation satellite system (GNSS) data, which are collected by an onboard dual-frequency GNSS receiver. The in-flight performance of the receiver is first assessed in terms of tracking ability, code multipath errors and noise levels of code and carrier phase observations. Then, the effects of refined non-gravitational force models and GNSS antenna phase center variations (PCVs) on the POD are analyzed. The estimated empirical accelerations are substantially reduced by 45% in the along-track direction using a macro-model compared to that using a cannonball model for drag computation. The application of antenna PCVs correction leads to better consistency between reduced-dynamic and kinematic orbit solutions. Satellite laser ranging validation shows that the accuracy of Tiangong-2 precise orbits is 1.7 cm after using the improved reduced-dynamic method. Based on the orbit determination results, the quality of Tiangong-2 orbit predictions is assessed for periods without and with the refined non-gravitational force models. The use of the macro-model and high-quality density models for drag computation is shown to help improve orbit prediction quality.

An overview on GNSS carrier-phase time transfer research

global navigation satellite system (GNSS) carrier phase observations are two orders of higher accuracy than pseudo-range observations, and they are less affected by multipath besides. As a result, the time transfer accuracy can reach 0.1 ns, and the frequency transfer stability can reach 1×10−15 with carrier phase (CP) method, therefore CP method is considered the most accurate and promising time transfer technology. The focus of this paper is to present a comprehensive summary of CP method, with specific attention directed toward day-boundary clock jump, ambiguity resolution (AR), multi-system time transfer and real-time time transfer. Day-boundary clock jump is essentially caused by pseudo-range noise. Several approaches were proposed to solve the problem, such as continuously processing strategy, sliding batch and bidirectional filtering methods which were compared in this study. Additionally, researches on AR in CP method were introduced. Many scholars attempted to fix the single-difference ambiguities to improve the time transfer result, however, owing to the uncalibrated phase delay (UPD) was not considered, the current studies on AR in CP method were still immature. Moreover, because four GNSS systems could be used for time-transfer currently, which was helpful to increase the accuracy and reliability, the researches on multi-system time transfer were reviewed. What’s more, real-time time transfer attracted more attention nowadays, the preliminary research results were presented.

GPS satellite inter-frequency clock bias estimation using triple-frequency raw observations

This study proposes a unified uncombined model to estimate GPS satellite inter-frequency clock bias (IFCB) in both triple-frequency code and carrier-phase observations. In the proposed model, the formulae of both phase-based and code-based IFCBs are rigorously derived. Specifically, satellite phase-based IFCB refers to its time-variant part and it is modeled as a periodic function related to the sun–spacecraft–earth angle. A zero-mean condition of all available GPS satellites that support triple-frequency data is introduced to render satellite code-based IFCB estimable. Three months of data from 40 globally distributed stations of the International GNSS Service Multi-GNSS Experiment are used to test our method. The results show that the four-order periodic function is suitable for eliminating the 12-h, 6-h, 4-h, and 3-h periods that exist in the a posteriori phase residuals when no periodic function is used. For comparison, the geometry-free and ionosphere-free (GFIF) phase combination and differential code bias (DCB) products released by DLR (German Aerospace Center) and IGG (Institute of Geodesy and Geophysics, China) are also used to calculate the satellite phase-based and code-based IFCBs, respectively. The results show that (1) the average root mean square (RMS) of the phase-based IFCB difference between the proposed method and the GFIF phase combination is 4.3 mm; (2) the average RMS in the eclipse period increased by 50% compared with the average RMS in the eclipse-free period; (3) the mean monthly STD for code-based IFCB from the proposed method is 0.09 ns; and (4) the average RMS values of code-based IFCB differences between the proposed method and the DCB products released by DLR and IGG are 0.32 and 0.38 ns. This proposed model also provides a general approach for multi-frequency GNSS applications such as precise orbit and clock determination.

GNSS pseudorange and time‐differenced carrier phase measurements least‐squares fusion algorithm and steady performance theoretical analysis

In Global Navigation Satellite System (GNSS) community, pseudorange observables, without integer ambiguity, have large measurement noise, while carrier phase observables, with high measurement accuracy, have integer ambiguity, which restricts the direct use either of them for high-accuracy navigation and positioning. In this regard, fusing pseudorange and ambiguity-free time-differenced carrier phase (TDCP) is a popular data processing technique. In this Letter, the least-squares fusion is studied. A theoretical analysis of the steady performance of this fusion is conducted. A set of formulas of the steady performance is derived, based on which simulations are carried out for different pseudorange-carrier-phase precision ratios. Results showed that the steady accuracy of fusion pseudorange is about two orders of magnitude higher than that of the original pseudorange, and is close to that of carrier phase observables. Besides, the convergence speed and the comparison to the Hatch filter are also checked in the simulations.

CS detection and correction techniques for RTK positioning using single‐frequency GNSS receivers: trends and comparison

Nowadays, high-accuracy satellite-based positioning and navigation solutions are obtained using carrier-phase observations together with a differential correction scheme. A slip of only a few carrier-phase cycles can, however, bias observations causing a reduction in position accuracy. Therefore, reliable detection and handling of cycle slips (CSs) is essential for achieving high-accuracy positioning performance. Generally, it is harder to resolve CS in single-frequency observations, but the area deserves attention as differential positioning using low-cost single-frequency receivers is expected to be the key for many emerging mass-market applications. This study reviews and compares CS detection and correction techniques for single-frequency GNSS receivers with respect to their application for low-cost real-time kinematic (RTK) positioning. No prior performance comparison of CS detection and correction techniques exists; thereby, the authors have proposed four parameters to assess performance quality of CS resolution scheme for RTK positioning. Subsequently, an up-to-date list of existing techniques, classified according to the CS detection strategy, is reviewed with respect to measurement model, CS correction approach and test results. The techniques are also analysed for performance quality and it is observed that they do not conform to all parameters. Finally, conclusions are drawn and future research directions are proposed at the end.