Global Navigation Satellite System Carrier-phase Research Articles

Enhancing Real-Time Kinematic Relative Positioning for Unmanned Aerial Vehicles

Real-time kinematic (RTK) positioning of the global navigation satellite systems (GNSS) is used to provide centimeter-level positioning accuracy. There are several ways to implement RTK but a Kalman filter-based RTK is preferred because of its superior capability to resolve GNSS carrier phase integer ambiguities. However, the positioning performance of the Kalman filter-based RTK is often compromised by various factors when it comes to determining a precise relative position vector between moving unmanned aerial vehicles (UAVs) equipped with low-cost GNSS receivers and antennas, where the locations of both GNSS antennas are not accurately known and change over time. Some of the critical factors that lead to a high rate of incorrect resolutions of carrier phase integer ambiguities are measurement time differences between GNSS receivers, frequent cycle slips with high noise in code and carrier phase measurements, and an improper Kalman filter gain due to a newly risen satellite. In this paper, effective methods to deal with those factors to achieve a seamless Kalman filter-based RTK performance in moving UAVs are presented. Using our extensive 45 flight tests data sets, conducted over a duration of 3 to 12 min, the RTK positioning results showed that the root-mean-square position error (RMSE) decreased by up to 95.13%, with an average of 65.31%, and that the percentage of epochs that passed the ratio test, which is the most common method for validating double differenced carrier phase integer ambiguity resolution, increased by up to 130%, with an average of 23.54%.

Global Navigation Satellite System Spoofing Detection in Inertial Satellite Navigation Systems

The susceptibility of global navigation satellite systems (GNSSs) to interference significantly limits the possibility of their use. From the standpoint of possible consequences, the most dangerous interference is the so-called spoofing. Simultaneously, in most cases of GNSS use, an inertial navigation system (INS) or an attitude and heading reference system (AHRS) is also present on the board of mobile objects. In this regard, the research goal is to assess the possibility of detecting GNSS spoofing in inertial satellite navigation systems. This paper examines the method for detecting GNSS spoofing by combining a pair of commercially available GNSS receivers and antennas with an INS or AHRS. The method is based on a comparison of the double differences of GNSS carrier phase measurements performed by receivers under conditions of resolved integer ambiguity and the values of the range double differences predicted using an INS. GNSS carrier phase integer ambiguity can be resolved using a strapdown inertial navigation system (SINS) or AHRS data. The mathematical model of GNSS phase difference measurements and the SINS-predicted satellite range differences model are given. The proposed algorithm calculates the moving average of the residuals between the SINS-predicted satellite range double differences and the measured GNSS carrier phase double differences. The primary criterion for spoofing detection is the specified threshold excess of the moving average of the double difference residuals. Experimental studies are performed using simulation and hardware-in-the-loop simulation. The experimental results allow us to evaluate the efficiency of the proposed approach and estimate the potential characteristics of the spoofing detection algorithm based on it.

100 Picosecond/Sub-10−17 Level GPS Differential Precise Time and Frequency Transfer

A Global Navigation Satellite System (GNSS) is a high-precision method for comparing clocks and time transfer. The GNSS carrier phase can provide more precise observable information than pseudorange. However, the carrier phase is ambiguous, and only pseudorange can provide the absolute time difference between two clocks. In our study, by taking full advantage of GNSS pseudorange and carrier-phase observables, a differential precise time transfer (DPT) method with a clustering constraint was employed to estimate the time difference between two clocks, aiming to achieve accurate and precise time and frequency transfer. Using this method, several time transfer results were analyzed for different baselines. For the common clock experiment, the time transfer results showed good consistency across different days, with an intra-day accuracy of within 20 ps. Furthermore, we evaluated the self-consistency of DPT using closure among three stations. DPT closure of the three stations had a peak-to-peak value of closure of about 25 ps. The closure did not change over time, indicating the self-consistency of the DPT processing in time transfer. Moreover, our results were compared to station clock solutions provided by the International GNSS Service (IGS), and the standard deviations (STDs) of the four baselines were all less than 100 ps within one month, confirming the time and frequency stability of the DPT method. In addition, we found that the time stability of DPT was less than 20 ps within one week. As for frequency stability, DPT achieved a 10−16 level of modified Allan deviation (MDEV) at an averaging time of about 1 day and a sub-10−17 level at an averaging time of one week.

Enhancing RTK Performance in Urban Environments by Tightly Integrating INS and LiDAR

High-precision and continuous positioning is a fundamental requirement for intelligent navigation applications. Nowadays, the global navigation satellite system (GNSS) real-time kinematic (RTK) technique is recognized as a feasible solution to provide precise positioning services, but its accuracy is susceptible to signal attenuation and will deteriorate drastically in urban environments. Fortunately, the low-cost inertial measurement units (IMU) and light detection and ranging (LiDAR) are available in modern vehicle systems and could be integrated to enhance GNSS performance. In this contribution, aiming to improve RTK performance in GNSS-challenging environments, we propose a tightly coupled RTK/Inertial navigation system (INS)/LiDAR integration method. The GNSS double-differenced pseudorange and carrier-phase measurements, IMU data, and LiDAR plane features are fused at the raw-data level via an extended Kalman filter (EKF). Both simulated tests and real-world experiments were conducted to evaluate the effectiveness of the proposed method. The results indicate that the proposed method is able to achieve sub-decimeter-level accuracy in GNSS-challenging environments, with the improvements of (51.8%, 82.0%, 75.0%) and (53.9%, 71.0%, 41.5%) compared to state-of-the-art LIO-SAM and loosely coupled GNSS/INS/LiDAR integration. Meanwhile, the ambiguity fixing rate could be improved by more than 10% with the assistance of LiDAR plane features. Similar improvements can also be achieved in velocity and attitude estimation.

A Robust Android Gnss Rtk Positioning Scheme Using Factor Graph Optimization

The release of raw Android global navigation satellite system (GNSS) measurements makes high-precision positioning achievable with low-cost smart devices. Affected by low-cost GNSS chips, linearly polarized antennas, and complex observation environments, Android GNSS observations usually contain a large number of outliers, which significantly degrade their positioning precision and reliability. To address this issue, a robust real-time kinematic (RTK) scheme with sliding window-based factor graph optimization (FGO) was developed. The scheme adopts the GNSS carrier-phase sliding window marginalization, models the carrier-phase ambiguity as a random constant, and incorporates multiple robust estimation strategies. Vehicle kinematic positioning validations were carried out in both open-sky and complex urban environments using representative Xiaomi Mi8 and Huawei P40 smartphones. Using the proposed scheme, the root mean square (rms) of the positioning errors in the east, north, and up components in the open-sky environments is 0.18, 0.13, and 0.38 m, respectively. In complex urban environments, the rms of the positioning precisions in the east, north, and up components was as decent as 1.42, 1.97, and 2.63 m, respectively.

A Comprehensive Analysis of Smartphone GNSS Range Errors in Realistic Environments.

Precise positioning using smartphones has been a topic of interest especially after Google decided to provide raw GNSS measurement through their Android platform. Currently, the greatest limitations in precise positioning with smartphone Global Navigation Satellite System (GNSS) sensors are the quality and availability of satellite-to-smartphone ranging measurements. Many papers have assessed the quality of GNSS pseudorange and carrier-phase measurements in various environments. In addition, there is growing research in the inclusion of a priori information to model signal blockage, multipath, etc. In this contribution, numerical estimation of actual range errors in smartphone GNSS precise positioning in realistic environments is performed using a geodetic receiver as a reference. The range errors are analyzed under various environments and by placing smartphones on car dashboards and roofs. The distribution of range errors and their correlation to prefit residuals is studied in detail. In addition, a comparison of range errors between different constellations is provided, aiming to provide insight into the quantitative understanding of measurement behavior. This information can be used to further improve measurement quality control, and optimize stochastic modeling and position estimation processes.

Resilient Smartphone Positioning Using Native Sensors and PPP Augmentation

<h3>Abstract</h3> With the ubiquitous use of global navigation satellite system (GNSS) receivers, navigation solutions from smartphones have become integrated in various applications throughout our lives. These ultra-low-cost GNSS receivers have the drawbacks of insufficient observations and poorer signal reception quality than higher-cost receivers. Since 2016, smartphones using the Android operating system have been able to output raw GNSS pseudorange and carrier-phase measurements, thereby enabling improved navigation capabilities. The realm of sensor fusion is also being explored by using smartphone sensors, including inertial measurement units (IMUs), cameras, and other fusion techniques. The research presented herein deployed only IMU and GNSS sensors native to existing smartphones and achieved a standalone solution using PPP/IMU integration that outperformed standard techniques. In open-sky vehicle experiments, the sensor integration algorithm achieved 1.6-m horizontal RMS, thus reducing 80% of horizontal errors in GNSS-challenging environments through a tightly coupled GNSS-PPP solution that is yet to appear in publications.

Continuous estimation of coseismic and early postseismic slip phenomena via the GNSS carrier phase to fault slip approach: a case study of the 2011 Tohoku-Oki sequence

The transition process from coseismic to early postseismic phenomena within a half-day remains a significant topic for understanding the slip budget and friction properties of the fault. However, the investigation of this phase has undergone limited advancement. This is mainly due to the lack of precision pertaining to the Global Navigation Satellite System (GNSS) analysis caused by difficulty of separation between fault slip and other unknown parameters such as tropospheric delay. Therefore, we propose an alternative approach (phase-to-slip; PTS) that detects fault slip directly from GNSS carrier phase variation without conventional positioning. Since the PTS simultaneously estimates fault slip and other unknowns, we can quantitatively evaluate their separation accuracy and contribution in the estimation. This study attempts to continuously estimate the coseismic and early postseismic slip of the 2011 Tohoku-Oki sequence using the PTS method. We analyzed 1-Hz carrier phase data for approximately 2 h before and after the mainshock origin (2011/03/11/05:46UTC). As a result, we successfully obtained the coseismic slip of the Mw9.0 mainshock and two major aftershocks in the off-Ibaraki (Mw7.8) and off Iwate (Mw7.4) regions. For all three events, the estimated slip distribution, equivalent moment magnitude, and calculated displacement field well agreed with those from the conventional positioning. Additionally, our results suggest postseismic slip mainly in the downdip area adjacent to the mainshock rupture. We obtained three major slip areas around the downdip region near Aomori, Iwate, and Miyagi. The estimated slip amount reaches approximately 0.1–0.2 m in 34 min immediately after the mainshock. The equivalent seismic moment of the slip areas near Iwate and Miyagi were approximately Mw7.4. This amount is similar or slightly greater than the estimations based on conventional positioning. Significant overlap is observed in the locations of the slip areas. In this manner, PTS continuously detected a series of coseismic and early postseismic slips with timescale ranging from a few minutes to an hour. Our results demonstrate the capability of the PTS method for broadband fault slip monitoring and its potential contribution to the investigation of early postseismic phenomena.

Continuous and Precise Positioning in Urban Environments by Tightly Coupled Integration of GNSS, INS and Vision

Accurate, continuous and seamless state estimation is the fundamental module for intelligent navigation applications, such as self-driving cars and autonomous robots. However, it is often difficult for a standalone sensor to fulfill the demanding requirements of precise navigation in complex scenarios. To fill this gap, this letter proposes to exploit the complementariness of the global navigation satellite system (GNSS), inertial measurement unit (IMU) and vision via a tightly coupled integration method, aiming to achieve continuous and accurate navigation in urban environments. Specifically, the raw GNSS carrier phase and pseudorange measurements, IMU data, and visual features are directly fused at the observation level through a centralized Extended Kalman Filter (EKF) to make full use of the multi-sensor information and reject potential outlier measurements. Furthermore, the widely used high-precision GNSS models including precise point positioning (PPP) and real-time kinematic (RTK) are unified in the proposed integrated system to increase usability and flexibility. We validate the performance of the proposed method on several challenging datasets collected in urban canyons and compare against the loosely coupled and state-of-the-art methods.

Using a Moving Antenna to Improve GNSS/INS Integration Performance Under Low-Dynamic Scenarios

The integration of inertial navigation system (INS) and global navigation satellite system (GNSS) with a single antenna is widely applied in consumer-level vehicle navigation. However, it is challenging for a low-cost single-antenna GNSS/INS integrated system to provide reliable, consistent state estimation under low-dynamic scenarios (e.g., low-speed robotic applications) as the limited dynamics could lead to degradation of the system observability. We propose a novel moving-antenna GNSS/INS integration method, in which the antenna is designed to perform specific motions on the platform during vehicle maneuver, thus to improve the system observability in degraded conditions, bringing about the advantage of multi-antenna GNSS using a single antenna. It turns out that a moving antenna with a maximum speed of just 0.15 m/s would improve the system performance dramatically by applying raw GNSS carrier phase observations into the integration. In the proposed method, firstly, a moving-antenna fast initial alignment algorithm is developed, which enables the system to perform instantaneous initial alignment in static. Secondly, for GNSS/INS integration filter, the moving-antenna scheme improves the heading angle estimation accuracy by more than 50% under typical dynamic scenarios, achieving comparable performance to dual-antenna GNSS/INS integration. This work shows that it is possible and even beneficial to continuously change the inter-sensor transformation in an integrated navigation system.

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.

GNSS Odometry: Precise Trajectory Estimation Based on Carrier Phase Cycle Slip Estimation

This letter proposes a highly accurate trajectory estimation method for outdoor mobile robots using global navigation satellite system (GNSS) time differences of carrier phase (TDCP) measurements. By using GNSS TDCP, the relative 3D position can be estimated with millimeter precision. However, when a phenomenon called cycle slip occurs, wherein the carrier phase measurement jumps and becomes discontinuous, it is impossible to accurately estimate the relative position using TDCP. Although previous studies have eliminated the effect of cycle slip using a robust optimization technique, it was difficult to completely eliminate the effect of outliers. In this letter, we propose a method to detect GNSS carrier phase cycle slip, estimate the amount of cycle slip, and modify the observed TDCP to calculate the relative position using the factor graph optimization framework. The estimated relative position acts as a loop closure in graph optimization and contributes to the reduction in the integration error of the relative position. Experiments with an unmanned aerial vehicle showed that by modifying the cycle slip using the proposed method, the vehicle trajectory could be estimated with an accuracy of 5-30 cm using only a single GNSS receiver, without using any other external data or sensors.

Fault-Free Protection Level Equation for CLAS PPP-RTK and Experimental Evaluations.

Centimeter level augmentation system (CLAS) of the quasi-zenith satellite system (QZSS) is the first precise point positioning-real time kinematic (PPP-RTK) augmentation system of the global navigation satellite system (GNSS), which is currently providing services for Japan. CLAS broadcasts the state-space representation of correction messages along with integrity messages regarding satellite faults and the quality index of each correction. In other GNSS augmentation systems, such as the space-based augmentation system (SBAS) of GNSS, the quality indices of correction messages are used to generate fault-free protection levels that represent a position bound containing a true user position with a probability of missed detections. Although the protection level equations are well defined for the SBAS, a protection level equation for the CLAS PPP-RTK service has not been rigorously discussed in the literature. This paper proposes a fault-free protection level equation for the PPP-RTK methods that considers the probability of correct integer ambiguity fixes in the GNSS carrier phase measurements as well as the CLAS correction quality messages. The computed protection levels with position errors were experimentally compared by processing the GNSS measurements from the GNSS Earth Observation Network (GEONET) stations in Japan and the L6 messages from the CLAS broadcast using the virtual reference station-real time kinematic (VRS-RTK) techniques. Our results, based on the GEONET dataset spanning 7 days, showed that the computed protection levels using the proposed equations were larger than the position errors for all epochs. In the dataset, the RMS errors of the CLAS VRS-RTK position were 4.6 and 14 cm in the horizontal and vertical directions, respectively, whereas the horizontal protection levels ranged from 25 cm to 2.3 m and the vertical protection levels ranged from 50 cm to 5.2 m based on fault-free integrity risk of .

Noises in Double-Differenced GNSS Observations

Precise data processing from the Global Navigation Satellite Systems (GNSS) reference station network is mainly based on a combination of double-differenced carrier phase and code observations. This approach allows most of the measurement errors to be removed or reduced and is characterized as the most accurate method. However, creating observation differences between two receivers and two satellites increases the measurement noise of the observations by a factor of 2. As a result, it increases the impact of the incorrect definition of the noise characteristic on the results of the estimation of the unknowns in the positioning model. This is especially important in Multi-GNSS solutions, which integrate measurements from different systems, for which the stochastic parameters of observation may differ significantly. In this paper, the authors prepared a complex analysis of the noise type in double-differenced GNSS (GPS, GLONASS and Galileo) observations, both carrier phase and code ones, with a 1 s sampling interval. The Autocorrelation Function (ACF) method, the Lomb–Scargle (L-S) periodogram method, and the Allan variance (AVAR) method were used. The results that were obtained for the weekly set of measurement data showed that, depending on the system and type of observation, the noise level and its type are significantly different. Among the code measurements, the lowest noise levels were obtained for the GPS C5Q and Galileo C7Q/C8Q observations, with the standard deviations not exceeding ±10 cm, while the noisiest observations were for the GLONASS C1C and C2C signals, which had standard deviations of about ±90 cm and ±45 cm, respectively. For the carrier phase observations, each signal type was characterized by very similar noise levels of ±1.5–3.5 mm. The ACF analysis showed that 1 Hz double-differenced GNSS data can only be treated as being not correlated to time for carrier phase observations; for code observations, an irrelevant autocorrelation may be considered for measurement intervals greater than 20 s. Depending on the GNSS signals, the spectral index k varies in a range from −1.3 to −0.2 for code data and k = 0.0 in the case of phase data. Using the modified Allan deviation (MDEV) allows for specific noise types for each signal and GNSS system to be determined. All of the code observations were characterized by either flicker PM or white PM. In the case of the phase observations, they were all uniquely characterized by white PM (GPS and Galileo or by white PM and flicker PM (GLONASS).

Kalman–Hatch dual‐filter integrating global navigation satellite system/inertial navigation system/on‐board diagnostics/altimeter for precise positioning in urban canyons

For improved positioning in urban canyons, this study proposes an efficient dual-filter method integrating multi-constellation global navigation satellite system (GNSS), an inertial navigation system (INS), a barometric altimeter and an on-board diagnostics (OBD) module. The proposed method consists of a position-domain (PD) Hatch filter and velocity Kalman filter. The Hatch filter is operated as the main positioning filter and the Kalman filter is operated as a sub-filter to aid the main filter for the occasional GNSS outages. The Hatch filter combines barometric altimeter measurements with GNSS pseudorange and carrier phase measurements. The Kalman filter integrates the inertial measurement unit (IMU) measurements with GNSS Doppler shift and OBD speed measurements. A semi-simulation method is applied for the accurate performance evaluation of the proposed method compared with the several conventional methods under deficient satellite visibility, multipath errors and cycle slips caused by urban canyons. By the test results, it is demonstrated that the proposed method can bound the positioning errors effectively by utilising low-cost all-weather sensors. The RMSEs of the proposed Kalman–Hatch dual-filter algorithm were shown as 0.05, 0.19 and 0.11 m, respectively, and the maximum errors were shown as 0.16, 0.26 and 0.40 m, respectively, in the east, north and upward directions.

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

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

Indoor Carrier Phase Positioning Technology Based on OFDM System.

Carrier phase measurement is a ranging technique that uses the receiver to determine the phase difference between the received signal and the transmitted signal. Carrier phase ranging has a high resolution; thus, it is an important research direction for high precision positioning. It is widely used in global navigation satellite systems (GNSS) systems but is not yet commonly used inwireless orthogonal frequency division multiplex (OFDM) systems. Applying carrier phase technology to OFDM systems can significantly improve positioning accuracy. Like GNSS carrier phase positioning, using the OFDM carrier phase for positioning has the following two problems. First, multipath and non-line-of-sight (NLOS) propagation have severe effects on carrier phase measurements. Secondly, ambiguity resolution is also a primary issue in the carrier phase positioning. This paper presents a ranging scheme based on the carrier phase in a multipath environment. Moreover, an algorithm based on the extended Kalman filter (EKF) is developed for fast integer ambiguity resolution and NLOS error mitigation. The simulation results show that the EKF algorithm proposed in this paper solves the integer ambiguity quickly. Further, the high-resolution carrier phase measurements combined with the accurately estimated integer ambiguity lead to less than 30-centimeter positioning error for 90% of the terminals. In conclusion, the presented methods gain excellent performance, even when NLOS error occur.

GNSS Precise Relative Positioning Using A Priori Relative Position in a GNSS Harsh Environment.

To enable Global Navigation Satellite System (GNSS)-based precise relative positioning, real-time kinematic (RTK) systems have been widely used. However, an RTK system often suffers from a wrong integer ambiguity fix in the GNSS carrier phase measurements and may take a long initialization time over several minutes, particularly when the number of satellites in view is small. To facilitate a reliable GNSS carrier phase-based relative positioning with a small number of satellites in view, this paper introduces a novel GNSS carrier phase-based precise relative positioning method that uses a fixed baseline length as well as heading measurements in the beginning of the operation, which allows the fixing of integer ambiguities with rounding schemes in a short time. The integer rounding scheme developed in this paper is an iterative process that sequentially resolves integer ambiguities, and the sequential order of the integer ambiguity resolution is based on the required averaging epochs that vary for each satellite depending on the geometry between the baseline and the double difference line-of-sight vectors. The required averaging epochs with respect to various baseline lengths and heading measurement uncertainties were analyzed through simulations. Static and dynamic field tests with low cost GNSS receivers confirmed that the positioning accuracy of the proposed method was better than 10 cm and significantly outperformed a conventional RTK solution in a GNSS harsh environment.

Cooperative Positioning for V2X Applications Using GNSS Carrier Phase and UWB Ranging

With the evolution of communication techniques, vehicle-to-vehicle (V2V) communications with low latency and high speed facilitate the study of cooperative positioning (CP) methods for vehicular applications. However, the current CP methods are incapable of bridging the gap between positioning accuracy required for crucial vehicular applications and what CP provides. The CP method with carrier-phase-based Real Time Kinematic (RTK) principle becomes a potential candidate for high-precision positioning. In this letter, we reveal a cooperative navigation filtering (CNF) algorithm fusing Global Navigation Satellite System (GNSS) data and Ultra-wideband (UWB) ranging data to achieve decimeter-level positioning. The main novelty of the proposed CP method is to include centimeter-level GNSS carrier phase information and derive a collaborative ambiguity resolution model. Numerical results and comparisons validate the feasibility and superiority of proposed method.

Influence of Precise Products on the Day-Boundary Discontinuities in GNSS Carrier Phase Time Transfer.

Global navigation satellite system (GNSS) precise point positioning (PPP) has been widely used for high-precision time and frequency transfer. However, the day-boundary discontinuities at the boundary epochs of adjacent days or batches are the most significant obstacle preventing PPP from continuous time transfer. The day-boundary discontinuities in station estimates and time comparisons are mainly caused by the code-pseudorange noise during the analysis of observation data in daily batches, where the absolute clock offset is determined by the average code measurements. However, some discontinuities with amplitudes even more than 0.15 ns may still appear in station clock estimates and time comparisons, although several methods had been proposed to remove such discontinuities. The residual small amplitude of the day-boundary discontinuities in some PPP station clock estimates and time comparisons through new GNSSs like Galileo seems larger, especially using precise clock products with large discontinuities. To further understand the origin of the day-boundary discontinuities, the influence of GNSS precise products on the day-boundary discontinuities in PPP station clock estimates and time comparisons is investigated in this paper. Ten whole days of Multi-GNSS Experiment (MGEX) from modified Julian date (MJD) 59028 to 59037 are used as the observation data. For a comparative analysis, the station clock estimates are compared with global positioning system (GPS) and Galileo observations through PPP and network solutions, separately. The experimental results show that the daily discontinuities in current combined GPS final and rapid clock products are less than 0.1 ns, and their influence on the origin of day-boundary discontinuities in PPP station clock estimates and time comparison are statistically negligible. However, the daily discontinuities in individual Analysis Centers (ACs) GPS products are more extensive, and their influence on the origin of the day-boundary discontinuities in GPS PPP station clock estimates cannot be ignored. The day-boundary discontinuities demonstrate random walk noise characteristics and deteriorate the station clocks’ long-term frequency stability, especially at an average time of more than one day. Although Galileo clock daily discontinuities are different from those of GPS, their influence on the day-boundary discontinuities in station clock estimates is nearly similar to the GPS PPP. The influence of daily discontinuities of Galileo clocks on PPP time comparison is similar to GPS and is not particularly critical to time comparison. However, combined and weighted MGEX products should be developed or Galileo IPPP should be used for remote comparison of high-stability clocks.