Carrier Phase Techniques Research Articles

Improved performance of BDS-3 time and frequency transfer based on an epoch differenced model with receiver clock estimation

The carrier phase (CP) technique based on the BeiDou Global Satellite Navigation System (BDS-3) has proven to be a crucial spatial tool for remote time and frequency transfer. The current CP technique models the receiver clock offset as a white noise stochastic process and easily absorbs some unmodeled errors, thus compromising the time and frequency transfer performance. To further improve the performance of time and frequency transfer, a new BDS-3 receiver clock estimation algorithm based on the epoch difference (ED) model is presented, and the mathematical principles and applied modes are discussed. The algorithm makes full use of both observations of the current epoch and practical variations of the receiver clock offset, further improving the performance of time and frequency transfer. Five Multi-Global Navigation Satellite System Experiment network stations equipped with various types of receivers and antennas with dual-frequency BDS-3 signals were used to establish four time transfer links (i.e., AMC4–PTBB, BRUX–PTBB, OP71–PTBB, and WTZS–PTBB) to evaluate their effectiveness. The ED model improves all the four time links in terms of noise level, with improvements of 17.0%, 18.3%, 20.3%, and 5.9%, respectively, when compared with the results from a non-ED model. The ED model outputs were better than the raw solutions in terms of frequency stability at all time links, particularly for average time intervals (tau) < 1000 s. The mean improvement was 8.1% for AMC4–PTBB, 16.1% for BRUX–PTBB, 10.0% for OP71–PTBB, and 18.6% for WTZS–PTBB when the average time (tau) was less than 1000 s.

Time-Differenced Carrier Phase Technique for Precise Velocity Estimation on an Android Smartphone.

GNSS (Global Navigation Satellite System) receivers are not only able to accurately determine position, but also velocity, knowledge of which could be important in several applications. The most adopted technique for velocity estimation exploits the Doppler shift due to the relative motion between the signal source and the receiver. Alternatively, the TDCP (Time-Differenced Carrier Phase) technique, based on the differences between consecutive carrier-phase measurements, can be used. TDCP is theoretically able to achieve better performance compared with the Doppler-based approach, exploiting the high precision of a carrier-phase observable, and without suffering the ambiguity issue. The main objective of this study is to analyze TDCP performance on a smartphone GNSS chip. Smartphones GNSS receivers are usually characterized by noisy observables owing to the low quality of the antenna used; it is, therefore, interesting to compare the smartphone TDCP performance with that of the Doppler-based technique. To evaluate the benefits that TDCP can provide, especially in terms of the smartphone chip, these two approaches to velocity determination are compared using three different devices: a Novatel geodetic receiver, a u-blox multi-frequency receiver, and a Xiaomi Mi8 smartphone. The results demonstrate a performance degradation in the smartphone GNSS chip when TDCP is used, compared with the performance of higher-grade receivers. In fact, the Xiaomi Mi8 maximum errors are greater than those of the Novatel geodetic receiver, but they are still acceptable as they do not exceed 6 cm/s, making the TDCP technique a valid approach for advanced algorithms; indeed, TDCP velocity demonstrates a few mm/s accuracy with a smartphone. The application of a RAIM algorithm enables error reduction and the achievement of reliable information; the obtained solution reliability is about 89%.

Performance of global positioning system precise time and frequency transfer with integer ambiguity resolution

The Global Positioning System (GPS) carrier-phase technique is a widely used spatial tool for remote precise time and frequency transfer. However, the performance of traditional GPS time and frequency transfer has been limited because the ambiguity parameter is still the float solution. This study focuses on the performance of GPS precise time and frequency transfer with integer ambiguity resolution and discusses the corresponding mathematical model. Fractional-cycle bias (FCB) products were estimated using an ionosphere-free combination. The results show that the satellite wide-lane (WL) FCB products are stable, with a standard deviation (STD) of 0.006 cycles. The narrow-lane (NL) FCB products were estimated over 15 min with a STD of 0.020 cycles. More than 98% of the WL and NL residuals are smaller than 0.25 cycles, which helps to fix the ambiguity into integers during the time and frequency transfer. Subsequently, the performance of time transfers with integer ambiguity resolution at two time links between international laboratories was assessed in real-time and post-processing modes and compared. The results show that fixing the ambiguity into an integer in the real-time mode significantly decreases the convergence time compared with the traditional float approach. The improvement is ∼49.5%. The frequency stability of the fixed solution is notably better than that of the float solution. Improvements of 48.15% and 27.9% were determined for the IENG–USN8 and WAB2–USN8 time links, respectively.

Performance of Multi-GNSS Real-Time UTC(NTSC) Time and Frequency Transfer Service Using Carrier Phase Observations

The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and clock determinations has enabled GNSS time and frequency transfer using the CP technique to be performed in real-time mode, without any issues associated with latency. In this contribution, we preliminarily built the prototype system of real-time multi-GNSS time and frequency transfer service in National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS), which undertakes the task to generate, maintains and transmits the national standard of time and frequency UTC(NTSC). The comprehensive assessment of the availability and quality of the service system were provided. First, we assessed the multi-GNSS state space representation (SSR) correction generated in real-time multi-GNSS prototype system by combining broadcast ephemeris through a comparison with the GeoForschungsZentrum (GFZ) final products. The statistical results showed that the orbit precision in three directions was smaller than 6 cm for global positioning system (GPS) and smaller than approximately 10 cm for BeiDou satellite system (BDS). The root mean square (RMS) values of clock differences for GPS were approximately 2.74 and 6.74 ns for the GEO constellation of BDS, 3.24 ns for IGSO, and 1.39 ns for MEO. The addition, the GLObal NAvigation Satellite System (GLONASS) and Galileo satellite navigation system (Galileo) were 4.34 and 1.32 ns, respectively. In order to assess the performance of real-time multi-GNSS time and frequency transfer in a prototype system, the four real-time time transfer links, which used UTC(NTSC) as the reference, were employed to evaluate the performance by comparing with the solution determined using the GFZ final products. The RMS could reach sub-nanosecond accuracy in the two solutions, either in the SSR or GFZ solution, or in GPS, BDS, GLONASS, and Galileo. The frequency stability within 10,000 s was 3.52 × 10−12 for SSR and 3.47 × 10−12 for GFZ and GPS, 3.63 × 10−12 for SSR and 3.53 × 10−12 for GFZ for BDS, 3.57 × 10−12 for SSR and 3.52 × 10−12 for GFZ for GLONASS, and 3.56 × 10−12 for SSR and 3.48 × 10−12 for GFZ for Galileo.

Atomic clock modelling augmenting time and frequency transfer using carrier phase observation

The carrier phase (CP) technique based on the global positioning system is a widely applied spatial tool for precise time and frequency transfer. However, the traditional CP technique considers the receiver clock offset to be a white noise stochastic process, which introduces unknown errors into the model and thereby compromises time and frequency transfer performance. To improve the performance of the traditional CP technique, an atomic clock modelling CP time transfer (AMCP) method is proposed. A first-order, one variable grey model is employed to establish the receiver clock offset forecast model for the formation of prior information. The results show that the AMCP approach, which uses an atomic clock correlation between nearby epochs, outperformed the traditional CP technique. The noise level of the AMCP solution was improved by 7.7% for the NTSC–PT11 link, and the improvement for the other three time links were all ∼2.0%. The average improvement of the absolute jumps in the day-boundary discontinuities was ∼13.1%. Additionally, the frequency stability of the AMCP solution was improved, and the mean improvement was 10.2, 12.0, 10.7, and 8.3% for TLT4–PT11, USN9–PT11, WAB2–PT11, and NTSC–PT11, respectively.

Precise instantaneous velocimetry and accelerometry with a stand-alone GNSS receiver based on sparse kernel learning

Abstract A new method is proposed to determine instantaneous velocities and accelerations with a stand-alone GNSS receiver. It is based on sparse kernel learning theory. Kernel trick is employed to represent the kinematics, and L1 norm regularization is used to get sparse solution. Analytical models rather than data series are provided, with which velocity and acceleration at any instant could be calculated. Between-epoch displacements, provided by GNSS time difference carrier phase technique, are used as training data. Efficient numerical algorithms, such as the tri-diagonal matrix algorithm and the fast iterative shrinkage thresholding algorithm, are employed to deal with the between-epoch correlations in the data and the L1 norm regularization, respectively. The hyperparameters are optimized using general cross validation or Akaike information criterion, both tailored for the L1 norm regularization problem. Both simulation and real-data results show the superior performance of the proposed method compared to the conventional finite difference method. Especially for dynamic cases, the proposed method can better represent the real dynamics and provide high-accuracy velocimetry and accelerometry results.

Evaluation of carrier-phase precise time and frequency transfer using different analysis centre products for GNSSs

The carrier-phase (CP) technique, based on the global navigation satellite system (GNSS), has proved to be a useful spatial tool for remote and precise time transfer. In this study, we analysed the performance of CP time and frequency transfer with different GNSSs, using a satellite orbit and clock products collected from three analysis centres (ACs): CODE, WHU, and GFZ. From the time and frequency transfer experiments with six international time links, we concluded that the CP technique, based on different GNSSs, can all achieve a sub-nanosecond level accuracy for time and frequency transfer. Statistical analysis of the experiments shows that the global positioning system (GPS) solution can obtain the mean root mean square (RMS) of the six time links: 0.321 ns for cod (satellite products of CODE), 0.347 ns for whn (satellite products of WHU), and 0.288 ns for gbm (satellite products of GFZ). For Russian global navigation satellite system (GLONASS) solutions, the mean RMS is 0.306 ns for cod, 0.371 ns for whn, and 0.298 ns for gbm. In terms of emerging GNSSs, the Galileo can achieve a mean RMS of 0.293 ns for cod, 0.356 ns for whn, 0.295 ns for gbm, and the BeiDou navigation satellite system (BDS) can achieve a mean RMS of 0.294 ns for cod, 0.333 ns for whn, and 0.303 ns for gbm. The mean RMS is 0.288 ns for GPS, 0.298 ns for GLONASS, 0.295 ns for Galileo, and 0.303 ns for BDS. Regarding the three ACs, cod and gbm solutions show better performance than whn solutions. With respect to the frequency stability of CP technique by different GNSSs, Galileo and BDS are comparable to GPS at different averaging time intervals, while GLONASS is significantly worse than GPS.

Improving Galileo's Carrier-Phase Time Transfer Based on Prior Constraint Information

The Carrier-Phase (CP) technique used in the Global Positioning System (GPS) has proved to be a useful spatial tool for remote precise time transfer. Galileo is a Global Navigation Satellite System like GPS. However, currently, given the low number of satellites at any one observation epoch, Galileo's accuracy and continuity of time transfer leave much to be desired. To achieve better performance of time transfer for Galileo, this study has developed a new approach for Galileo CP time transfer, using prior constraint information such as precise coordinates and troposphere zenith delay constraints. The new approach was applied for precise time transfer in real-time mode and post-processed mode for short baseline and long baseline observations. For the short baseline time link in real-time mode, compared with the standard Galileo CP, the standard deviation improved by 51·4% for the troposphere zenith delay constraint, 47·6% for the station coordinates constraint, and 49·5% when considering both constraints simultaneously. At a 10,000 s time interval, in comparison to the standard CP, the three constraint approaches show stable results as well as improvements of nearly an order of magnitude. In post-processed mode, the constraint approach for Galileo time transfer showed little improvement compared to the standard CP technique for both the short baseline and long baseline time links.

Comparative study of GPS-TEC smoothing techniques

The availability of permanent global positioning system (GPS) stations makes the ionosphere monitoring and space weather studies more attainable. In order to obtain precise ionosphere total electron content (TEC) measurements, a smoothing technique has to be used. The objective of this research is to examine the accuracy and performance of two different TEC smoothing techniques; the carrier phase smoothed code and code levelled carrier phase techniques. GPS data from three stations in North America, located in different latitudes, are used. The accuracy of the smoothed TEC is compared with international GNSS service global ionospheric maps (IGS-GIM) and national oceanic and atmospheric administration (NOAA) ionospheric maps. The results reveal that the accuracy of the estimated TEC from the phase-smoothed code method depends upon the quality of data, number of observations used in the smoothing interval, receiver and satellite differential code biases (DCB). The levelled carrier phase method produces more calibrated TEC, however, with the influence of the systematic errors and the differential code biases.

Time-differenced carrier phases technique for precise GNSS velocity estimation

Classically, a stand-alone GNSS receiver estimates its velocity by forming the approximate derivative of consecutive user positions or more often by using the Doppler observable. The first method is very inaccurate, while the second one allows estimation of the order of some cm/s. The time-differenced carrier phase (TDCP) technique, which consists in differencing successive carrier phases, enables accuracies at the mm/s level. A study on the existing TDCP velocity estimation algorithms has revealed that the use of different broadcast ephemeris sets to calculate the satellite positions and clock offsets produces a discontinuity in the TDCP measurements that affects the velocity estimation. We propose a method to overcome this limitation based on the use of the same set of ephemeris to calculate the satellite positions and clock offsets at consecutive epochs. We describe in detail the TDCP algorithm used, and the complete implementation in MATLAB is included.

High precision GPS positioning with multiple receivers using carrier phase technique and sensor fusion

This paper presents a carrier phase differential GPS technique for vehicle navigation. The orientation and position of the vehicle can reliably be calculated by the proposed solutions. The developed methods are aided by inertial and magnetic sensors. They are designed for dead reckoning and to handle phase slip. Therefore these solutions can be applied when the set of the available satellites changes frequently. Extended Kalman filters perform state estimation. The paper also presents the low-cost hardware/software architecture of the navigation system. The effectiveness of the methods have been proven in real car and flight tests.

Carrier-Phase Differential Global Positioning System Navigation Filter for High-Altitude Spacecraft

A new navigation Kalman filter has been developed which uses carrier-phase differential Global Positioning System techniques in a framework that includes integer ambiguities to estimate the relative states of high-altitude, formation-flying spacecraft. This model-based approach to relative navigation allows spacecraft formations to use carrier-phase techniques above the Global Positioning System constellation. The filter uses dynamics models for the spacecraft orbits, receiver clocks, ionospheric total electron content, and Global Positioning System satellite residual position and clock errors. The process noise driving the orbital dynamics is separated into a common-mode part and lower intensity differential-mode part to better model how disturbances influence formations. The ionospheric total electron content model contains information that allows the filter to decide when to use the dual-frequency measurements to correct for the ionosphere and when to use them to aid in integer ambiguity resolution. The filter tracks undifferenced carrier-phase ambiguities, but still resolves the double-differenced integer ambiguities for use in the relative navigation solution. Monte Carlo simulations are used to evaluate the filter's performance. In geostationary scenarios, the filter's mean relative position error magnitude is 1.2 cm, and its maximum error magnitude is 6 cm. In high-Earth-orbit scenarios at an apogee distance of 18 Earth radii, the filter's mean error magnitude is 11 cm, and its maximum error magnitude is 54 cm. The correct integer ambiguities are resolved in one or two 30 s measurement steps in most cases.

Mapping Dilution of Precision (MDOP) and map-matched GPS

A novel method of map matching using the Global Positioning System (GPS) has been developed which uses digital mapping and height data to augment point position computation. This method reduces the error in position, which is a sum from several sources, including signal delay due to the ionosphere and atmosphere and until recently from ‘selective availability’ (S/A). S/A was imposed by the US military to degrade purposefully the accuracy of GPS, but was switched off on 2 May 2000, and is to be replaced with ‘regional denial capabilities in lieu of global degradation’ (Interagency GPS Executive Board, 2000). Taylor et al. (2001) describe the Road Reduction Filter (RRF) in detail. RRF is a method of detecting the correct road on which a vehicle is travelling. In the work described here, the position error vector is estimated in a formal least squares procedure, as the vehicle is moving. This estimate is a map-matched correction, that provides an autonomous alternative to DGPS for in-car navigation and fleet management. In this paper, a formula is derived for ‘Mapped Dilution of Precision’ (MDOP), defined as the theoretical ratio of position precision using map-matched corrections to that using perfect Differential GPS (DGPS) correction. This is shown to be purely a function of route geometry, and is computed for examples of basic road shapes. MDOP is favourable unless the route has less than a few degrees curvature for several kilometres. MDOP can thus provide an objective estimate of positioning precision to a vehicle driver. Precision estimates using MDOP are shown to agree well with ‘true’ positioning errors determined using high precision (cm) GPS carrier phase techniques. The exact location of a vehicle on a road is essential for accurate surveying applications. These include close range photogrammetry using digital video or still cameras and the verification of digital mapping by measured (GPS and other sensors) trajectories.

Road Reduction Filtering for GPS‐GIS Navigation

A novel method of map matching using the Global Positioning System (GPS) has been developed for civilian use, which uses digital mapping data to infer the systematic position errors of less than 100m which result largely from ‘selective availability’ (S/A) imposed by the US military. Selective availability was switched off on the 2nd of May 2000, and is to be replaced with ‘regional denial capabilities in lieu of global degradation’. The system tracks a vehicle on all possible roads (road centre‐lines) in a computed error region, then uses a method of rapidly detecting inappropriate road centre‐lines from the set of all those possible. This is called the Road Reduction Filter (RRF) algorithm. Point positioning is computed using C/A code pseudorange measurements direct from a GPS receiver. The least squares estimation is performed in the software developed for the experiment described in this paper. Virtual differential GPS (VDGPS) corrections are computed and used from a vehicle's previous positions, thus providing an autonomous alternative to DGPS for in‐car navigation and fleet management. Height aiding is used to augment the solution and reduce the number of satellites required for a position solution. Ordnance Survey (OS) digital map data was used for the experiment, i.e. OSCAR 1 m resolution road centre‐line geometry and Land Form PANORAMA 1:50,000, 50 m‐grid digital terrain model (DTM). Testing of the algorithm is reported and results are analysed. Vehicle positions provided by RRF are compared with the ‘true’ position determined using high precision (cm) GPS carrier phase techniques. It is shown that height aiding using a DTM and the RRF significantly improve the accuracy of position provided by inexpensive single frequency GPS receivers.

A GPS Attitude Determination System

In 1991 Trimble Navigation introduced a Global Positioning System (Gps)-based attitude determination receiver capable of 3-axis solutions with accuracy to several milliradians for airborne, sea and land platforms. This paper discusses the physical, architectural, and operational features of this receiver system. Analysis of system performance will also be reviewed for various configurations and user applications. The Trimble Navigation attitude determination receiver uses differential carrier phase techniques to determine azimuth, pitch and roll angles of a 3-antenna array. This product is designed to operate in a variety of user applications and to withstand rugged operating environments. Trimble Navigation has expanded its proven GPS sensor architecture to incorporate three independent RF sections and additional processing channels to measure and process the differential phase between antennas on two orthogonal baselines. Direct measurement of differential phase utilizing a common local oscillator provides highly accurate relative phase data. The navigation and attitude processor computes azimuth, pitch, and roll angles as well as position, velocity and time. The solution accuracy and stability statistics are sensitive to various parameters. Antenna baseline length, signal multipath, platform dynamics and filtering are investigated. Test data from static and various dynamic platforms are also presented.