Time-differenced Carrier Phase Measurements Research Articles

Smoothened Absolute Kinematic Position Estimation Of Leo Satellite Using Gps Observables

In this paper, our objective is to use the navigation signals (pseudorange and carrier phase measurements) from GPS to kinematically estimate the absolute position of a low Earth orbit satellite and its receiver clock biases. GPS observables can estimate the precise position of a satellite in near real time. The GPS satellite navigation file is downloaded from Scripps Orbit and Permanent Array Centre (SOPAC) website for starting epoch of 01-01-2016 00:00 UT. The observables are then generated for a Low-Earth-Orbit (LEO) satellite at an altitude of 901.4 km. The absolute position is estimated using pseudorange measurements. The accuracies obtained are (5.68 8.04 6.17) m in ECEF frame. This estimated absolute position is then smoothened with the time-differenced carrier phase measurements. The Kalman filter gains are computed in near real time. The smoothened accuracies obtained are (2.24 2.60 2.6982) m in ECEF frame, thus showing improved estimated absolute position accuracy.

GNSS precise positioning for smartphones based on the integration of factor graph optimization and solution separation

Currently, the global navigation satellite system on smartphones suffers from frequent outliers (faults) in the measurements, limiting their precise positioning applications. To mitigate, the factor-graph optimization (FGO) method is used, where the Doppler and time-differenced carrier-phase (TDCP) measurements determine the velocities. However, their estimations are vulnerable since the Doppler measurements are inaccurate, while the TDCP measurements suffer from frequent cycle slips. Statistical testing methods can be used to exclude measurement outliers, but they have high volumes of false alarms and missed detections. In this study, we propose an improved scheme of FGO with a solution separation (SS) test to improve smartphone precise positioning. After excluding measurement outliers with the SS test for TDCP and time-differenced pseudorange observation models, we apply an improved FGO scheme for positioning. We conducted an experiment with Xiaomi Mi 8 and Google Pixel 5, showing that our method outperforms the conventional FGO and Kalman filtering methods.

An improved TDCP-GNSS/INS integration scheme considering small cycle slip for low-cost land vehicular applications

An improved global navigation satellite system (GNSS)/inertial navigation system (INS) tightly coupled scheme based on a time-differenced carrier phase (TDCP) was proposed for a low-cost vehicle navigation system. The proposed scheme aims to improve the navigation performance and computational efficiency of the system for low-cost GNSS receivers and low-accuracy INS. The traditional measurement model based on the TDCP has either high accuracy with a large computational load or high efficiency with low accuracy. Considering both the positioning accuracy and computational burden, an accurate and efficient measurement model was derived in this paper. In positioning based on the carrier phase, it is an indispensable task to handle the cycle slips, especially small ones. However, the cycle slip of a certain moment only contaminates the current TDCP measurement, but not the subsequent TDCP measurements. Based on this characteristic of the TDCP measurement, a novel cycle slip processing strategy was proposed for the TDCP-GNSS/INS integration scheme, in which cycle slip is directly handled as a gross error with a robust extended Kalman filter (EKF). The vehicular test has been conducted to evaluate the performance of the improved TDCP-GNSS/INS integration scheme. Experiment results show: (a) compared with the traditional position error parameter-based measurement model, the proposed measurement model can improve the accuracy of the horizontal and vertical position by 58.4% and 12.5%, respectively. Compared with the traditional velocity error parameter-based measurement model, the proposed measurement model does not improve the positioning accuracy, but improves the computational efficiency by 25.2%. (b) The strategy of treating cycle slip as a gross error is feasible in the TDCP-GNSS/INS tightly coupled navigation system. Although a small cycle slip can seriously affect the positioning performance of the system, the robust EKF can effectively avoid the long-term harm caused by small cycle slips.

The Design a TDCP-Smoothed GNSS/Odometer Integration Scheme with Vehicular-Motion Constraint and Robust Regression

Global navigation satellite system (GNSS) is widely regarded as the primary positioning solution for intelligent transport system (ITS) applications. However, its performance could degrade, due to signal outages and faulty-signal contamination, including multipath and non-line-of-sight reception. Considering the limitation of the performance and computation loads in mass-produced automotive products, this research investigates the methods for enhancing GNSS-based solutions without significantly increasing the cost for vehicular navigation system. In this study, the measurement technique of the odometer in modern vehicle designs is selected to integrate the GNSS information, without using an inertial navigation system. Three techniques are implemented to improve positioning accuracy; (a) Time-differenced carrier phase (TDCP) based filter: A state-augmented extended Kalman filter is designed to incorporate TDCP measurements for maximizing the effectiveness of phase-smoothing; (b) odometer-aided constraints: The aiding measurement from odometer utilizing forward speed with the lateral constraint enhances the state estimation; the information based on vehicular motion, comprising the zero-velocity constraint, fault detection and exclusion, and dead reckoning, maintains the stability of the positioning solution; (c) robust regression: A weighted-least-square based robust regression as a measurement-quality assessment is applied to adjust the weightings of the measurements adaptively. Experimental results in a GNSS-challenging environment indicate that, based on the single-point-positioning mode with an automotive-grade receiver, the combination of the proposed methods presented a root-mean-square error of 2.51 m, 3.63 m, 1.63 m, and 1.95 m for the horizontal, vertical, forward, and lateral directions, with improvements of 35.1%, 49.6%, 45.3%, and 21.1%, respectively. The statistical analysis exhibits 97.3% state estimation result in the horizontal direction for the percentage of epochs that had errors of less than 5 m, presenting that after the intervention of proposed methods, the positioning performance can fulfill the requirements for road level applications.

A Low-Cost, High-Precision Vehicle Navigation System for Deep Urban Multipath Environment Using TDCP Measurements.

In this study, we developed a low-cost, high-precision vehicle navigation system for deep urban multipath environments using time-differenced carrier phase (TDCP) measurements. Although many studies are being conducted to navigate autonomous vehicles using the global positioning system (GPS), it is difficult to obtain accurate navigation solutions due to multipath errors in urban environments. Low-cost GPS receivers that determine the solution based on pseudorange measurements are vulnerable to multipath errors. We used carrier phase measurements that are more robust for multipath errors. Without correction information from reference stations, the limited information of a low-cost, single-frequency receiver makes it difficult to quickly and accurately determine integer ambiguity of carrier phase measurements. We used TDCP measurements to eliminate the need to determine integer ambiguity that is time-invariant and we combined TDCP-based GPS with an inertial navigation system to overcome deep urban multipath environments. Furthermore, we considered a cycle slip algorithm for its accuracy and a multi-constellation navigation system for its availability. The results of dynamic field tests in a deep urban area indicated that it could achieve horizontal accuracy of at the submeter level.

Dual-frequency carrier smoothed code filtering with dynamical ionospheric delay modeling

In GNSS applications, carrier-smoothed-code is a widely used technique to combine code pseudo-range and carrier phase measurements. A dynamical ionospheric delay modeling method is proposed based on Kalman filter and least-squares theory. The level of the process noise is adaptively tuned along with the real-time KF state estimation, based on the online variance component estimation method. Meanwhile, the correlations of the time differenced carrier phase measurements are considered. This approach avoids overly optimistically evaluating the estimate and improves the transient accuracy of the estimates. A real GPS dataset is employed to check the performance of the proposed method under different conditions. The results show that the new algorithm can model the ionospheric delay variation well with different sampling intervals or even in ionospheric abnormal environment. The positioning accuracy can be confirmed, about 21%, 35% and 16% better are obtained in the N, E, and U direction than raw dataset.

Benefits of Multi-Constellation/Multi-Frequency GNSS in a Tightly Coupled GNSS/IMU/Odometry Integration Algorithm.

Localization algorithms based on global navigation satellite systems (GNSS) play an important role in automotive positioning. Due to the advent of autonomously driving cars, their importance is expected to grow even further in the next years. Simultaneously, the performance requirements for these localization algorithms will increase because they are no longer used exclusively for navigation, but also for control of the vehicle’s movement. These requirements cannot be met with GNSS alone. Instead, algorithms for sensor data fusion are needed. While the combination of GNSS receivers with inertial measurements units (IMUs) is a common approach, it is traditionally executed in a single-frequency/single-constellation architecture, usually with the Global Positioning System’s (GPS) L1 C/A signal. With the advent of new GNSS constellations and civil signals on multiple frequencies, GNSS/IMU integration algorithm performance can be improved by utilizing these new data sources. To achieve this, we upgraded a tightly coupled GNSS/IMU integration algorithm to process measurements from GPS (L1 C/A, L2C, L5) and Galileo (E1, E5a, E5b). After investigating various combination strategies, we chose to preferably work with ionosphere-free combinations of L5-L1 C/A and E5a-E1 pseudo-ranges. L2C-L1 C/A and E5b-E1 combinations as well as single-frequency pseudo-ranges on L1 and E1 serve as backup when no L5/E5a measurements are available. To be able to process these six types of pseudo-range observations simultaneously, the differential code biases (DCBs) of the employed receiver need to be calibrated. Time-differenced carrier-phase measurements on L1 and E1 provide the algorithm with pseudo-range-rate observations. To provide additional aiding, information about the vehicle’s velocity obtained by an odometry model fed with angular velocities from all four wheels as well as the steering wheel angle is incorporated into the algorithm. To evaluate the performance improvement provided by these new data sources, two sets of measurement data are collected and the resulting navigation solutions are compared to a higher-grade reference system, consisting of a geodetic GNSS receiver for real-time kinematic positioning (RTK) and a navigation grade IMU. The multi-frequency/multi-constellation algorithm with odometry aiding achieves a 3-D root mean square (RMS) position error of / in these data sets, compared to / for the single-frequency GPS algorithm without odometry aiding. Odometry is most beneficial to positioning accuracy when GNSS measurement quality is poor. This is demonstrated in data set 1, resulting in a reduction of the horizontal position error’s 95% quantile from without odometry aiding to with odometry aiding.

An enhanced tightly-coupled integrated navigation approach using phase-derived position increment (PDPI) measurement

In this paper, an enhanced tightly coupled navigation approach using pseudorange, Doppler and carrier phase measurements is proposed. Firstly, the PDPI vector is obtained by differencing time-differenced carrier phase measurements between satellites. Then, the difference between PDPI and position increment derived from SINS recursion is determined. Finally, navigation system states are adjusted by the precise difference of position increment. Compared with time-differenced carrier phase measurements, the introduction of precise PDPI measurements, derived from time-differenced carrier phase, can increase computation efficiency without iteration calculations. A field vehicular test is performed to verify the proposed approach.In comparison with the method using pseudorange and Doppler measurements, the PDPI-aided method improves performance of navigation system significantly. On one hand, since high-precise PDPI measurement is added in the new approach, accuracy of the integrated navigation system is improved. The results show horizontal position error is reduced by 56.9% and horizontal velocity error is reduced by 39.2%. Vertical velocity error is reduced by 81.0% and the heading error is reduced by 19.3%. On the other hand, the PDPI measurement in this new approach establishes the relationship between two successive epochs, which leads to a smoothing effect.

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-Accuracy Point Positioning with Low-Cost GPS Receivers

: Dual-frequency, geodetic-quality GPS receivers are routinely used both in static and kinematic applications for high-accuracy point positioning. However, use of low-cost, single-frequency GPS receivers in similar applications creates a significant challenge because of how the measurement error sources are handled. In this paper, we examine the potential use of such receivers to provide horizontal positioning accuracies of a few decimetres. Applications include a myriad of terrestrial and space-borne applications, where the size, power consumption, and cost of the GPS unit is an issue. Our processing technique uses pseudorange and time-differenced carrier-phase measurements in a sequential least-squares filter. The technique was first tested on L1 measurements extracted from static, high-quality GPS receiver datasets. Accuracies better than two decimeters in horizontal components (northing and easting r.m.s.), and three decimeters in the vertical component (r.m.s.), were obtained. Horizontal positioning accuracies obtained from a low-cost receiver were within the few decimeter level.

Tightly coupled GPS/INS integration for missile applications

An approach to enhance the performance of tightly coupled GPS/INS systems is described. First, the advantages of tightly coupled systems compared to loosely coupled systems are clarified. Then, it is shown in hardware-in-the-loop tests and in a test drive that processing time differenced carrier phase measurements instead of delta-range measurements results in an increased velocity and attitude accuracy for the tightly coupled system, which is of great importance in the beginning of a time interval with purely inertial navigation, e.g. when GPS is lost due to jamming. A measurement equation is derived allowing to process the time differenced carrier phase measurements in the navigation Kalman filter. Finally, the proposed method is applied to missile navigation systems, where significant vibrations enter the inertial sensor data.