Differential Carrier Phase Research Articles

GNSS/IMU integrated navigation heading angle enhancement algorithm based on dual-antenna TDCP

In the integrated navigation system of Global Navigation Satellite System (GNSS) and Inertial Measurement Unit (IMU), attitude estimation, especially accurate estimation of heading angle, is particularly important for real-time monitoring of vehicle driving status. However, since IMU is divergent in the altitude channel, its error will gradually accumulate if it is not accurately constrained. Therefore, the estimation accuracy of heading angle is insufficient in vehicle-mounted applications where the heading angle changes frequently. In order to solve the problem of poor navigation attitude estimation accuracy in the loose combination of traditional GNSS and IMU, this paper proposes a GNSS/IMU integrated navigation heading angle enhancement algorithm based on dual-antenna epoch carrier phase difference (TDCP). This method solves the vehicle heading angle through dual-antenna TDCP to increase the input dimension of the integrated navigation filter fusion observation value, and uses Hatch filtering and anti-error adaptive filtering to improve the observation domain pseudorange accuracy and GNSS/IMU integrated navigation positioning and attitude determination performance respectively. Experimental results show that compared with the traditional GNSS/IMU integrated navigation method, the proposed algorithm improves the positioning and speed measurement accuracy in the three-dimensional direction by and respectively 22.12%, 41.27%and the vehicle heading angle accuracy is improved 46.29%.

A novel method for cycle slip detection and restoration of BDS carrier phase

The chief purpose of this present study is to develop a new approach to cycle slip detection and restoration of the BeiDou Navigation Satellite System (BDS) carrier phase. Based on the RAIM algorithm in the application of aviation safety, we extend the application to ensure the precision of the carrier phase. To stand-alone receivers of a low-cost single frequency, carrier phase data is made different between adjacent epochs. Then least-square residuals were to design a RAIM scheme with differential carrier phase data to find out the epoch with cycle slip, and finally repair cycle slip by Chebyshev polynomial. Results indicate that the approach can detect cycle slip effectively and both big cycle slip and small cycle slip could be repaired.

Real-time high-precision baseline measurement of satellite formation flying based on GNSS

With the establishment of the Chinese space station, a series of space science missions will be conducted in its vicinity. One of the extended tasks for the in-orbit service of space station is the formation flying of small satellites centered around the space station. Satellite formations can perform simultaneous three-dimensional observations of the space station, generating three-dimensional images and monitoring and assessing the status of critical components of the space station. The real-time and accurate relative position measurement is one of the key issues in formation flying. It is a fundamental prerequisite for maintaining and reconfiguring formation configurations, collision avoidance and safety assurance. GNSS-based relative positioning is a low-cost and high-precision measurement method, which is not constrained by light, weather, or relative attitude of satellites. This study introduces a novel approach to determine the relative position of satellites based on single-epoch Global Navigation Satellite System (GNSS) carrier phase difference measurements. Unlike traditional methods, the proposed technique eliminates the need for precise ephemeris and clock bias files and does not require historical observation data. The algorithm avoids the complexity associated with full cycle ambiguity jumps, facilitating real-time, high-precision calculations of relative position baseline vectors. Special attention is given to the influence of Geostationary Earth Orbit (GEO) satellites in the BeiDou Navigation Satellite System (BDS), and measures are taken to mitigate their impact on measurement accuracy by adjusting their observation weights. Our newly developed GNSS-based real-time measurement module, designed for high-quality GNSS signal reception and data communication, was tested on terrestrial and simulated low-orbit platforms. Remarkably, over baselines ranging from 10 m to 9.3 km, while traditional pseudorange differential measurements showed errors up to 1.5571 m, our proposed method consistently held errors under 5 cm and ensured computational speeds within 0.1 s per epoch. High-dynamic zero-baseline tests further validated its potential, with errors less than 1 cm. The innovations encapsulated in this work, resonating with the evolving trends of miniaturized and scalable satellites, present a cost-efficient and real-time solution for inter-satellite relative position measurement. This promises a new horizon in satellite formation technology, with future endeavors focusing on on-orbit experiments.

Assessment Accuracy of Standard Point Positioning Enhanced by Observation and Position Domain Filtering Utilizing a Multi-Epoch Least-Squares Integration Method

To enhance the positioning accuracy of standalone GNSS receivers in environments unable to provide precise ephemeris and clock offset, such as undeveloped forest areas that lack network communication and power supply, this study employed the Time Difference Carrier Phase (TDCP) technology to improve the positioning accuracy of Standard Point Positioning (SPP), where the Least-Squares (LS) and the extended Multi-Epoch Least Squares (MELS) method were applied in the position domain filtering for a single GNSS receiver and compare its performance with the existing observation domain filtering method. Firstly, the simulated data sets with various positioning accuracies were used to verify the effectiveness and convergence of the LS filtering methods. The results indicate that the LS filtering method produces a lower root mean square (RMS) error than the original strategy. Secondly, this study uses two kinematic GNSS data sets to evaluate the performance of the observation and position domain filtering, with an emphasis on the MELS method. The numerical experiment results show that the position domain LS filtering method outperforms the other two methods. The open environment experiments result shows that the positioning domain filtering method achieved positioning accuracies of 0.202 m, 0.843 m, and 2.036 m in the E, N, and U directions, respectively, with improvements of 68.0%, 21.6%, and 24.0%, compared to the original algorithm which achieved positioning accuracies of 0.631 m, 1.076 m, and 2.680 m. It also achieved improvements of 24.0%, 4.0%, and 18.3%, respectively, compared to the observation domain filtering method with positioning accuracies of 0.353 m, 0.886 m, and 2.526 m. The forest scenes experiments result shows that the positioning domain filtering method achieved positioning accuracies of 1.308 m, 1.375 m, and 2.133 m in the E, N, and U directions, respectively, with improvements of 42.4%, 36.2%, and 27.6%, compared to original algorithm which achieved positioning accuracies of 1.863 m, 1.873 m, and 2.722 m, and also achieved improvements of 27.0%, 19.4% and 10.6%, respectively, comparing to observation domain filtering method with positioning accuracies of 1.661 m, 1.642 m and 2.359 m. Moreover, the examination of the LS method results based on different epochs reveals that the filtering accuracy increases as more epochs are incorporated into the position domain integration and the enhancement value reaches a few millimeters.

Path planning of substation inspection robot based on high-precision positioning and navigation technology

Abstract Outdoor substation is an important part of power system. Substation inspection robot based on intelligent autonomous inspection system has become the research focus of substation unmanned inspection. In order to improve the positioning accuracy and speed of the system, a high-precision positioning algorithm of transformer detection robot is proposed in this paper. Tikhonov regularization is used to correct the pathological problem of the localization algorithm model. The observation amount of the receiver is increased by using four signals of a single base station with double frequency and double antenna, and the position is solved by using single difference carrier phase observation and the integer ambiguity is fixed. The input–output mapping of the neural network is designed according to the information acquisition and two-wheel angular velocity control of the detection robot. Using the hyperbolic tangent function as the activation function of MLP neural network, the MLP neural network with 32 neurons in each of the three hidden layers is determined. By optimizing reinforcement learning reward function, adding scoring rules, and reward parameters, this paper carries out the following simulation exploration work. The high-precision positioning algorithm of transformer inspection robot is compared with the existing algorithm, and the superiority of the algorithm is verified. The basic motion ability of the robot installed with the system was tested.

Galileo-Based Doppler Shifts and Time Difference Carrier Phase: A Static Case Demonstration.

The European Commission is designing and implementing new regulations for vehicle navigation in different sectors. Commission Delegated Regulation 2017/79 defines the compatibility and performance of the 112-based eCall in-vehicle systems. The regulation has a large impact on road transportation because it requires that all cars and light duty vehicles must be equipped with eCall devices. For heavy duty vehicles, a set of new regulations has been developed, starting from EU Regulation No 165/2014, in which the concept of smart tachographs was introduced to enforce the EU legislation on professional drivers' driving and resting times. In addition, intelligent speed assistance (ISA) devices increase the safety of road users. These new devices fully exploit the Global Navigation Satellite System (GNSS) to compute position velocity and time (PVT) information. In all these systems, the velocity of the vehicle plays a fundamental role; hence, a reliable and accurate velocity estimate is of utmost importance. In this work, two methods for velocity estimation using Galileo are presented and compared. The first exploits Doppler shift measurements, while the second uses time difference carrier phase (TDCP) measurements. The Doppler-based technique for velocity estimation is widely adopted in current devices, while the TDCP technique is emerging due to its promising high accuracy. The two methods are compared considering all the Galileo signals including E1, E5a, E5b, E5 Alt BOC and E6. The methods are compared in terms of velocity errors for both horizontal and vertical components using real static data. From the tests performed, it emerged that the TDCP has increased performance with respect to the Doppler-based solution. Among the Doppler-based solutions, the most accurate solution is the one obtained with the E5 Alt BOC signal.

Polarization Diversity-Enabled LOS/NLOS Identification via Carrier Phase Measurements

The provision of accurate localization is an increasingly important feature of wireless networks. To this end, a reliable distinction between line-of-sight (LOS) and non-LOS (NLOS) radio links is necessary to avoid degenerative localization estimation biases. Interestingly, LOS and NLOS transmissions affect the polarization of the received signals differently. In this work, we leverage this phenomenon to propose a threshold-based LOS/NLOS classifier exploiting weighted differential carrier phase measurements over a single link with different polarization configurations. Operation in either full or limited polarization diversity systems is possible. We develop a framework for assessing the performance of the proposed classifier, and show through simulations the performance impact of the reflecting materials in NLOS scenarios. For instance, the classifier is far more efficient in NLOS scenarios with wooden reflectors than in those with metallic reflectors. Numerical results evince the potential performance gains from exploiting full polarization diversity, properly weighting the differential carrier phase measurements, and using multi-carrier/tone transmissions. Finally, we show that the optimum decision threshold is inversely proportional to the path power gain in dB, while it does not depend significantly on the material of potential NLOS reflectors.

Ionosphere Delay Extraction in GNSS using DSP Algorithm

With multiple GNSS availability and wider applications, many positioning modes like SPS, DGNSS, RTK and PPP have been developed to cover these flexible employments. Currently, some intricate influences such as ionosphere delays and environmental interference have caused obvious impacts to accurate positioning, and they are therefore formed highlighted research points for worldwide researchers and scholars. To deal with the ionosphere delay, this submission has proposed an intrinsic approach to identify and extract the ionospheric disturbance from GNSS observations in which Digital Signal Process (DSP) is employed to form an adaptive band pass filter for combined observations in the form of either code minus phase (CMP) or double differential (DD) carrier phase. Related mechanism for identification and extraction of the ionosphere delay using DSP are introduced and analyzed. We have also discussed the separation of ionosphere delay with multipath caused by signal reflections from nearby surroundings when deformation monitoring is conducted on some restricted environments. Effects achieved by DSP have been verified combining with typical SPS and carrier based relative positioning conducted in Guangzhou metro construction sites. Results exhibit that the suggested standalone approach to extract ionosphere delays is an innovative technical frame to achieve accurate positioning regardless of assistant messages from base stations or satellite navigation broadcast.

Time-differenced double difference method for measurement of Navigation with Indian Constellation (NavIC) receiver differential phase bias

The pseudo-range (PR) and carrier phase (CP) observations of Global Navigation Satellite System (GNSS)/Navigation with Indian Constellation (NavIC) receivers are influenced due to various errors like ionosphere delay, troposphere delay, receiver and satellite clock error, multipath, integer ambiguity, receiver hardware noise etc. However, the real-time positioning and navigation applications are in quest of high-quality carrier phase measurements with zero bias. The GNSS/NavIC receiver hardware noise is one of the critical error sources that degrade the quality of carrier phase measurements. And it can be measured by computing the differential phase bias or carrier phase bias employing the double-difference method. This research article proposes a novel approach called Time Differenced Double Difference Carrier Phase (TDDDCP) for estimating differential phase bias or carrier phase bias of NavIC receiver. Moreover, the proposed TDDDCP technique has the advantage over the Double Difference Carrier Phase (DDCP) because it requires data from only one satellite with two zero base length receivers for which the differential phase bias is to be measured. The experimental results show that the differential phase bias value differs for different satellites, ranging from −0.3904 m to 0.3168 m. The bias-free carrier phase observations based on position coordinates (X, Y, Z) found improved precision of standard deviation of 0.4176 m, 0.645 m, and 0.328 m, respectively.

Supervised Machine Learning of High Rate GNSS Velocities for Earthquake Strong Motion Signals

AbstractHigh rate Global Navigation Satellite System (GNSS) processed time series capture a broad spectrum of earthquake strong motion signals, but experience regular sporadic noise that can be difficult to distinguish from true seismic signals. The range of possible seismic signal frequencies amidst a high, location‐varying noise floor makes filtering difficult to generalize. Existing methods for automatic detection rely on external inputs to mitigate false alerts, which limit their usefulness. For these reasons, geodetic seismic signal detection makes for a compelling candidate for data‐driven machine learning classification. In this study we generated high rate GNSS time differenced carrier phase (TDCP) velocity time series concurrent in space and time with expected signals from 77 earthquakes occurring over nearly 20 years. TDCP velocity processing has increased sensitivity relative to traditional geodetic displacement processing without requiring sophisticated corrections. We trained, validated and tested a random forest classifier to differentiate seismic events from noise. We find our supervised random forest classifier outperforms the existing detection methods in stand‐alone mode by combining frequency and time domain features into decision criteria. The classifier achieves a 90% true positive rate of seismic event detection within the data set of events ranging from MW4.8–8.2, with typical detection latencies seconds behind S‐wave arrivals. We conclude the performance of this model provides sufficient confidence to enable these valuable ground motion measurements to run in stand‐alone mode for development of edge processing, geodetic infrastructure monitoring and inclusion in operational ground motion observations and models.

Global Navigation Satellite System Real-Time Kinematic Positioning Framework for Precise Operation of a Swarm of Moving Vehicles.

The global navigation satellite system (GNSS) real-time kinematic (RTK) technique is used to achieve relative positioning centimeter levels among multiple agents on the move. A typical GNSS RTK estimates the relative positions of multiple rover receivers with respect to a single-base receiver. In a fleet of rover GNSS receivers, this approach is inefficient because each rover receiver only uses GNSS measurements of its own and those sent from a single-base receiver. In this study, we propose a novel GNSS RTK framework that facilitates the precise positioning of a swarm of moving vehicles through the GNSS measurements of multiple receivers and broadcasts fixed-integer ambiguities of GNSS carrier phases. The proposed framework not only provides efficient RTK positioning but also reliable performance with a limited number of GNSS satellites in view. Our experimental flight tests with six GNSS receivers showed that the systematic procedure of the proposed framework could maintain lower than 6 cm of 3D RMS positioning errors, whereas the conventional RTK failed to resolve the correct integer ambiguities of double difference carrier phase measurements more than 13% in five out of nine total baselines.

Time-Correlated Window-Carrier-Phase-Aided GNSS Positioning Using Factor Graph Optimization for Urban Positioning

This article proposes an improved global navigation satellite system (GNSS) positioning method that explores the time correlation between consecutive epochs of the code and carrier-phase measurements, which significantly increases the robustness against outlier measurements. Instead of relying on the time difference carrier phase which only considers two neighboring epochs using an extended Kalman filter estimator, this article proposed to employ the carrier-phase measurements inside a window, the so-called window carrier phase (WCP), to constrain the states inside a factor graph. A left null space matrix is employed to eliminate the shared unknown ambiguity variables and, therefore, correlate the associated states inside the WCP. Then, the pseudorange, Doppler, and the constructed WCP measurements are integrated simultaneously using factor graph optimization to estimate the state of the GNSS receiver. We evaluated the performance of the proposed method in two typical urban canyons in Hong Kong, achieving the mean positioning errors of 1.76 and 2.96 m, respectively, using the automobile-level GNSS receiver. Meanwhile, the effectiveness of the proposed method is further evaluated using a low-cost smartphone-level GNSS receiver, and similar improvement is also obtained when compared with several existing GNSS positioning methods.

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

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

A multipath migration method for common clock source SDCP observation using polynomial fitting technique

The multipath error is the major error source for high precision positions. One sidereal filtering multipath migration method is proposed for single difference carrier phase(SDCP) measurement based on polynomial fitting technique. The multipath error prediction is estimated by constructing a piecewise polynomial function based on polynomial fitting of one sidereal period multipath errors. Then the multipath error of the measurement is eliminated by subtracting the corresponding prediction. The effectiveness of the proposed method was verified by field experiments. The experimental results show that the 3-dimension (3D) accuracy of proposed method is improved by 68.9%, compared with the results that without multipath error eliminating.

Four-Channel Interference of Dual-Antenna GNSS Reflectometry and Water Level Observation

The signals at higher elevation angles could be received by a left-handed circularly polarized (LHCP) antenna because LHCP components dominate the reflected signals at higher elevation angles. This letter explores a four-channel interference method of dual-antenna global navigation satellite system (GNSS) reflectometry capable and its application in retrieving the water level. Compared to single-antenna observation using a oscillating signal-to-noise ratio (SNR), due to the capability of receiving the reflected signals at high elevation angles, the proposed method has higher temporal resolution. The criterion based on the effective value of the time series is proposed to evaluate the quality of oscillating carrier phase difference. The Lomb–Scargle method and cosine fitting are used to estimate the oscillated frequency of carrier phase difference. Through normalizing cosine oscillation and time scale by the GNSS signal amplitude and wavelength, the time-series from multisatellites could be combined to retrieve the height. At last, the experiment is conducted to demonstrate the proposed method, and the results show that when the criterion threshold is under 0.2, the centimeter-level precision of the retrieved height could be achieved. Two-satellite observation combining satellite pseudorandom noise (PRN) 15 and 24 could decrease the time span of the observation to 320 s from 480 s for only using single satellite, and the root mean square error (RMSE) reduces to 6.2 cm from 9.5 and 18.9 cm of the satellite PRN 15 and 24.

Improvement of Multi-GNSS Precision and Success Rate Using Realistic Stochastic Model of Observations

With the advancement of multi-constellation and multi-frequency global navigation satellite systems (GNSSs), more observations are available for high precision positioning applications. Although there is a lot of progress in the GNSS world, achieving realistic precision of the solution (neither too optimistic nor too pessimistic) is still an open problem. Weighting among different GNSS systems requires a realistic stochastic model for all observations to achieve the best linear unbiased estimation (BLUE) of unknown parameters in multi-GNSS data processing mode. In addition, the correct integer ambiguity resolution (IAR) becomes crucial in shortening the Time-To-Fix (TTF) in RTK, especially in challenging environmental conditions. In general, it is required to estimate various variances for observation types, consider the correlation between different observables, and compensate for the satellite elevation dependence of the observable precision. Quality control of GNSS signals, such as GPS, GLONASS, Galileo, and BeiDou can be performed by processing a zero or short baseline double difference pseudorange and carrier phase observations using the least-squares variance component estimation (LS-VCE). The efficacy of this method is investigated using real multi-GNSS data sets collected by the Trimble NETR9, SEPT POLARX5, and LEICA GR30 receivers. The results show that the standard deviation of observations depends on the system and the observable type in which a particular receiver could have the best performance. We also note that the estimated variances and correlations among different observations are also dependent on the receiver type. It is because the approaches utilized for the recovery techniques differ from one type of receiver to another kind. The reliability of IAR will improve if a realistic stochastic model is applied in single or multi-GNSS data processing. According to the results, for the data sets considered, a realistic stochastic model can increase the computed empirical success rate to 100% in multi-GNSS as well as a single system. As mentioned previously, the realistic precision of the solution can be achieved with a realistic stochastic model. However, using the estimated stochastic model, in fact, leads to better precision and accuracy for the estimated baseline components, up to 39% in multi-GNSS.

A linear-circular regression estimate for data fusion: Application to GNSS carrier-phase signal processing

This article is dedicated to the estimation of the parameters of a linear-circular regression model. For this model, the response is circular and defined between −π and π, the predictor is linear and several sensors provide noisy observations of the response. In our approach, the noise is assumed to be distributed according to a von Mises distribution with a concentration parameter that models the accuracy of the sensors. We propose a maximum likelihood circular fusion operator for the estimation of the intercept, the slope of the regression line and the concentration parameter associated with each sensor. The proposed estimate is not direct as in the linear case and requires an iterative algorithm to maximize a periodic contrast function. In order to characterize the accuracy of our fusion operator, the theoretical expression of the variance of the proposed estimator slope is first derived. For this derivation, we approximate the von Mises distribution by a Wrapped normal distribution and we consider unwrapped observations. Then, we derive an iterative procedure to maximize the contrast function. We show, using synthetic data, that the variance of the slope of the regression line derived using the proposed estimate is in good agreement with that obtained using the theoretical expression of the variance. The proposed estimator is also used to process the carrier-phase difference between GNSS signals provided by two antennas. The objective in terms of signal processing is to estimate the linear parameters of this difference in order to derive the height between the two antennas. We show that fusing the observations provided by several satellite signals improves the accuracy of the estimated height. We also show, using real data, that the theoretical study of the proposed estimator can be used to predict the length of integration of the signal necessary for obtaining an estimate of the height with a given accuracy.

Vehicle's Instantaneous Velocity Reconstruction by Combining GNSS Doppler and Carrier Phase Measurements Through Tikhonov Regularized Kernel Learning

GNSS has become a widely accessible technique for vehicle instantaneous velocimetry. GNSS time difference carrier phase (TDCP) velocimetry can provide high-accuracy displacement increments, through which the between-epoch average velocity can be derived. However, there are always so-called modelling errors in such velocity, i.e., the deviation between the average velocity and the instantaneous one. GNSS Doppler velocimetry offers exactly instantaneous velocity, but its measurement is much noisier. In this work, we propose to integrate TDCP with Doppler for estimating vehicle's instantaneous velocity. The TDCP-derived displacements and the Doppler-derived instantaneous velocity are treated as two sets of measurements, whereas the vehicle's kinematics is represented by kernel model. Rather than directly solving for vehicle's velocity, we indirectly seek for the kernel weights to establish an analytical kernel model of vehicle's motion state. Tikhonov regularization is introduced to deal with the ill-conditioned problem in kernel weights estimation, and it can significantly smooth/denoise the noisy Doppler measurements. The hyperparameters involved are optimized using generalized cross validation criterion. The constructed kernel model can provide vehicle's velocity at any instants, not necessarily at the sampling epochs. The static and dynamic vehicle field experiments demonstrate that the proposed TDCP/Doppler integrated velocimetry can provide both high accuracy and efficiency.

Carrier phase difference measurement method for GNSS-simulator navigation signal

A method for measuring phase difference of carrier frequency of GNSS-simulator navigation signal, based on the use of a multichannel analogue-to-digital converter and phase processing at intervals of its linear change is proposed. The developed method makes it possible to measure the phase difference of carrier frequency of radio navigation signal with a non-excluded systematic error 1.5°.

Performance Analysis and Architectures for a MEMS-SINS/GPS Ultratight Integration System

In order to analyze the performance of strapdown inertial navigation system/global position system (SINS/GPS) ultratight integration system with low-precision microelectromechanical system (MEMS) under challenging environments, a new MEMS-SINS/GPS ultratight integration scheme is designed. The time-space difference carrier phase velocity (TSDCP-v) is used to assist the carrier tracking loop, the measurement model including nonlinear term is established, and the corresponding filtering algorithm is designed. A simulation and verification platform is established to analyze and verify the performance of the MEMS-SINS/GPS ultratight integration system designed in this paper. Compared with the SINS/GPS tight integration navigation system, the MEMS-SINS/GPS ultratight integration system has higher dynamic performance, anti-interference capability, and navigation performance. At the same time, the MEMS-SINS/GPS ultratight integration system improves the carrier tracking performance of SINS-assisted GPS ultratight integration system when using low-precision MEMS and in high dynamics, strong interference environments.