Receiver Clock Error Research Articles

Chip-scale atomic clock (CSAC) aided GNSS in urban canyons

In urban canyons, the reflections and obstructions of Global Navigation Satellite System (GNSS) signals frequently lead to significant errors in measurements, the number of which can be larger than that of the correct measurements. This leads to a severe degradation of GNSS performance in urban canyons. Various fault detection and exclusion (FDE) algorithms have been developed to cope with these outliers caused by multipath effects. Most of these FDE algorithms check the consistency among measurements. However, in urban canyons, their effectiveness is significantly compromised by the lack of fault-free measurements. There is an urgent need to develop new constraints for enhancing GNSS FDE performance. In recent years, the advent of Chip-Scale Atomic Clock (CSAC), known for their affordability and high frequency stability, offers a promising solution for accurately predicting receiver clock errors. Additionally, using city maps to establish height constraints is another way to increase redundancy. The purpose of this study is to improve the GNSS positioning accuracy in urban canyons with the aid of CSAC and city map data. A novel FDE algorithm is developed to search for positions through the constraints of height and receiver clock. Extensive tests were conducted in urban canyons to evaluate the performance of the system. Results showed that the positioning accuracy can be improved from tens of meters to less than 6 m.

Single-station single-frequency GNSS cycle slip estimation with receiver clock error increment and position increment constraints

Single-station single-frequency GNSS cycle slip estimation with receiver clock error increment and position increment constraints

GNSS performance enhancement using measurement estimation in harsh environment.

Global navigation satellite systems (GNSSs) are commonly used to measure the position and time globally. A GNSS is convenient owing to its ability to measure accurate position relatively without using assistive tools for navigation by comparing with other sensors. Based on these benefits, the applicable area is expanding to commercial and social uses (e.g., vehicle navigation, smart grids, and smartphone apps). In the future, various services and technologies (e.g., the use of autonomous vehicles, unmanned delivery, and industrial field robots), which make Internet of Things (IOT) more active, will be used in our society. Conversely, the performance of GNSS can degrade in harsh environments, such as urban areas, owing to the property of GNSS, which calculates position and time via satellite signal reception. However, buildings in a city can block navigation satellite signals and generate multi-path errors. The blocked signals exacerbate the dilution of precision (DOP), which indicates the accuracy of the navigation solution and increases the navigation solution error. This study proposes methods to improve navigation performance by leveraging various techniques (e.g., range differences, receiver clock error hold, and virtual satellites). The methods were validated in harsh environments where visible satellites were reduced. In the simulation, each proposed method improved the navigation performance by creating an environment similar to a normal situation, despite the receiver entering a harsh environment. The results confirmed that the navigation performance deteriorated compared to the normal situation where the number of visible satellites decreased. However, the navigation performance was recovered gradually by applying the proposed techniques. Using the proposed methods, navigation performance can be maintained continuously even in situations where satellite signals are blocked.

Common-clock GPS single differences: An improved correlation model for GPS phase observations based on turbulence theory

Microwave signals, for example, those from Global Navigation Satellite System (GNSS) and Very Long Baseline Interferometry (VLBI), are affected by tropospheric turbulence in such a way that the random fluctuations of the atmospheric index of refractivity correlate the phase measurements. A proper modeling of correlations is mandatory to avoid biased analysis, particularly when statistical tests are used. In this contribution, we analyze single differences (SD) computed from Global Positioning System (GPS) phase observations for which the between receiver clock error could be strongly mitigated by a specific common clock setting. We estimate specific parameters from the power spectral density (psd), which is directly related to the correlation function, with the debiased Whittle maximum likelihood and investigate their dependencies with the satellite geometry (elevation, azimuth angles) and the time of the day. We show that (i) the estimated slopes of the psd follow the one predicted by the Kolmogorov turbulence theory and (ii) the cut-off at high frequencies shows daily variations that may be linked with the strength of the turbulence. Based on these findings, we derive an improved spectral density model for GPS phase SD. The results of this study contribute to improving the stochastic description of random effects impacting VLBI and GNSS phase observations by studying variations of parameters from the von Karman spectrum.

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.

An Efficient Method to Compensate Receiver Clock Jumps in Real-Time Precise Point Positioning

In global navigation satellite systems (GNSSs)-based positioning, user receiver clock jump is a common phenomenon on the low-cost receiver clocks and can break the continuity of observation time tag, carrier phase and pseudo range. The discontinuity may affect precise point positioning-related parameter estimation, including receiver clock error, position, troposphere and ionosphere parameters. It is important to note that these parameters can be used for timing, positioning, atmospheric inversion and so on. In response to this problem, the receiver clock jumps are divided into two types. The first one can be expressed by the carrier phase and pseudo range having the same scale jump, and the second one is that they are having different scale jumps. For the first type, if a small priori variance of receiver clock error is provided, it can affect the accuracy of ionospheric delay estimation both in static and kinematic mode, while in the latter mode, it also affects position estimation. However, if large process noise is provided, numerical problems may arise since other parameters’ process noises are usually small, it is proposed to use the single point positioning with pseudo ranges to provide a priori value of receiver clock error, and an empiric value is assigned to its prior variance, this handle can avoid the above problems. For the second type, instead of compensating so many raw observations in the traditional methods, it is proposed to compensate the ambiguities at the clock jump epochs only in a new method. The new method corrects the Melbourne–Wubbena (MW) combination firstly in order to avoid the misjudging of cycle slips for current epoch, and the second step is to compensate the corresponding ambiguities, then, after Kalman filtering, the MW and its mean should be corrected back in order to avoid the misjudging of cycle slips at the next epoch. This approach has the advantage of handling the clock jump epoch-wise and can avoid correcting the rest of the observations as the traditional methods used to. With the numerical validation examples both in static and kinematic modes, it shows the new method is simple but efficient for real time precise point positioning (PPP).

Reconstructed doppler cycle slip detection method based on inter satellite difference

Aiming at the problem of single frequency cycle slip detection in GNSS location, a new cycle slip detection method is proposed. This method uses the position and speed of the satellite and the position and speed of the receiver to calculate the Doppler frequency shift, then uses the integral value of the Doppler frequency shift to make a difference with the station satellite distance, and uses the inter satellite difference method to eliminate the receiver clock error, which can accurately detect the small cycle slip of one cycle. This method is not affected by the coordinates of the receiver, and can be realized only by the pseudo range single point positioning result.

Double difference method with zero and short base length carrier phase measurements for Navigation with Indian Constellation satellites L5 (1176.45 MHz) signal quality analysis

SummaryThe carrier phase (CP) measurements should be unambiguous to achieve the enhanced accuracy of Global Navigation Satellite System (GNSS) services. However, all the real‐time CP measurements are manipulated by different errors, namely, satellite and receiver clock error, ionosphere delay, troposphere delay, integer ambiguity, etc. Even after removing or minimizing all these errors, the CP measurements are influenced by multipath error and receiver hardware residual or bias. In this research article, a double difference (DD) method is proposed to estimate residual or bias in CP observations of Navigation with Indian Constellation (NavIC). The proposed method abolishes all the common errors and provides bias. However, the CP measurement with a bit of bias value can be considered a high‐quality signal. Here, we investigate the quality of NavIC satellites L5 (1176.45 MHz) signal with real‐time measurements obtained through zero base length (ZBL) and short base length (SBL) experiments conducted at Kurnool (15.79°N, 78.07°E), India. The results show that the CP measurement bias of the L5 signal is within the range ±0.338 and ±1.688 m, respectively, for stationary and moving receivers. The bias was enhanced to 3.71 m for the SBL measurements. The results also demonstrate that the bias is low when carrier to noise (C/No) is high, and its range is nearly the same for all the days. This research would be helpful to estimate the bias that improves accuracy of precise point positioning (PPP) applications.

High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock

A global navigation satellite system (GNSS) receiver with multi-antenna using clock synchronization technology is a powerful piece of equipment for precise attitude determination and reducing costs. The single-difference (SD) can eliminate both the satellites and receiver clock errors with the common clock between antennas, which benefits the GNSS short-baseline attitude determination due to its lower noise, higher redundancy and stronger function model strength. However, the existence of uncalibrated phase delay (UPD) makes it difficult to obtain fixed SD attitude solutions. Therefore, the key problem for the fixed SD attitude solutions is to separate the SD UPD and fix the SD ambiguities into integers between antennas. This article introduces the one-step ambiguity substitution approach to separate the SD UPD, through which we merge the SD UPD parameter with the SD ambiguity of the reference satellite ambiguity as the new SD UPD parameter. Reconstructing the other SD ambiguities, the rank deficiency can be remedied by nature, and the new SD ambiguities can have a natural integer feature. Finally, the fixed SD baseline and attitude solutions are obtained by combining the ambiguity substitution approach with integer ambiguity resolution (IAR). To verify the effect of the ambiguity substitution approach and the advantages of the SD observables with a common clock in practical applications, we conducted static, kinematic, and vehicle experiments. In static experiments, the root mean squared errors (RMSEs) of the yaw and pitch angles obtained by the SD observables with a common clock were improved by approximately 80% and 93%, respectively, compared to double-difference (DD) observables with a common clock in multi-day attitude solutions. The kinematic results show that the dispersion of the SD-Fix in the pitch angle is two times less that of the DD-Fix, and the standard deviations (STDs) of the pitch angle for SD-Fix can reach 0.02°. Based on the feasibility, five bridges with low pitch angles in the vehicle experiment environment, which the DD observables cannot detect, were detected by the SD observables with a common clock. The attitude angles obtained by the SD observables were also consistent with the fiber optic gyroscope (FOG) inertial navigation system (INS). This research on the SD observables with a common clock provides higher accuracy.

Study on GNSS‐R multi‐target detection and location method based on consistency checking

The use of GNSS reflected signals to carry out passive detection of space targets is an emerging technical field. Unlike the traditional GNSS-R in large-scale environments such as oceans, vegetation, ice and snow, it is required to identify different targets within the detection range, which is one of the biggest challenges. To solve this problem, a hyperboloid observation equation based on the TDOA location model is constructed, which can eliminate the GNSS satellite orbit error, the satellite atomic clock error and the detection receiver clock error via differential technique. The consistency checking theory based on hypothesis and test is used to detect and distinguish different targets while locating. The simulation results show that the target detection and location accuracy can reach tens of metres, and when the different space targets are separated by 50 m, 100 m, 150 m, 200 m, and 250 m in sequence, the detection success rate of the method is 67.25%, 87.50%, 95.75%, 99.25%, and 99.75%, respectively, which indicates the feasibility and effectiveness of the method. The study provides a feasible technical approach for solving the multi-target problem in GNSS-R space target passive detection.

Real‐time detection of BDS orbit manoeuvres based on the combination of GPS and BDS observations

The construction of the third generation of the Chinese BeiDou navigation satellite system (BDS), which provides global positioning, navigation, and timing (PNT) services, will be completed in 2020. As BDS satellites contain the geostationary orbit (GEO), inclined geosynchronous (IGSO), and medium earth orbit (MEO), orbital manoeuvres occur more frequently. Thus, orbit manoeuvre detection is important for continuous and reliable PNT services. A BDS orbit manoeuvre detection method based on the combination of global positioning system (GPS) and BDS observations is proposed in this study. The standard deviations of the observation residuals of the epoch-differenced velocity estimation of the single BDS system and combined GPS + BDS system were compared to determine the beginning and end of the orbit manoeuvre. The results show that the orbital manoeuvre leads to a position, velocity, and receiver clock error bias of approximately tens to hundreds of metres, several centimetres per second, and tens to hundreds of metres, respectively. Based on the proposed method, the start and end times can be detected in real time and the usable observation time can be extended by >157 min.

Determination of GNSS receiver elevation-dependent clock bias accuracy

The differentiation of observation equations allows for the elimination of most ofGNSS errors. The receiver clock error (bias) is eliminated by the measurements of two satellites in a single difference observation equation combination. The satellite clock error is eliminated by the observations of two receivers and its magnitude is correlated with geometric error due tothe speed of light. Motivation for this paper was commonly used erroneous statement says that the receiver's clock correction must be known at the same level as satellite’s ones. As previously stated, this is mistakenly treated as a direct derivative of the speed of light, i.e. 1 µs = 300 m, 1 ns = 30 cm etc. This paper presents the method of calculation of receiver clock bias depending on zenith angle. Hypothesis is showed in a theoretical part, where radial velocity of the satellite with relation to the receiver and error in geometric distance generated by receiver with 1 µs clock error were calculated for four different GNSS (GPS, GLONASS, Galileo and Beidou) systems. In a practical part reference station located near equator was selected and together with satellite positions of four GNSS systems, obtained from precise orbit files calculations were made. A result on the base on selected sort of data both theoretical and practical calculations were consistent. Concluding, the receiver is unblinking in relation tothe satellite, thus the receiver clock error is correlated with the satellite zenith angle and must be known within 3–4 orders of magnitude better compared to the satellite one. A novelty and innovation is proved by the fact that these kinds of calculations have never been published before. Both theoretical and practical calculation part proves that receiver clock error at 1 μs level leads to only 1 mm geometrical error and might be eliminated by the usage of precise oscillator providing this level of accuracy.

Real-time monitoring of the dynamic variation of satellite orbital maneuvers based on BDS observations

The BeiDou Navigation Satellite System (BDS) frequently experiences orbital maneuvers. This study proposed a method for the real-time monitoring of the dynamic variation of satellite orbital maneuvers. Based on the epoch-differenced velocity estimation model, the epoch variation of the receiver clock error can be calculated for each station. The dynamic variation of the orbital maneuver can then be estimated real-time by the monitoring model, using observations from three or more BDS tracking stations. The feasibility and effectiveness of this method is validated by different datasets. The results show that the method can precisely detect orbital maneuvers, thereby extending the usable observations for about three hours. Thus, it is useful for improving the positioning, navigation, and timing service. The dynamic variations of orbital maneuvers can be monitored in real-time, which is useful for precise orbit control, and is helpful for keeping the satellite healthy and monitoring the navigation system operation.

Two-way laser regeneration pseudocode rangefinder of intersatellite optical crosslink

The millimeter-level bidirectional long-distance asynchronous ranging has long been a huge challenge in the field of measurement and instrumentation. Correspondingly, a laser pseudocode ranging algorithm based on regenerative synchronization mechanism is proposed to address the problems obstructing precise distance measurement between asynchronous satellites. First, the synchronization strategy of a double-ended asynchronous terminal based on the regenerative pseudocode is discussed. Subsequently, we look at the algorithm of the generation, transmission, detection, and the code phase tracking loop, which forms the base of obtaining high precision of pseudocode ranging. On this basis, the error of laser pseudocode ranging link is analyzed, which mainly incorporates receiver noise and clock error. In terms of receiver noise, the influence of the photodetector carrier-to-noise ratio on random noise distribution is evaluated, and the design of receiver parameters is guided as such. As for the clock error, we look at the constraint relationship between the range and the precision under the action of the clock error, which provides the basis for the selection of the clock. Finally, the optimized system is tested when a double-ended laser link is set up in the laboratory. As a result, the comprehensive accuracy results of 3.47 mm systematic error and ±1.73 mm random error is obtained, and the long-scale measurement performance has been tested by the temperature-compensated crystal oscillator pulse frequency experiment. In conclusion, the experiment is consistent with the theory proposed in this study, which provides a theoretical and experimental basis for long-distance high-precision intersatellite ranging.

Dual Mode Pseudo-Range Differential Positioning Method

Use the Beidou/GPS dual-mode pseudo-range differential positioning method is used to perform high-precision positioning and navigation for the UAV. The error separation differential positioning method is proposed to solve the problem that the correction difference calculated by the traditional differential positioning method is affected by the change of the baseline length, the reference inter-satellite difference method eliminates the reference station receiver clock error and performs ultra-short baseline and short baseline positioning tests. The positioning accuracy is better than 0.4 meters in the horizontal direction and the elevation is better than 0.5 meters.

Robust Vehicular Localization and Map Matching in Urban Environments Through IMU, GNSS, and Cellular Signals

A framework for ground vehicle localization that uses cellular signals of opportunity (SOPs), a digital map, an inertial measurement unit (IMU), and a Global Navigation Satellite System (GNSS) receiver is developed. This framework aims to enable localization in an urban environment where GNSS signals could be unusable or unreliable. The proposed framework employs an extended Kalman filter (EKF) to fuse pseudorange observables extracted from cellular SOPs, IMU measurements, and GNSS-derived position estimates (when available). The EKF is coupled with a map-matching approach. The framework assumes the positions of the cellular towers to be known, and it estimates the vehicle's states (position, velocity, orientation, and IMU biases) along with the difference between the vehicle-mounted receiver clock error states (bias and drift) and each cellular SOP clock error state. The proposed framework is evaluated experimentally on a ground vehicle navigating in a deep urban area with a limited sky view. Results show a position root-mean-square error (RMSE) of 2.8 m across a 1,380-m trajectory when GNSS signals are available and an RMSE of 3.12 m across the same trajectory when GNSS signals are unavailable for 330 m. Moreover, compared to localization with a loosely coupled GNSS?IMU integrated system, a 22% reduction in the localization error is obtained whenever GNSS signals are available, and an 81% reduction in the localization error is obtained whenever GNSS signals are unavailable.

Retrieving geophysical signals from GPS in the La Plata River region

Over the last few years, efforts to model short-term deformations of the Earth’s crust have multiplied. Sudden water level rise can cause sporadic, but significant, motions in the solid Earth’s surface. In this work, we address the problem of retrieving reliable estimates of the vertical displacement of a Global Positioning System (GPS) station located very close to the eastern shore of the La Plata River, during a strong storm surge event. Capturing sub-daily GPS displacements demands an elaborate processing strategy because several highly correlated parameters must be estimated simultaneously. We present a successful strategy that reduces the number of unknowns that have to be estimated simultaneously, by using an empirical model that describes the elastic response of the Earth’s crust to the hydrological load variations. We incorporate this model into the observation equations so that, instead of estimating the station position, we estimate every epoch a single parameter of the empirical model, i.e., the empirical elastic parameter EEP, that is assumed to be a constant of the Earth’s crust in the region of the GPS station. We verify that the estimated parameter agrees well with the value calculated from the CRUST 1.0-A model of the Earth’s crust. The GPS receiver was tied to an external cesium clock, which allowed us to process the data according to two different strategies: (a) estimating the receiver clock error (Δt) as an epoch-wise free parameter, which is equivalent to ignoring the presence of the external clock, and (b) conditioning the variability of that estimate with a small a priori variance compatible with the external clock’s variability. We find that, without having an external atomic clock, the estimation of all the parameters, i.e., the zenith tropospheric delay, Δt, and the EEP, worsens when the GPS station is affected by sub-daily vertical displacements.

The Unified Form of Code Biases and Positioning Performance Analysis in Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) Precise Point Positioning Using Real Triple-Frequency Data

Multi- system and multi-frequency are two key factors that determine the performance of precise point positioning. Both multi-frequency and multi-system lead to new biases, which are not solved systematically. This paper concentrates on mathematical models of biases, influences of these biases, and positioning performance analysis of different observation models. The biases comprise the inter-frequency clock bias in multi-frequency and the inter-system clock bias in multi-system. The former is the residual differential code biases (DCBs) from receiver clock and satellite clock and usually occurs at the third frequency, the latter is the deviation of the receiver clock errors in different systems. Unified mathematical models of the biases are presented by analyzing the general formula of observation equations. The influences of these biases are validated by experiments with corresponding observation models. Subsequently, the experiments, which are based on the data at five globally distributed stations in Multi-Global Navigation Satellite System (GNSS) Experiment (MGEX) on day of year 100, 2018, assess positioning performance of different observation models with combination of frequencies (dual-frequency or triple- frequency) and systems (BeiDou Navigation Satellite System (BDS) or Global Positioning System (GPS)). The results show that the performances of triple-frequency models are almost as the same level as the dual-frequency models. They provide scientific support for the triple-frequency ambiguity-fixed solution which has a better convergence characteristic than dual-frequency ambiguity-fixed solution. Furthermore, the biases are expressed as an unified form that gives an important and valuable reference for future research on multi-frequency and multi-system precise point positioning.

Time-Domain Evaluation Method for Clock Frequency Stability Based on Precise Point Positioning

The Global Navigation Satellite System (GNSS) and GNSS receivers can be used to measure the time-frequency errors of receiver clocks so as to evaluate their frequency stability. The calculation of receiver clock error by single point positioning (SPP) is not highly accurate, resulting in the limited evaluation of clock frequency stability. Therefore, this study proposes a precision point positioning (PPP) evaluation method. In this method, the receiver is driven by an external clock to be evaluated, and the receiver clock error calculated by PPP is used as the measured clock phase error to calculate the Allan variance. The frequency stability of three clocks with different grades (temperature compensated crystal oscillator [TCXO], oven controlled crystal oscillator [OCXO], and rubidium clock) are evaluated with the PPP evaluation method. The PPP evaluation method can evaluate the frequency stabilities of TCXO and OCXO for an average interval of more than 1 s, and the evaluation error of OCXO is less than 1.3 × 10 -11 . As for the rubidium clock, its frequency stability can be evaluated by the PPP evaluation method for an average interval of more than 66 s, and the error is less than 2 × 10 -13 . In general, the PPP evaluation method involves simple operations, achieves high accuracy, and is easily popularized.

Nonvisible satellite estimation algorithm for improved uav navigation in mountainous regions

Global Navigation Satellite System (GNSS) is one of the most used technologies around the world for navigation. This technology is integrated in aircraft, ship, and submarine guidance systems; it is available in cell phones and cars, and also used to monitor Earth surface movements. The system accuracy spans from a range of a few centimeters up to meters. This variation is related to different sources of error such as the receiver clock error, Earth's ionospheric and tropospheric signal delay [1], or multipath effect in semiobstructed areas. If the surrounding objects have highly reflective surfaces, the error magnitude might surge to several hundred meters due to multiple reflections that the signal experiences before reaching the receiving antenna. A further source of error is present when the same signal is received more than once. As the present work is focused only on the effect of nonvisible satellites, multipath effect is not further investigated.