Receiver Clock Research Articles

PPP time transfer using an adaptive clock constraint model

ABSTRACT In the processing of Precise Point Positioning (PPP) data, the receiver clock is approached with nearly infinite uncertainty, rendering it difficult to fulfill the requirements of high-precision time frequency applications. Therefore, a receiver clock model is essential. In this study, we first analyze the “over-constraint” problem in the existing clock model and subsequently propose a new clock model, called the Adaptive Clock Constraint (ACC) model, which relies on a sliding window to update covariance and frequency characteristics parameters in real-time. To verify the robustness of the ACC model, three experiments were conducted, and the results show that the ACC model not only is suitable for different types of atomic clock stations but also has superior frequency stability and time transfer precision in contrast to the BIPM PPP, the IGS products and White Noise (WN) model results. Using the optical fiber results as a time reference, the STD of the time difference between the ACC model and optical fiber results is 0.13 ns and the frequency stability is 1.28 × 10−16 on average for one week, representing improvements of more than 10% and 15% compared with the BIPM PPP results.

Regional multi-station real-time time transfer using an undifferenced multi-GNSS network solution

Real-time time transfer is the basis for the time synchronization and establishment and maintenance of time scales. In this contribution, we present a regional multi-station real-time time transfer approach, in which observations from multi-global navigation satellite system (GNSS) received at regional multi-station are integrated to conduct an undifferenced network solution. Consequently, the simultaneous estimation of receiver clock offsets for multiple stations becomes possible, enabling the execution of real-time time transfer. One week of observation data from five multi-GNSS Experiment (MGEX) stations located in Europe are selected to generate four links (distances from 919.7 to 2153.4 km), and four schemes are designed, i.e., GPS-only, BDS-3-only, Galileo-only, and GPS/BDS-3/Galileo (GCE) solutions, respectively. Experiment results show that the mean number of observations, time dilution of precision (TDOP) values, and standard deviation (STD) of clock offset difference time series between the Center for Orbit Determination in Europe (CODE) and the estimated solutions for four time links are 90, 76, 72, 239 and 0.34, 0.38, 0.39, 0.21 and 0.039, 0.050, 0.043, 0.036 ns for GPS-only, BDS-3-only, Galileo-only, and GCE solutions, respectively. When the averaging time is shorter than 7680 s, the frequency stability of GCE solutions shows the best performance. The mean frequency stability of four time links at 7680 s is 6.59 × 10–15,7.25 × 10–15, 6.88 × 10–15 and 5.96 × 10–15 for GPS-only, BDS-3-only, Galileo-only, and GCE solutions, respectively. The GCE solution shows the best performance among the four schemes in terms of the number of observations, TDOP, STD, and frequency stability. The experiment results demonstrate that this approach is suitable for regional multi-station real-time time transfer.

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.

Perspectives for Improvements on Real-Time GNSS Positioning with the Use of New Observables

The research aims to analyze Global Navigation Satellite System (GNSS) positioning solutions using the Precise Point Positioning (PPP) method in kinematic mode, in which the position is obtained epoch by epoch through data from only one GNSS receiver, precise ephemerides, and satellite clock corrections, both with high accuracy. In this context, the adopted methodology employs the open-source software RTKLIB, which, through its data post-processing capability, enables the evaluation of kinematic PPP performance by incorporating new observables such as L5 and E5a bands, crucial for enhancing positional accuracy and mitigating multipath effects. Additionally, for survey simulations, data from the UFPR and POVE stations of the Brazilian Network for Continuous Monitoring of GNSS (RBMC) were utilized. The selected stations are located in the Northern and Southern regions of Brazil. The GNSS data were processed with the same tracking duration for a 45-minute cold-start, aimed at observing solution convergence. Subsequently, the estimated outputs in RTKLIB were obtained based on station origins using coordinates provided by SIRGAS-CON. Moreover, by utilizing precise ephemerides data, it was possible to conclude that the addition of new observables for triple-frequency positioning led to an improvement in the accuracy of the obtained coordinates, particularly in the Vertical component. In this regard, the increase in accuracy in experiments using only triple-frequency data with a 15° elevation mask was approximately 25% at the UFPR station and about ~37% at the POVE station. Furthermore, it was observed that reducing the elevation mask from 15° to 10° had a positive impact on dual-frequency positioning at the UFPR station, resulting in gains of over 3% in the East component and around ~21% in the North component compared to values obtained with the 15° mask. Similarly, during triple-frequency positioning at the POVE station, gains exceedingly approximately 16% in the North component and around ~22% in the Vertical component were observed.

A Linear Regression-Based Methodology to Improve the Stability of a Low-Cost GPS Receiver Using the Precision Timing Signals from an Atomic Clock

The global positioning system (GPS) is widely known for its applications in navigation, timing, and positioning. However, its accuracy can be greatly impacted by the performance of its receiver clocks, especially for a low-cost receiver equipped with lower-grade clocks like crystal oscillators. The objective of this study is to develop a model to improve the stability of a low-cost receiver. To achieve this, a machine-learning-based linear regression algorithm is proposed to predict the differences of the low-cost GPS receiver compared to the precision timing source. Experiments were conducted using low-cost receivers like Ublox and expensive receivers like Septentrio. The model was implemented and the clocks of low-cost receivers were steered. The outcomes demonstrate a notable enhancement in the stability of low-cost receivers after the corrections were applied. This improvement underscores the efficacy of the proposed model in enhancing the performance of low-cost GPS receivers. Consequently, these low-cost receivers can be cost-effectively utilized for various purposes, particularly in applications requiring the deployment of numerous GPS receivers to achieve extensive spatial coverage.

BDS-3 full-frequency precise point positioning: models and performance comparison

With the BDS-3 six-frequency integration, there are more choices to implement the precise point positioning (PPP) technology. To take full advantage of the multi-frequency combination, six typical BDS-3 six-frequency PPP models using uncombined observation (UC), five dual-frequency ionospheric-free (IF) combinations (IF2), four triple-frequency IF combinations (IF3), three four-frequency IF combinations (IF4), two five-frequency IF combinations (IF5), and a single six-frequency IF combination (IF6) were constructed and compared. The results indicate that the positioning accuracies of the six models are similar. The static positioning accuracies reach 4, 3–5, and 12–14 mm in the east, north, and up directions, respectively, while the kinematic positioning accuracies are 24–26, 16–17, and 42–43 mm, respectively. Regarding the convergence times, the UC model is slightly worse than the five IF combined models, except for some cases in the up direction. In the static mode, benefiting from the smallest noise amplification factor, the average convergence times of the IF6 model are the shortest, reaching 12.1, 5.5, and 13.4 min in the three directions, respectively, and are 7%, 15%, and 6% shorter than those of the UC model. In the kinematic mode, with the combination of more signals into a single IF combination, the noise level of the IF combined observables gradually decreases, but the convergence times gradually increase. The kinematic average convergence times of the IF2 model are 15.3, 3.6, and 18.0 min in the three directions, which are 6%, 22%, and 10% and 1%, 16%, and 20% shorter than those of the UC and IF6 models, respectively. In addition, the observation residuals, and the estimates of inter-frequency bias, tropospheric zenith wet delay, and receiver clock offsets from different models were compared and analyzed. The specific selection of the model should be based on actual situations.

Prospects of GENESIS and Galileo joint orbit and clock determination

The European Space Agency (ESA) is preparing a satellite mission called GENESIS to be launched in 2027 as part of the FutureNAV program. GENESIS co-locates, for the first time, all four space geodetic techniques on one satellite platform. The main objectives of the mission are the realization of the International Terrestrial Reference Frames and the mitigation of biases in geodetic measurements; however, GENESIS will remarkably contribute to the determination of the geodetic parameters. The precise GENESIS orbits will be determined through satellite-to-satellite tracking, employing two GNSS antennas to observe GPS and Galileo satellites in both nadir and zenith directions. In this research, we show results from simulations of GENESIS and Galileo-like constellations with joint orbit and clock determination. We assess the orbit quality of GENESIS based on nadir-only, zenith-only, and combined nadir–zenith GNSS observations. The results prove that GENESIS and Galileo joint orbit and clock determination substantially improves Galileo orbits, satellite clocks, and even ground-based clocks of GNSS receivers tracking Galileo satellites. Although zenith and nadir GNSS antennas favor different orbital planes in terms of the number of collected observations, the mean results for each Galileo orbital plane are improved to a similar extent. The 3D orbit error of Galileo is improved from 27 mm (Galileo-only), 23 mm (Galileo + zenith), 16 mm (Galileo + nadir), to 14 mm (Galileo + zenith + nadir GENESIS observations), i.e., almost by a factor of two in the joint GENESIS + Galileo orbit and clock solutions.

Characterization of the BigRock 28 nm fast timing Analog Front End

An initial characterization of the BigRock high-speed, low-power Analog Front End (AFE) is presented. The BigRock AFE previously described in [1] has been refined in a second generation testbed ASIC, Pebbles. The AFE utilizes a current-mode signal path that has been designed for 4D tracking applications with precision time resolution of order 50 ps. The preamplifier concept is based on a prior art current-feedback CMOS topology in [2]. An on-chip test bench comprised of a variable injection circuit and high-resolution TDC measures the AFE timing resolution. An array of integrated load capacitors and IO IPs enhance the characterization capability. These full-custom pads include LVDS and clock receivers, CML output driver, and simple analog buffer pads designed at the process core voltage (0.9 V) on a 90 μm/180 μm pitch. Critical noise and timing metrics for an array of input detector capacitance ranging 0 to 100 fF have been measured.

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

Global Navigation Satellite System Receiver Positioning in Harsh Environments via Clock Bias Prediction by Empirical Mode Decomposition and Back Propagation Neural Network Method.

This paper proposes a novel method to improve the clock bias short-term prediction accuracy of navigation receivers then solve the problem of low positioning accuracy when the satellite signal quality deteriorates. Considering that the clock bias of a navigation receiver is equivalent to a virtual satellite, the predicted value of clock bias is used to assist navigation receivers in positioning. Consequently, a combined prediction method for navigation receiver clock bias based on Empirical Mode Decomposition (EMD) and Back Propagation Neural Network (BPNN) analysis theory is demonstrated. In view of systematic errors and random errors in the clock bias data from navigation receivers, the EMD method is used to decompose the clock bias data; then, the BPNN prediction method is used to establish a high-precision clock bias prediction model; finally, based on the clock bias prediction value, the three-dimensional positioning of the navigation receiver is realized by expanding the observation equation. The experimental results show that the proposed model is suitable for clock bias time series prediction and providing three-dimensional positioning information meets the requirements of navigation application in the harsh environment of only three satellites.

Clock-modeling-constrained Epoch Relative Positioning for GPS coseismic displacement estimation

High-rate GNSS technology is invaluable for capturing surface displacements. However, vertical displacement is strongly linked to zenith tropospheric delay (ZTD) and receiver clock bias, compromising accuracy and impeding the detection of weak seismic waves. Some GNSS stations, fortunately, feature high-stability oscillators, enabling receiver clock modeling instead of epoch-wise estimation. This paper introduces an epoch relative positioning approach (ERP)with receiver clock modeling (CMC-ERP) to enhance coseismic displacement accuracy. Applied to earthquakes in Japan and the United States, the method improves vertical displacement accuracy by 24% to 61%. Furthermore, P-wave arrival times are determined by processing displacement sequences extracted through both CMC-ERP and ERP methods using STA/LTA. Compared to theoretical arrival times calculated by TauP software, CMC-ERP accuracy is enhanced by 74%–99%, further confirming its effectiveness.

Smart forwarding deceptive jamming distribution optimal algorithm

AbstractWith the frequent occurrence of drone black flying in large stadiums and airports, the requirement of precise electromagnetic interference to achieve unmanned aerial vehicle (UAV) displacement and forced landing in these protected area became urgent. Since traditional suppression jamming will affect normal communication, and forwarding deceptive jamming has coverage hole, a smart forwarding deceptive jamming distribution optimal algorithm (SFDJDO) is proposed. It gives a mapping error scale factor and the optimal distribution of multistation forwarding equivalent mapping to solve the problem of distortion on the mapping scale caused by different distribution methods and reduces the influence of the mapping errors and the differences between the virtual and real point neighborhoods of the jamming source. A comparison of the proposed SFDJDO method to the existing jamming source distribution optimisation method is conducted in the aspect of area mapping and trajectory mapping. The findings reveal that when the GNSS receiver clock bias is within the capture range, SFDJDO demonstrates significant enhancements in mapping precision and jamming success rates.

Impacts of satellite clock errors on GPS/BDS/Galileo real-time PPP time transfer

By utilizing the real-time precise orbit and clock products provided by International GNSS Service (IGS), it is feasible to calculate real-time PPP (RTPPP) time and frequency transfer. The quality of these real-time precise products has a significant effect on the performance of clock comparisons and time transfer. This paper focuses on real-time clock comparisons with IGS real-time multi-GNSS precise products, which tries to explore the potential of GNSS RTPPP time transfer in time and frequency community. By using real-time precise satellite orbit and clock products from two IGS analysis centers, i.e. CNES and WHU, the clock comparisons and time transfer performance of four time links are comprehensively investigated. It is shown that the statistical uncertainty of real-time clock comparison based on multi-GNSS is within 0.15 ns, and GPS RTPPP provides time transfer results with better performance than BDS-3 and Galileo. In addition, the deviations occur in remote time links results of BDS-3 and Galileo-only between using CNES and WHU, the maximum difference can reach up to 1.10 ns. It is shown that real-time BDS-3 and Galileo satellite products of CNES and WHU are inconsistent, and will affect the time transfer performance. The paper also investigates the receiver clock offset solutions determined by using different available satellites. The results show that there are significant satellite-related biases between different satellites, especially for BDS-3 and Galileo. Thus, the reference time scales determined by using different satellites are inconsistent, and further, the time transfer for long baseline time links will be affected as there are few common view satellites for remote stations.

GMM-based GNSS spoofing detector using double differential phase measurement

GNSS spoofing is an intentional interference wherein a GNSS receiver tracks counterfeit signals, resulting in incorrect outcome positions. This is the most dangerous type of intervention in the GNSS technology. In this study, we introduce a novel method for detecting spoofing signals using a Gaussian mixture model (GMM) on the double-carrier phase difference (DD) created by two independent receivers. The DD can completely eliminate errors caused by the satellite clock, receiver clock, and atmospheric layers; hence, the signal angle of arrival (AoA) is clearly expressed in the DD measurement. We utilized the GMM to model the probability density function of the DD measurement computed from the phase measurement of the receivers. Theoretically, AoA values of an authentic signal change over time owing to the nature of the signal broadcast from an orbiting satellite. However, fake signals are often transmitted from the generator, resulting in a central distribution of the corresponding AoA values. Existing studies deal with the spoofing detection problem using the above theoretical assumptions. However, it is practical to broadcast spoofing signals from several sources, and random noise can be mixed into the generated phase to render the DD measurement noisy. In such complicated scenarios, existing approaches are not sufficiently robust to detect non-authentic signals. Another observation is that because real satellites are moving in fixed orbits, there should be a correlation among the AoA values of the signals coming from these satellites. In contrast, counterfeit signals (with the main purpose of causing the wrong position or noisy phase) do not follow the pattern of the real signals. Therefore, instead of using the above hard assumption about the signal AoA, we propose a statistical model GMM to learn the hidden relationship of the AoA values among real signals from different real satellites, which are then used to detect spoofing signals.

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.

An Interstation Undifferenced Real-Time Time Transfer Method with Refined Modeling of Receiver Clock

Due to their advantages of high measurement accuracy and wide coverage, global navigation satellite systems (GNSSs) can carry out long-distance time transfers, among which the precise point positioning (PPP) method is widely used. However, the accuracy and stability of PPP real-time time transfer are restricted by the real-time satellite clock offset products. In addition, the receiver clock offset is usually estimated using the white noise model, which ignores the correlation of the clock offsets between adjacent epochs and the stability of the atomic clock itself. In order to obtain higher performance time transfer results, we propose an interstation undifferenced time transfer method with refined modeling of the receiver clock. This method takes the satellite clock offset as the parameter to be estimated, which can avoid the influence of external satellite clock offset products. In addition, the refined modeling of the receiver clock can improve the strength of the model and the accuracy of time transfer. Based on the ultrarapid satellite orbit products provided by the International GNSS Service (IGS), time transfer experiments are carried out using data from IGS observatories and self-collected data. The results show that sub-nanosecond accuracy can be achieved in real-time time transfer using this method. Compared with the traditional PPP model, the accuracies of the four time links are increased by 88.4%, 92.9%, 88.6%, and 74.5%, respectively, and the stability is increased by approximately 66.4% on average. Moreover, after applying the clock offset constraint model, frequency stability is further improved, in which the short-term stability is improved significantly, with a maximum of 86.9% and an average improvement of approximately 66.8%.

Adverse effects of receiver clock bias and drift on NavIC user position coordinates and their mitigation

We investigated the effects of receiver clock bias and drift on NavIC receiver position coordinates at a low latitude station and proposed a mitigation technique. For this, Five weeks data of Accord IRNSS-GPS-SPS (AIGS) receiver are considered. Error in each position coordinates (X, Y and Z) is estimated and observed that the maximum error occurred in user position Z-coordinate. CEP for 2D position is analyzed and observed that the Circular Error Probability (CEP) values are high in Z coordinate of YZ and ZX planes. Further, it is noticed that the timing of sudden enhancement of both clock bias and drift parameters coincides with the periodic anomaly of the X, Y and Z coordinates. The error in individual position coordinates is minimized by applying 6th order Butterworth low pass filter resulting in improved position accuracy. If such errors are not mitigated, the position estimation of the receiver becomes highly erroneous.

Stochastic modeling of the receiver clock parameter in Galileo-only and multi-GNSS PPP solutions

In Precise Point Positioning (PPP), the receiver clock parameter is typically estimated independently in each observation epoch, which increases the noise of the estimated station coordinates and troposphere parameters due to correlations. Applying stochastic modeling to the receiver clock parameter stabilizes PPP solutions and reduces clock noise for the time transfer. However, the receiver clock modeling is possible only for the GNSS receivers connected to the utmost stable atomic clocks. We propose receiver clock modeling that involves the Markov stochastic process in the form of a random walk. We test different levels of random walk constraints for GNSS stations equipped with different types of clocks for Galileo-only and multi-GNSS solutions in kinematic and static PPP. In multi-GNSS solutions, the common clock parameter is derived with inter-system biases (ISBs). This raises the question of the constraints that should be imposed on the common clock only or also on the ISBs. We found that similar results can be achieved by imposing constraints on the common clock parameter and estimating ISB as a constant parameter and when constraining the common clock parameter and ISBs with a ratio of 1:100. Other ratios of clock-to-ISB constraints, such as 1:1 and 1:10, give inferior results. In the kinematic PPP, stochastic clock modeling has a marginal impact on the North and East coordinate components, whereas the Up component is substantially improved for GNSS receivers equipped with hydrogen masers. In the static PPP, the clock modeling improves the time transfer, due to the reduced noise of the clocks.

Undifferenced precise time transfer with information‐constraints

AbstractSatellite navigation systems enable long‐distance and high‐precision time transfers. The authors proposed an undifferenced precise time transfer method with information constraints in this study. A more accurate receiver clock offset can be obtained by constraining the station coordinate parameters and receiver clock offset parameters to achieve a precise time transfer. In this example, the research object is the time transfer link established by the Global Positioning System observation station using a caesium clock, rubidium clock, and hydrogen clock. The clock difference sequence of the time‐transfer link was calculated by combining the observation data and precise products. Following analysis of the examples, the following conclusions were reached. The undifferenced precise time transfer method based on information constraints can effectively be used to smooth the clock difference sequence of the receiver and the clock difference sequence of the time transfer link. To some extent, this method can also be used to reflect the performance of atomic clocks at Global Positioning System stations and is better suited for the precise time transfer of the equal‐clock long‐baseline time transfer link. Simultaneously, the frequency stability of this method is improved significantly in the short term compared to the traditional scheme without any constraints. The improvement of frequency stability is helpful to improve the accuracy of time transfer.

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.