Research and Verification of a Novel Interferometry Method by Joint Processing of Downlink Pseudo-Noise Ranging and DOR Signals for Deep Space Exploration.

The remarkably long distances covered by deep space probes result in extremely weak downlink signals, which poses great challenges for ground measurement systems. In the current climate, improving the comprehensive utilization of downlink signal power to increase the detection distance or enhance the measurement accuracy is of great significance in deep space exploration. Facing this problem, we analyze the delta Differential One-way Range (ΔDOR) error budget of the X-band of the China Deep Space Network (CDSN). Then, we propose a novel interferometry method that detunes one group of DOR beacons and reuses the clock components of regenerative pseudo-code ranging signals for interferometry delay estimation. The primary advantage of this method is its ability to enhance the power utilization efficiency of downlink signals, thereby facilitating more efficient tracking and measurement without necessitating additional design requirements for deep space transponders. Finally, we analyze and verify the correctness and effectiveness of our proposed method using measured data from CDSN. Our results indicate that the proposed method can save approximately 13% of the downlink signal power and increase the detection distance by about 6.25% using typical modulation parameters. Furthermore, if the relative power of other signal components remains unchanged, the power of the DOR tone can be directly increased by more than 100%, improving the deep space exploration ability more significantly.

The Processing of Lexical Ambiguity: Evidence from Child and Adult Greek.

The aim of the study is to examine the effect of sentential context on lexical ambiguity resolution in Greek adults and typically developing children. Context and word frequency are factors that can affect lexical processing, however, the role of them has not been thoroughly examined in Greek. To this aim, we assessed sentence context effects in homonym meaning activation in monolingual speakers of Greek, children and adults, using a cross-modal priming paradigm. Additionally, all participants conducted a verbal working memory task and an inhibition task so as to examine whether the use of sentential context for lexical ambiguity resolution relates to age and/or cognitive processing capacity. The data analysis showed (a) major processing differences between adults and children due to ambiguity and sentential context, (b) children's processing times affected by cognitive skills while adults' processing unaffected, and (c) visual word recognition intact for all participants.

Performance Analysis of Real-Time GPS/Galileo Precise Point Positioning Integrated with Inertial Navigation System.

The integration of global navigation satellite system (GNSS) precise point positioning (PPP) and inertial navigation system (INS) is widely used in navigation for its robustness and resilience, especially in case of GNSS signal blockage. With GNSS modernization, a variety of PPP models have been developed and studied, which has also led to various PPP/INS integration methods. In this study, we investigated the performance of a real-time GPS/Galileo zero-difference ionosphere-free (IF) PPP/INS integration with the application of uncombined bias products. This uncombined bias correction was independent of PPP modeling on the user side and also enabled carrier phase ambiguity resolution (AR). CNES (Centre National d'Etudes Spatiales) real-time orbit, clock, and uncombined bias products were used. Six positioning modes were evaluated, including PPP, PPP/INS loosely coupled integration (LCI), PPP/INS tightly coupled integration (TCI), and three of these with uncombined bias correction through a train positioning test in an open sky environment and two van positioning tests at a complex road and city center. All of the tests used a tactical-grade inertial measurement unit (IMU). In the train test, we found that ambiguity-float PPP had almost identical performance with LCI and TCI, which reached an accuracy of 8.5, 5.7, and 4.9 cm in the north (N), east (E) and up (U) direction, respectively. After AR, significant improvements on the east error component were achieved, which were 47%, 40%, and 38% for PPP-AR, PPP-AR/INS LCI, and PPP-AR/INS TCI, respectively. In the van tests, frequent signal interruptions due to bridges, vegetation, and city canyons make the IF AR difficult. TCI achieved the highest accuracies, which were 32, 29, and 41 cm for the N/E/U component, respectively, and also effectively eliminated the solution re-convergence in PPP.

An Improved Ambiguity Resolution Algorithm for Smartphone RTK Positioning.

Ambiguity resolution based on smartphone GNSS measurements can enable various potential applications that currently remain difficult due to ambiguity biases, especially under kinematic conditions. This study proposes an improved ambiguity resolution algorithm, which uses the search-and-shrink procedure coupled with the methods of the multi-epoch double-differenced residual test and the ambiguity majority tests for candidate vectors and ambiguities. By performing a static experiment with Xiaomi Mi 8, the AR efficiency of the proposed method is evaluated. Furthermore, a kinematic test with Google Pixel 5 verifies the effectiveness of the proposed method with improved positioning performance. In conclusion, centimeter-level smartphone positioning accuracy is achieved in both experiments, which is greatly improved compared with the float and traditional AR solutions.

A Partial Ambiguity Resolution Algorithm Based on New-Breadth-First Lattice Search in High-Dimension Situations.

With the development and integration of GNSS systems in the world, the positioning accuracy and reliability of GNSS navigation services are increasing in various fields. Because the current multisystem fusion leads to an increase in the ambiguity dimension and the ambiguity parameters have discrete characteristics, the current conventional search algorithm leads to low search efficiency when the ambiguity dimension is large. Therefore, this paper describes a new algorithm that searches the optimal lattice points by lattice theory through the breadth-first algorithm and reduces the search space of ambiguity by calculating and judging the Euclidean distance between each search variable and the target one so as to propose a new lattice ambiguity search algorithm based on the breadth-first algorithm. The experimental results show that this method can effectively improve the search efficiency of ambiguity in high-dimension situations.

On the Problem of Double-Filtering in PPP-RTK.

To obtain single-receiver Global Navigation Satellite System (GNSS) parameter solutions, the PPP-RTK user-filter combines measurements with time-correlated corrections that are separately computed by the filter of an external provider. The consequence of exercising such double-filtering is that the Kalman filter's standard assumption of having uncorrelated measurements in time becomes violated. This leads the user-filter to lose its 'minimum variance' property, thereby delivering imprecise parameter solutions. The solutions' precision-loss becomes more pronounced when one experiences an increase in the correction latency, i.e., the delay in time after the corrections are estimated and the time they are applied to the user measurements. In this contribution, we propose a new multi-epoch formulation for the PPP-RTK user-filter upon which both the uncertainty and the temporal correlation of the corrections are incorporated. By a proper augmentation of the user-filter state-vector, the corrections are jointly measurement-updated with the user parameter solutions. Supported by numerical results, the proposed formulation is shown to outperform its commonly used counterpart in the minimum-variance sense.

Word vs. World Knowledge: A developmental shift from bottom-up lexical cues to top-down plausibility.

Both 5-year-old children and adults infer the structure of a sentence as they are hearing it. Prior work, however, has found that children do not always make use of the same information that adults do to guide these inferences. Specifically, when hearing ambiguous sentences like "You can tickle the frog with the feather," children seem to ignore the aspects of the referential context that adults rely on to resolve the ambiguity-e.g., are there two frogs in the scene, one with a feather and one without? Or is there only one frog to be tickled by using a feather? The present study explored two hypotheses about children's failure to use high-level, top-down context cues to infer the structure of these ambiguous sentences: First, children may be less likely to use any top-down cue during comprehension. Second, children may only have difficulties with top-down cues that are unreliable predictors of which syntactic structure is being used. Thus, to disentangle these hypotheses, we conducted a visual world study of adults' and children's ambiguity resolution, manipulating a more reliable top-down cue (the plausibility of the interpretation) and pitting it against a robust bottom-up cue (lexical biases). We find that adults' and children's final interpretations are influenced by both sources of information: adults, however, give greater weight to the top-down cue, whereas children primarily rely on the bottom-up cue. Thus, children's tendency to make minimal use of top-down information persists even when this information is highly valid and dominates adult comprehension. We propose that children have a systematic propensity to rely on bottom-up processing to a greater degree than adults, which could reflect differences in the architecture of the adult and child language comprehension systems or differences in processing speed.

Indoor Carrier Phase Positioning Technology Based on OFDM System.

Carrier phase measurement is a ranging technique that uses the receiver to determine the phase difference between the received signal and the transmitted signal. Carrier phase ranging has a high resolution; thus, it is an important research direction for high precision positioning. It is widely used in global navigation satellite systems (GNSS) systems but is not yet commonly used inwireless orthogonal frequency division multiplex (OFDM) systems. Applying carrier phase technology to OFDM systems can significantly improve positioning accuracy. Like GNSS carrier phase positioning, using the OFDM carrier phase for positioning has the following two problems. First, multipath and non-line-of-sight (NLOS) propagation have severe effects on carrier phase measurements. Secondly, ambiguity resolution is also a primary issue in the carrier phase positioning. This paper presents a ranging scheme based on the carrier phase in a multipath environment. Moreover, an algorithm based on the extended Kalman filter (EKF) is developed for fast integer ambiguity resolution and NLOS error mitigation. The simulation results show that the EKF algorithm proposed in this paper solves the integer ambiguity quickly. Further, the high-resolution carrier phase measurements combined with the accurately estimated integer ambiguity lead to less than 30-centimeter positioning error for 90% of the terminals. In conclusion, the presented methods gain excellent performance, even when NLOS error occur.

A Partial Carrier Phase Integer Ambiguity Fixing Algorithm for Combinatorial Optimization between Network RTK Reference Stations.

In the face of a complex observation environment, the solution of the reference station of the ambiguity of network real-time kinematic (RTK) will be affected. The joint solution of multiple systems makes the ambiguity dimension increase steeply, which makes it difficult to estimate all the ambiguity. In addition, when receiving satellite observation signals in the environment with many occlusions, the received satellite observation values are prone to gross errors, resulting in obvious deviations in the solution. In this paper, a new network RTK fixation algorithm for partial ambiguity among the reference stations is proposed. It first estimates the floating-point ambiguity using the robust extended Kalman filtering (EKF) technique based on mean estimation, then finds the optimal ambiguity subset by the optimized partial ambiguity solving method. Finally, fixing the floating-point solution by the least-squares ambiguity decorrelation adjustment (LAMBDA) algorithm and the joint test of ratio (R-ratio) and bootstrapping success rate index solver. The experimental results indicate that the new method can significantly improve the fixation rate of ambiguity among network RTK reference stations and thus effectively improve the reliability of positioning results.

A Comparative Study of BDS Triple-Frequency Ambiguity Fixing Approaches for RTK Positioning.

Concerning the triple-frequency ambiguity resolution, in principle there are three different realizations. The first one is to fix all the ambiguities of the original frequencies together. However, it is also believed that fixing the combined integer ambiguities with longer wavelength, such as extra-wide-lane (EWL), wide-lane (WL), should be advantageous. Also, it is demonstrated that fixing sequentially EWL, WL and one type of original ambiguities provides better results, as the previously fixed ambiguities increase parameters' precision for later fixings. In this paper, we undertake a comparative study of the three fixing approaches by means of experimental validation. In order to realize the three fixing approaches from the same information in terms of adjustment, we developed a processing strategy to provide fully consistent normal equations. We first generate the normal equation with the original undifferentiated carrier phase ambiguities, then map it into that with the combined and double-differenced ambiguities required by the individual approach for fixing. Four baselines of 258 m, 22 km, 47 km and 53 km are selected and processed in both static and kinematic mode using the three ambiguity-fixing approaches. Indicators including time of first fixed solution (TFFS), the correct fixing rate, positioning accuracy and RATIO are used to evaluate and investigate results. We also made a preliminary theoretical explanation of the results by looking into the decorrelation procedure of the ambiguity searching algorithm and the intermediate results. As conclusions, integrated searching of original ambiguities or combined ambiguities has almost the same fixing performance, whereas the sequential fixing of EWL, WL and B1 ambiguities overperforms the integrated searching. By the way, the third-frequency data can shorten the TFFS significantly but can hardly improve the positioning.

Cloud-Based Single-Frequency Snapshot RTK Positioning.

With great potential for being applied to Internet of Things (IoT) applications, the concept of cloud-based Snapshot Real Time Kinematics (SRTK) was proposed and its feasibility under zero-baseline configuration was confirmed recently by the authors. This article first introduces the general workflow of the SRTK engine, as well as a discussion on the challenges of achieving an SRTK fix using actual snapshot data. This work also describes a novel solution to ensure a nanosecond level absolute timing accuracy in order to compute highly precise satellite coordinates, which is required for SRTK. Parameters such as signal bandwidth, integration time and baseline distances have an impact on the SRTK performance. To characterize this impact, different combinations of these settings are analyzed through experimental tests. The results show that the use of higher signal bandwidths and longer integration times result in higher SRTK fix rates, while the more significant impact on the performance comes from the baseline distance. The results also show that the SRTK fix rate can reach more than 93% by using snapshots with a data size as small as 255 kB. The positioning accuracy is at centimeter level when phase ambiguities are resolved at a baseline distance less or equal to 15 km.

Effect Analysis of GNSS/INS Processing Strategy for Sufficient Utilization of Urban Environment Observations.

The occlusion of buildings in urban environments leads to the intermittent reception of satellite signals, which limits the utilization of observations. This subsequently results in a decline of the positioning and attitude accuracy of Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integrated system (GNSS/INS). This study implements a smooth post-processing strategy based on a tightly coupled differential GNSS/INS. Specifically, this strategy used the INS-estimated position to reinitialize integer ambiguity. The GNSS raw observations were input into the Kalman filter to update the measurement. The Rauch-Tung-Striebel smoothing (RTSS) algorithm was used to process the observations of the entire period. This study analyzed the performance of loosely coupled and tightly coupled systems in an urban environment and the improvement of the RTSS algorithm on the navigation solution from the perspective of fully mining the observations. The experimental results of the simulation data and real data show that, compared with the traditional tightly coupled processing strategy which does not use INS-aided integer ambiguity resolution and RTSS algorithm, the strategy in this study sufficiently utilized INS observations and GNSS observations to effectively improve the accuracy of positioning and attitude and ensure the continuity of navigation results in an obstructed environment.

Phonology and orthography in deaf readers: Evidence from a lateralized ambiguity resolution paradigm.

This study explored differences between the two hemispheres in processing written words among deaf readers. The main hypothesis was that impoverished phonological abilities of deaf readers may lead to atypical patterns of hemispheric involvement. To test this, deaf participants completed a metalinguistic awareness test to evaluate their orthographic and phonological awareness. Additionally, they were asked to read biased or neutral target sentences ending with an ambiguous homograph, with each sentence followed by the request to make a rapid lexical decision on a target word presented either to the left (LH) or right hemisphere (RH). Targets were either related to the more frequent, dominant, meaning of the homograph, to the less frequent, subordinate, meaning of the homograph or were not related at all. An Inverse Efficiency Score based on both response latency and accuracy was calculated and revealed that deaf readers' RH perform better than their LH. In contrast to hearing readers who in previous studies manifested left hemisphere dominance when completed the same research design. The apparent divergence of deaf readers' hemisphere lateralization from that of hearing counterparts seems to validate previous findings suggesting greater reliance on RH involvement among deaf individuals during visual word recognition.

Extra-Wide Lane Ambiguity Resolution and Validation for a Single Epoch Based on the Triple-Frequency BeiDou Navigation Satellite System.

The ambiguity resolution (AR) and validation of the global navigation satellite system (GNSS) have been challenging tasks for some decades. Considering the reliability problem of extra-wide-lane (EWL) ambiguity in the triple-carrier ambiguity resolution (TCAR), a method for validating the reliability of the EWL ambiguity using a single epoch was proposed for the BeiDou Navigation Satellite System (BDS). For the initial EWL ambiguity, obtained using a rounding estimator with a geometry-free (GF) model, the double-difference ionospheric delay was first estimated to construct a relative positioning model with an initial fixed ambiguity. Second, based on the theory of gross error detection and the AR characteristics of EWL, the second-best ambiguity candidate was constructed. Finally, among the two sets of ambiguities, the one with the smaller posterior variance was taken as the reliable ambiguity. The study showed that, for a single epoch, when only one or two satellites had incorrect ambiguities, the AR success rate after ambiguity validation and correction could reach 100% for medium baselines. For long baselines, due to the increase of atmospheric error, the validation was affected to some extent. However, the AR success rates for two long baselines increased from 96.82% and 98.44% to 98.80% and 99.67%, respectively.

Instantaneous Ambiguity Reinitialization and Fast Ambiguity Initialization for L1-L2 GPS Measurements.

This paper presents a PREcise and Fast Method of Ambiguity Reinitialization/Resolution (PREFMAR) for L1 and L2 in GPS measurements. The method determines NL1 and NL2 ambiguities based on the ambiguity functions: Ψ(NL1)NL1NL2 and Ψ(NL2)NL2NL1. These ambiguity functions have been described in detail in this work. The developed method of ambiguity initialization and reinitialization in relative positioning can use Global Positioning System (GPS) measurements from only two satellites and one measurement epoch. To resolve NL1 and NL2 ambiguities, a variance-covariance (VC) matrix of the float solution is not needed. The size of the search area in the PREFMAR method depends on code and phase accuracy as well as on the GNSS signal frequencies. Therefore, the search area is specific for every double or triple Global Navigation Satellite Systems (GNSS) data frequency. However, this part of the research only presents the ambiguity search area for L1 and L2 of GPS measurements. Additionally, a numerical example has been analyzed in detail with the use of the PREFMAR method and a float solution (NL1, NL2). Finally, the elaborated algorithms were successfully tested on real L1 and L2 GPS measurements for instantaneous ambiguity reinitialization. The PREFMAR method allows instantaneous ambiguity reinitialization if all satellites lose contact with a GNSS antenna, for short and long baselines. Therefore, the PREFMAR has a great potential for precise real-time kinematic GNSS navigation.

Kinematic ME-MAFA for Pseudolite Carrier-Phase Ambiguity Resolution in Precise Single-Point Positioning.

Precise single-point positioning using carrier-phase measurements can be provided by the synchronized pseudolite system. The primary task of carrier phase positioning is ambiguity resolution (AR) with rapidity and reliability. As the pseudolite system is usually operated in the dense multipath environment, cycle slips may lead the conventional least-squares ambiguity decorrelation adjustment (LAMBDA) method to incorrect AR. A new AR method based on the idea of the modified ambiguity function approach (MAFA), which is insensitive to the cycle slips, is studied in this paper. To improve the model strength of the MAFA and to eliminate the influence of constant multipath biases on the time-average model in static mode, the kinematic multi-epoch MAFA (kinematic ME-MAFA) algorithm is proposed. A heuristic method for predicting the 'float position' corresponding to every Voronoi cell of the next epoch, making use of Doppler-based velocity information, is implemented to improve the computational efficiency. If the success rate is very close to 1, it is possible to guarantee reliable centimeter-level accuracy positioning without further ambiguity validation. Therefore, a computing method of the success rate for the kinematic ME-MAFA is proposed. Both the numerical simulations and the kinematic experiment demonstrate the feasibility of the new AR algorithm according to its accuracy and reliability. The accuracy of the horizontal positioning solution is better than 1.7 centimeters in our pseudolite system.

Ambiguity of Residual Constraint-Based Precise Point Positioning with Partial Ambiguity Resolution under No Real-Time Network Corrections Using Real Global Positioning System (GPS) Data.

Although precise point positioning (PPP) is a well-established and promising technique with the use of precise satellite orbit and clock products, it costs a long convergence time to reach a centimeter-level positioning accuracy. The PPP with ambiguity resolution (PPP-AR) technique can improve convergence performance by resolving ambiguities after separating the fractional cycle bias (FCB). Now the FCB estimation is mainly realized by the regional or global operating reference station network. However, it does not work well in the areas where network resources are scarce. The contribution of this paper is to realize an ambiguity residual constraint-based PPP with partial ambiguity resolution (PPP-PARC) under no real-time network corrections to speed up the convergence, especially when the performance of the float solution is poor. More specifically, the update strategy of FCB estimation in a stand-alone receiver is proposed to realize the PPP-PAR. Thereafter, the solving process of FCB in a stand-alone receiver is summarized. Meanwhile, the influencing factors of the ambiguity success rate in the PPP-PAR without network corrections are analyzed. Meanwhile, the ambiguity residual constraint is added to adapt the particularity of the partial ambiguity-fixing without network corrections. Moreover, the positioning experiments with raw observation data at the Global Positioning System (GPS) globally distributed reference stations are conducted to determine the ambiguity residual threshold for post-processing and real-time scenarios. Finally, the positioning performance was verified by 22 GPS reference stations. The results show that convergence time is reduced by 15.8% and 26.4% in post-processing and real-time scenarios, respectively, when the float solution is unstable, compared with PPP using a float solution. However, if the float solution is stable, the PPP-PARC method has performance similar to the float solution. The method shows the significance of the PPP-PARC for future PPP applications in areas where network resource is deficient.

Real-Time PPP-RTK Performance Analysis Using Ionospheric Corrections from Multi-Scale Network Configurations.

The long convergence time required to achieve high-precision position solutions with integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is driven by the presence of ionospheric delays. When precise real-time ionospheric information is available and properly applied, it can strengthen the underlying model and substantially reduce the time required to achieve centimeter-level accuracy. In this study, we present and analyze the real-time PPP-RTK user performance using ionospheric corrections from multi-scale regional networks during a day with medium ionospheric disturbance. It is the goal of this contribution to measure the impact the network dimension has on the ambiguity-resolved user position through the predicted ionospheric corrections. The user-specific undifferenced ionospheric corrections are computed at the network side, along with the satellite phase biases needed for single-receiver ambiguity resolution, using the best linear unbiased predictor. Such corrections necessitate the parameterization of an estimable user receiver code bias, on which emphasis is given in this study. To this end, we process GPS dual-frequency data from four four-station evenly distributed CORS networks in the United States with varying station spacings in order to evaluate if and to what extent the ionospheric corrections from multi-scale networks can improve the user convergence times. Based on a large number of samples, our experimental results showed that sub-10 cm horizontal accuracy can be achieved almost instantaneously in the ionosphere-weighted partially-ambiguity-fixed kinematic PPP-RTK solutions based on corrections from a network with 68 km spacing. Most of the solutions (90%) were shown to require less than 6.0 min, compared to the ionosphere-float PPP solutions that needed 68.5 min. In case of sparser networks with 115, 174 and 237 km spacing, 50% of the horizontal positioning errors are shown to become less than one decimeter after 1.5, 4.0 and 7.0 min, respectively, while 90% of them require 10.5, 16.5 and 20.0 min. We also numerically demonstrated that the user's convergence times bear a linear relationship with the network density and get shorter as the density increases, for both full and partial ambiguity resolution.

Precise Point Positioning Algorithm for Pseudolite Combined with GNSS in a Constrained Observation Environment.

In urban canyon environments, Global Navigation Satellite System (GNSS) satellites are heavily obstructed with frequent rise and fall and severe multi-path errors induced by signal reflection, making it difficult to acquire precise, continuous, and reliable positioning information. To meet imperative demands for high-precision positioning of public users in complex environments, like urban canyons, and to solve the problems for GNSS/pseudolite positioning under these circumstances, the Global Navigation Satellite System (GNSS) Precision Point Positioning (PPP) algorithm combined with a pseudolite (PLS) was introduced. The former problems with the pseudolite PPP technique with distributed pseudo-satellites, which relies heavily on known points for initiation and prerequisite for previous high-precision time synchronization, were solved by means of a real-time equivalent clock error estimation algorithm, ambiguity fixing, and validation method. Experiments based on a low-cost receiver were performed, and the results show that in a weak obstructed environment with low-density building where the number of GNSS satellites was greater than seven, the accuracy of pseudolite/GNSS PPP with fixed ambiguity was better than 0.15 m; when there were less than four GNSS satellites in severely obstructed circumstances, it was impossible to obtain position by GNSS alone, but with the support of a pseudolite, the accuracy of PPP was able to be better than 0.3 m. Even without GNSS, the accuracy of PPP could be better than 0.5 m with only four pseudolites. The pseudolite/GNSS PPP algorithm presented in this paper can effectively improve availability with less GNSS or even without GNSS in constrained environments, like urban canyons in cities.

Fast Time Synchronization on Tens of Picoseconds Level Using Uncombined GNSS Carrier Phase of Zero/Short Baseline.

Since the observation precision of the Global Navigation Satellite System (GNSS) carrier phase is on the order of millimeters, if the phase ambiguity is correctly solved, while calibrating the receiver inter-frequency bias, time synchronization on the order of tens of picoseconds is expected. In this contribution, a method that considers the prior constraints of the between-receiver inter-frequency bias (IFB) and its random variation characteristics is proposed for the estimation of the between-receiver clock difference, based on the uncombined GNSS carrier phase and pseudorange observations of the zero and short baselines. The proposed method can rapidly achieve the single-difference ambiguity resolution of the zero and short baselines, and then obtain the high-precision relative clock offset, by using only the carrier phase observations, along with the between-receiver IFBs being simultaneously determined. Our numerical tests, carried out using GNSS observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, show that the method can fix the between-receiver single-difference ambiguity successfully within an average of fewer than 2 epochs (interval 30 s). Then, a clock difference between two receivers with millimeter precision is obtained, achieving time synchronization on tens of picoseconds level, and deriving a frequency stability of 5 × 10-14 for averaging times of 30,000 s. Furthermore, the proposed approach is compared with the precise point positioning (PPP) time transfer method. The results show that, for different types of receivers, the agreement between the two methods is between -6.7 ns and 0.2 ns.