Considering Receiver Clock Modeling in PPP Time Transfer with BDS-3 Triple-Frequency Un-combined Observations

Precise point positioning (PPP) technique is an effective tool for time and frequency applications. Using phase/code observations and precise products, the PPP time transfer allows an accuracy of sub-nanoseconds within a latency of several days. Although the PPP time transfer is usually implemented in the post-processing mode, using the real-time PPP (RT-PPP) technique for time transfer with the shorter latency remains attractive to time community. In 2012, the IGS (International GNSS Service) launched an open-access real-time service (RTS) project, broadcasting satellite orbit and clock corrections on the Internet, which enables PPP time transfer in the real-time mode. In this contribution, we apply the RT-PPP for high-precision time transfer and synchronization. The GNSS receiver is required to be equipped with an atomic clock as the external local clock. We use the RT-PPP technique to compute the receiver clock offset with respective to the GNSS time scale. On the basis of clock offsets, we steer the local clock by frequency adjustment method. In this way, all the local clocks are synchronized to the GNSS time scale, making local clocks synchronized with each other.The time scales of the RTS products are evaluated at first. Six kinds of the RTS products (IGS01, CLK10, CLK53, CLK80 and CLK93) on DOY220-247, 2019 are pre-saved to compute the receiver clock offsets. The clock offset with respect to the GPST (GPS Time) obtained from the IGS final product is applied as the reference. The standard deviations (STDs) of the clock offsets with respect to the reference are 0.63, 1.76, 0.28, 0.27 and 1.28 ns for IGS01, CLK10, CLK53, CLK80 and CLK93, respectively.Finally, we set up a hardware system to examine the validity of our time synchronization method. The baseline of the time synchronization experiment is about 5 m. The synchronization error of the 1 PPS outputs is precisely measured by the frequency counter. The STD of the 4-days results is about 0.48 ns. The peak-to-peak value of the synchronization error is about 2.5 ns.

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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

Sensors ◽

10.3390/s19112469 ◽

2019 ◽

Vol 19 (11) ◽

pp. 2469 ◽

Cited By ~ 1

Author(s):

Peng Liu ◽

Honglei Qin ◽

Li Cong

Keyword(s):

Global Positioning System ◽

Precise Point Positioning ◽

Satellite System ◽

Navigation Satellite ◽

Dual Frequency ◽

Triple Frequency ◽

Global Positioning ◽

Receiver Clock ◽

Point Positioning ◽

Fixed Solution

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.

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Initial Performance Evaluation of Precise Point Positioning with Triple-Frequency Observations from BDS-2 and BDS-3 Satellites

Journal of Navigation ◽

10.1017/s0373463319000754 ◽

2020 ◽

Vol 73 (4) ◽

pp. 763-775 ◽

Cited By ~ 1

Author(s):

Wenjie Zhang ◽

Hongzhen Yang ◽

Chen He ◽

Zhiqiang Wang ◽

Weiping Shao ◽

...

Keyword(s):

Precise Point Positioning ◽

Convergence Time ◽

Asia Pacific ◽

Basic Model ◽

Triple Frequency ◽

Ionosphere Model ◽

Receiver Clock ◽

Combined Solution ◽

Code Bias ◽

Point Positioning

This paper presents an investigation of the precise point positioning (PPP) performance of a combined solution from BDS-2 and BDS-3 satellites. To simultaneously process different BDS signal observations, i.e., B1/B1C, B2/B2a and B3C, undifferenced and uncombined observations with ionosphere delay constrained by the deterministic plus stochastic ionosphere model are used in the basic model. Special attention is paid to code bias and receiver clock parameters in the derivation of the observation model. The analysis is carried out using more than one-month data for BDS-2 and BDS-3 collected at the CANB, DWIN, KNDY and PETH stations in the Asia-Pacific region. The results suggest that compared with BDS-2 alone, the BDS-2 and BDS-3 solution provides significantly more accurate PPP, with increases of 28%, 21% and 5% in the up, north and east directions, respectively. In addition, the average root mean square error decreases to 0·21, 0·13 and 0·16 m for the three directions. Furthermore, the PPP convergence time for BDS-2 and BDS-3 is about 1·5 h and less than 1 h for the horizontal and vertical components, respectively, whereas that for BDS-2 alone is about 2·3 h for both directions.

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Evaluation of the Effect of Higher-Order Ionospheric Delay on GPS Precise Point Positioning Time Transfer

Remote Sensing ◽

10.3390/rs12132129 ◽

2020 ◽

Vol 12 (13) ◽

pp. 2129 ◽

Cited By ~ 1

Author(s):

Haiyan Yang ◽

Xuhai Yang ◽

Zhe Zhang ◽

Baoqi Sun ◽

Weijin Qin

Keyword(s):

Northern Hemisphere ◽

High Precision ◽

Precise Point Positioning ◽

Time Transfer ◽

Low Latitude ◽

Constant Bias ◽

Receiver Clock ◽

Long Time ◽

The Difference ◽

Short Time

In high-precision GPS precise point positioning (PPP) time transfer, errors caused by the effect of ionosphere delay have to be corrected. Usually the ionosphere-free combinations of the pseudo code and the carrier phase is used in GPS PPP data processing, and it effectively eliminates the effect of the first-order ionospheric delay. This study quantitatively analyzes the errors caused by higher-order ionospheric (Ion2+) delays in precise PPP time transfer. Data of two 7-day test periods, including low and moderate ionospheric conditions, from 20 stations located in middle- and low-latitude, were analyzed. The difference in clock solution with and without the Ion2+ correction, including the receiver clock solution and time-link clock solution, was deeply analyzed and discussed. The difference sequence shows a constant bias plus some variations with a diurnal variation. For the difference of the receiver clock solutions, the mean standard deviation of the variations is 3.92 ps in low-latitude, which is much larger than that of 2.59 ps in mid-latitude due to the influence of the larger ionospheric electron density on the low-latitude. The maximum constant bias reached more than 15 ps and was negative at most stations in the northern hemisphere, while it was positive at most stations located in the southern hemisphere. The difference in the time-link solutions correlates not only with time and region, but also with the length of the time-links. The largest difference in the long time-link SYDN-PTBB, BJNM-SYDN, AMC2-SYDN, etc., reaches more than 25 ps, while that of the short time-link IENG-PTBB, BRUX-PTBB, etc., is less than 3.5 ps. Therefore, the Ion2+ correction is necessary for high-precision PPP time transfer over long time-links, especially time-links made by one station located in the northern hemisphere and another located in the south hemisphere; however, it could be ignored for short time-links.

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Performance of Multi-GNSS Precise Point Positioning Time and Frequency Transfer with Clock Modeling

Remote Sensing ◽

10.3390/rs11030347 ◽

2019 ◽

Vol 11 (3) ◽

pp. 347 ◽

Cited By ~ 15

Author(s):

Yulong Ge ◽

Peipei Dai ◽

Weijin Qin ◽

Xuhai Yang ◽

Feng Zhou ◽

...

Keyword(s):

White Noise ◽

Precise Point Positioning ◽

Noise Model ◽

Single System ◽

Time Transfer ◽

Receiver Clock ◽

Maximum Improvement ◽

Frequency Transfer ◽

White Noise Model ◽

Point Positioning

Thanks to the international GNSS service (IGS), which has provided multi-GNSS precise products, multi-GNSS precise point positioning (PPP) time and frequency transfer has of great interest in the timing community. Currently, multi-GNSS PPP time transfer is not investigated with different precise products. In addition, the correlation of the receiver clock offsets between adjacent epochs has not been studied in multi-GNSS PPP. In this work, multi-GNSS PPP time and frequency with different precise products is first compared in detail. A receiver clock offset model, considering the correlation of the receiver clock offsets between adjacent epochs using an a priori value, is then employed to improve multi-GNSS PPP time and frequency (scheme2). Our numerical analysis clarify how the approach performs for multi-GNSS PPP time and frequency transfer. Based on two commonly used multi-GNSS products and six GNSS stations, three conclusions are obtained straightforwardly. First, the GPS-only, Galileo-only, and multi-GNSS PPP solutions show similar performances using GBM and COD products, while BDS-only PPP using GBM products is better than that using COD products. Second, multi-GNSS time transfer outperforms single GNSS by increasing the number of available satellites and improving the time dilution of precision. For single-system and multi-GNSS PPP with GBM products, the maximum improvement in root mean square (RMS) values for multi-GNSS solutions are up to 7.4%, 94.0%, and 57.3% compared to GPS-only, BDS-only, and Galileo-only solutions, respectively. For stability, the maximum improvement of multi-GNSS is 20.3%, 84%, and 45.4% compared to GPS-only, BDS-only and Galileo-only solutions. Third, our approach contains less noise compared to the solutions with the white noise model, both for the single-system model and the multi-GNSS model. The RMS values of our approach are improved by 37.8–91.9%, 10.5–65.8%, 2.7–43.1%, and 26.6–86.0% for GPS-only, BDS-only, Galileo-only, and multi-GNSS solutions. For frequency stability, the improvement of scheme2 ranges from 0.2 to 51.6%, from 3 to 80.0%, from 0.2 to 70.8%, and from 0.1 to 51.5% for GPS-only, BDS-only, Galileo-only, and multi-GNSS PPP solutions compared to the solutions with the white noise model in the Eurasia links.

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Modeling and Assessment of Precise Time Transfer by Using BeiDou Navigation Satellite System Triple-Frequency Signals

Sensors ◽

10.3390/s18041017 ◽

2018 ◽

Vol 18 (4) ◽

pp. 1017 ◽

Cited By ~ 14

Author(s):

Rui Tu ◽

Pengfei Zhang ◽

Rui Zhang ◽

Jinhai Liu ◽

Xiaochun Lu

Keyword(s):

Satellite System ◽

Navigation Satellite ◽

Time Transfer ◽

Beidou Navigation Satellite System ◽

Triple Frequency ◽

Precise Time

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An Approach to a Clock Offsets Model for Real-Time PPP Time and Frequency Transfer During Data Discontinuity

Applied Sciences ◽

10.3390/app9071405 ◽

2019 ◽

Vol 9 (7) ◽

pp. 1405 ◽

Cited By ~ 2

Author(s):

Weijin Qin ◽

Yulong Ge ◽

Pei Wei ◽

Xuhai Yang

Keyword(s):

Real Time ◽

Real Data ◽

Time Transfer ◽

Short Term ◽

Clock Model ◽

Simulation Data ◽

Term Stability ◽

Adaptive Prediction ◽

Receiver Clock ◽

The Stability

To resolve the dilemma in any post-processing strategy, i.e., the difficulty of monitoring the real-time time and frequency signals in a timely manner, real-time GPS time and the frequency transfer have recently become trending topics. Unfortunately, data interruption occurs when conducting real-time time transfer, sometimes from unexpected reasons. In this study, to ensure the stability and precision of real-time time transfer, an adaptive prediction model and a between-epoch constraint receiver clock model are applied as the mathematic models. The purpose of prediction is to solve the ambiguity from re-convergence when the data reappear. Moreover, compared to the conventional method, the between-epoch constraint receiver clock model is employed in this study to consider the correlation of epoch-wise clock parameters to avoid wasting useful information. The simulation data and real data are compared to verify the performance of the new approach. The simulation data for 165 days are designed with random daily interruptions of 10, 30, 60 and 90 min. Real data from 12 days is captured from the incomplete data in routine observation records. Ignoring the simulation data and real data, the investigation of six stations shows that the results with the between-epoch constraint receiver clock model were smoother than those with a white noise model. With an adaptive prediction model and the between-epoch constraint receiver clock model, the simulation results illustrate that the average root mean squares (RMS) values of all the stations are significantly reduced, i.e., by 66.03% from 0.43 to 0.14 ns, by 64.91% from 0.44 to 0.15 ns, by 57.47% from 0.43 to 0.18 ns, and by 51.67% from 0.44 to 0.21 ns for the 10, 30, 60 and 90 min data interruptions, respectively. The stability of all the stations is improved by at least 50%. The improvement increases to 100% for short-term stability. The real results show that the stability of four links is boosted by at least 5%. The model proposed in this paper is more effective in producing short-term stability than long-term stability.

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