Real-Time PPP Based on the Coupling Estimation of Clock Bias and Orbit Error with Broadcast Ephemeris
Abstract
:1. Introduction
2. Estimation for the Parameter of Coupling Clock Bias with Orbit Error (PCCO)
2.1. Coupling of Clock Bias and Orbit Error
2.2. Joint Weighted Estimation of PCCO Based on Regional CORS
- At the first epoch, the satellite clock bias is calculated by using the pseudorange observation equation;
- At epoch n, through the difference among the phase observations, the epoch differential phase observations are added to the pseudorange observation and the initial epoch to create a new pseudorange observation . The expression is expressed as follows:
2.3. PCCO Effect on Observation Equations
3. Real-Time PPP System Based on PCCO
- (1)
- The “regional CORS reference stations” receive GNSS observations and broadcast ephemeris.
- (2)
- The “data control and processing center” receives observation data and the broadcast ephemeris from the regional CORS and then calculates the PCCO after data preprocessing.
- (3)
- The PCCO is encoded, instantaneously broadcasted to the rover user by a mobile network, and uploaded to the database for post-processing users. Since the single-difference results clock the bias of a pair of satellites, the satellite clock bias is given to the rover in pairs.
- (4)
- The PPP user receives observation data and broadcast ephemeris and obtains the clock bias coupled with orbit error followed by PPP.
- (1)
- In this system, satellite clock bias is coupled with orbit error as an estimation parameter. Therefore, precise ephemeris is no longer demanded because broadcast ephemeris is enough for real-time PPP.
- (2)
- PCCO can generate real-time clock bias coupled with orbit error by regional CORS and can broadcast to the rover instantaneously. PCCO has better real-time performance than the IGS real-time data stream.
- (3)
- PCCO only needs regional CORS and does not rely on global distribution station; thus, the PCCO method is easy to implement and is suitable for engineering practice.
4. Experiment and Analysis
4.1. Experiment within the Network
Station Name | RSDI | PCCO | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Directional Error (cm) | Position Error (cm) | Convergence Time (min) | Directional Error (cm) | Position Error (cm) | Convergence Time (min) | |||||
N | E | U | N | E | U | |||||
P289 | 2.65 | 4.48 | 6.28 | 8.16 | 36.25 | 0.75 | 2.74 | 5.62 | 6.30 | 16.25 |
P287 | 2.52 | 3.91 | 7.33 | 8.68 | 26.75 | 2.42 | 4.14 | 2.50 | 5.41 | 8.25 |
P299 | - | - | - | - | - | 2.67 | 3.87 | 1.47 | 4.93 | 14.75 |
P285 | 0.94 | 4.36 | 4.35 | 6.23 | 13.00 | 0.58 | 1.54 | 3.14 | 3.55 | 9.75 |
P175 | 2.97 | 6.42 | 1.78 | 7.29 | 38.00 | 2.07 | 1.89 | 1.78 | 3.32 | 9.75 |
4.2. Experiment Outside the Network
Station Name | Distance (km) | RSDI | PCCO | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Directional Error (cm) | Position Error (cm) | Convergence Time (min) | Directional Error (cm) | Position Error (cm) | Convergence Time (min) | ||||||
N | E | U | N | E | U | ||||||
P229 | 190.0 | - | - | - | - | - | 0.86 | 1.80 | 1.84 | 2.71 | 14.50 |
P571 | 195.1 | - | - | - | - | - | 1.95 | 2.60 | 2.16 | 3.90 | 12.50 |
P629 | 200.3 | 3.59 | 1.76 | 7.75 | 8.72 | 34.75 | 0.69 | 2.83 | 1.01 | 3.08 | 9.25 |
P579 | 297.7 | 1.61 | 2.79 | 8.12 | 8.74 | 53.00 | 1.54 | 4.80 | 3.46 | 6.11 | 7.75 |
P091 | 308.0 | 2.10 | 4.77 | 9.06 | 10.45 | 46.75 | 1.24 | 2.63 | 3.55 | 4.59 | 7.50 |
P617 | 407.9 | 0.96 | 3.78 | 6.34 | 7.44 | 11.75 | 1.01 | 3.84 | 3.54 | 5.32 | 5.75 |
P604 | 413.2 | 1.18 | 8.18 | 2.22 | 8.56 | 15.25 | 1.48 | 4.49 | 4.84 | 6.77 | 7.25 |
P611 | 492.2 | 2.03 | 8.04 | 3.95 | 9.19 | 42.75 | 1.82 | 5.21 | 5.01 | 7.45 | 9.25 |
P601 | 510.6 | 2.13 | 8.07 | 2.06 | 8.60 | 44.50 | 2.38 | 4.56 | 3.63 | 6.30 | 26.25 |
P490 | 511.6 | 2.72 | 4.74 | 3.91 | 6.72 | 12.25 | 1.93 | 2.06 | 2.98 | 4.10 | 16.00 |
5. Conclusions
- (1)
- The projection of satellite orbit error was similar to the clock bias on PPP; hence, they can be coupled as one parameter for estimation purposes. During PPP by the user, the OMC vectors of GNSS equations by coupling estimation were almost the same as the traditional PPP (with a difference in millimeters). Therefore, the orbit error was availably absorbed by clock bias, whereas the residual unabsorbed orbit error did not affect the positioning in a regional area.
- (2)
- For the stations inside and outside (with a distance less than 500 km) the network, the proposed approach performs better than RSDI. The position accuracy of the stations inside and outside the network improves by 38.8% and 36.1%, respectively, and the convergence speed improves by 61.4% and 65.9%, respectively. This new approach has the advantages of autonomy, real-time processes, and simple parameters, which is an improvement over traditional PPP. It could be an alternative solution for regional positioning service before global PPP service comes into operation.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Pan, S.; Chen, W.; Jin, X.; Shi, X.; He, F. Real-Time PPP Based on the Coupling Estimation of Clock Bias and Orbit Error with Broadcast Ephemeris. Sensors 2015, 15, 17808-17826. https://doi.org/10.3390/s150717808
Pan S, Chen W, Jin X, Shi X, He F. Real-Time PPP Based on the Coupling Estimation of Clock Bias and Orbit Error with Broadcast Ephemeris. Sensors. 2015; 15(7):17808-17826. https://doi.org/10.3390/s150717808
Chicago/Turabian StylePan, Shuguo, Weirong Chen, Xiaodong Jin, Xiaofei Shi, and Fan He. 2015. "Real-Time PPP Based on the Coupling Estimation of Clock Bias and Orbit Error with Broadcast Ephemeris" Sensors 15, no. 7: 17808-17826. https://doi.org/10.3390/s150717808
APA StylePan, S., Chen, W., Jin, X., Shi, X., & He, F. (2015). Real-Time PPP Based on the Coupling Estimation of Clock Bias and Orbit Error with Broadcast Ephemeris. Sensors, 15(7), 17808-17826. https://doi.org/10.3390/s150717808