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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

By the end of 2012, China had launched 16 BeiDou-2 navigation satellites that include six GEOs, five IGSOs and five MEOs. This has provided initial navigation and precise pointing services ability in the Asia-Pacific regions. In order to assess the navigation and positioning performance of the BeiDou-2 system, Wuhan University has built up a network of BeiDou Experimental Tracking Stations (BETS) around the World. The Position and Navigation Data Analyst (PANDA) software was modified to determine the orbits of BeiDou satellites and provide precise orbit and satellite clock bias products from the BeiDou satellite system for user applications. This article uses the BeiDou/GPS observations of the BeiDou Experimental Tracking Stations to realize the BeiDou and BeiDou/GPS static and kinematic precise point positioning (PPP). The result indicates that the precision of BeiDou static and kinematic PPP reaches centimeter level. The precision of BeiDou/GPS kinematic PPP solutions is improved significantly compared to that of BeiDou-only or GPS-only kinematic PPP solutions. The PPP convergence time also decreases with the use of combined BeiDou/GPS systems.

As a global navigation satellite system (GNSS) compatible with other worldwide navigation satellite systems, the BeiDou System (BDS) was independently established and operated by China. High accuracy and high reliability positioning, navigation and timing (PNT) services are expected to be provided to all kinds of users in any time, all-weather and anywhere in the World by 2020. Until the end of 2012, the constellation of BeiDou regional navigation satellite system consists of 16 satellites including six GEOs, five IGSOs and five MEOs with 14 satellites including five GEOs, five IGSOs and four MEOs operating well. The test version of Interface Control Document (ICD) for the signal-in-space of the BeiDou system was announced on December 27, 2011. This indicated that the BeiDou system started to provide Initial Operational Service. The formal version of ICD was announced and the Full Operational Service was provided for China and its surrounding areas on December 27, 2012. This indicated that the regional navigation satellite system had been set up. Domestic and foreign enterprises are being encouraged to participate in the research and development of BeiDou system application terminals (see

Since M01, the first satellite of BeiDou-2 system, was successfully launched, there have been various research projects studying the signal structure, the precise orbit determination of BeiDou satellites and the precise positioning performances. The signals of M01 have been tracked and the structure of the pseudo-random noise (PRN) code in the E2 (B1), E5b (B2), and E6 (B3) frequency bands has been analyzed [

The improvement of performance of a single Global Navigation Satellite System (GNSS) mainly depends on increasing the number of navigation satellites, optimizing the spatial geometric configuration and improving of the accuracy of the system's spatial signals, including the improvement of the accuracy of the precise orbit and satellite clock biases, whereas, the fusion of multiple GNSSs can significantly increase the number of observed satellites, optimize the spatial geometry and improve continuity and reliability of positioning [

In order to obtain the precise orbits and satellite clock biases of BeiDou satellites to assess the performance of precise positioning, since 2011 Wuhan University has established a continuous worldwide observation reference network, called the BeiDou Experimental Tracking Stations (BETS), which includes nine tracking stations in China and six tracking stations abroad. All the stations are equipped with UB240-CORS receivers produced by the Beijing Unicore Communication Company, which can acquire the pseudo-range and phase observations of dual frequencies and dual systems. The Unicore UA240 dual-frequency dual-system high gain antenna is used in the network. The accuracy of phase observations can reach millimeter level [

The multipath combination (MPC) is often used to assess the multipath and code noise level of a receiver [_{1} and _{2} are the frequencies of _{1} and _{2}.

We processed the data of the CHDU station on September 24, 2012 to analyze the multipath and noise error. The station is equipped with the Unicore UB240-CORS receiver and UA240 antenna. The mask elevation is 7° and the interval is 30 s.

The Position and Navigation Data Analyst (PANDA) software package, developed by the GNSS Research Center at Wuhan University, was used to process the BeiDou/GPS observations of “BETS”. Since 2003, the functions of the software have been extended continuously. PANDA software can be applied in the precise orbit determination for the GPS, GLONASS, the low-orbit satellites, PPP, PPP-RTK, the network adjustment, the precise relative positioning as well as the gravity field modeling using satellite-to-satellite tracking data [

The PPP parameters to be estimated contain the coordinates, the receiver clock biases, the delay of the wet troposphere component and the ambiguities when only processing BeiDou data. When BeiDou/GPS observations are processed in a combined mode, we need to introduce an inter-system bias between multiple GNSS signals in the receiver end [

BeiDou precise orbit and satellite clock bias products used in the contribution are based on the ITRF2008 reference frame, which is the same as used in single GPS data processing [

In order to assess the precision of BeiDou PPP solutions, we processed 27 days' data from September 4 to September 30 in 2012 (day of year from 248 to 274) by using the PANDA software package in the modes of BeiDou, GPS, and BeiDou/GPS static daily PPP solutions. Among the stations used below in

The RMS values of the East, North and Up components also show spatial variations. The RMS values of three components of BeiDou static PPP against the “ground truth” are less than 1.0 cm, 1.0 cm and 3.0 cm in the Asian-Pacific in the period. However, the results get worse for the LEID and GREECE stations, which are far from the Asia-Pacific region. Their RMS values are less than 4.0 cm due to the fewer BeiDou satellites observed as shown in

The RMS values of the difference between the East, North and Up components of BeiDou/GPS static PPP and the “ground truth” for all the stations are almost all less than 1.0 cm and the average values of the RMS values are 0.53, 0.28 and 1.04 cm, respectively. Those of GPS static PPP for all the stations are 0.50, 0.29 and 0.89 cm, respectively. The results illustrate that the accuracy of GPS static PPP do not improve obviously with the introduction of BeiDou data. Probably, the orbit error of BeiDou satellites may still have biases with respect to that of GPS satellites.

The kinematic PPP performance was also assessed for the modes of BeiDou-only, GPS-only and BeiDou/GPS by processing the daily data from September 24 to September 30 in 2012 at CHDU station. The interval is 30 s. We analyzed the precisions of BeiDou-only, GPS-only and BeiDou/GPS kinematic PPP solutions after convergence. The solutions are compared with the “ground truth” of CHDU station. Meanwhile, the convergence time was also analyzed.

The north component of BeiDou-only kinematic PPP converges faster than the East and Up components at CHDU station. The coordinates difference against the “ground truth” for the North and East components of BeiDou-only kinematic PPP after convergences are within ±10 cm while that of the up component are within ±20 cm.

The north component of BeiDou-only kinematic solutions converge as fast as that of GPS-only while the East and Up components converge more slowly than that of GPS-only, but as

As

The accuracy of the horizontal components of BeiDou-only kinematic PPP is within 1.0–2.0 cm except DOY 269 and the accuracy of the vertical component is within 4.0–7.0 cm except DOY 271. The average values of BeiDou-only kinematic PPP in the East, North and Up components are 1.93, 1.57 and 5.86 cm respectively, and those of GPS-only kinematic PPP are 1.99, 1.21 and 6.11 cm, respectively.

The accuracy of the horizontal components of BeiDou/GPS kinematic PPP is within 1.0–2.0 cm and that of the vertical component is within 2.0–5.0 cm. The average values of BeiDou/GPS kinematic PPP solutions are 1.14, 0.87 and 3.70 cm, respectively, which significantly improve compared to that of BeiDou-only and GPS-only kinematic PPP, thanks to the increasing of satellite numbers and the improvement of the PDOP.

Observations residuals mainly contain the observation noises, multipath errors, orbit errors and mismodelled errors so that the residuals can be used as an important index to assess positioning accuracy [

The RMS values of the PC residuals of BeiDou satellites for “BETS” are smaller than 3 m and the RMS values of the LC residuals of GEO and IGSO satellites are smaller than 1.5 cm while those of MEO satellites are within 1–3 cm. By contrast, the RMS values of the LC and PC residuals of GPS satellites have the similar accuracy. The RMS values of the LC and PC residuals of GPS satellites are smaller than 2 cm and 2 m, respectively. The average values of the RMS of the undifferenced LC and PC residuals of BeiDou satellites for “BETS” are 0.95 cm and 1.42 m, respectively. And the average values of the RMS of the undifferenced LC and PC residuals of GPS satellites are 0.91 cm and 1.25 m, respectively. That BeiDou system has larger LC and PC residuals than GPS may be caused by the multipath error.

The RMS values of the residuals of GEO C01 and C03 are smaller than that of GEO C04 and C05 and the IGSOs, while those of the MEOs are the worst. This may be due to the fact that the elevations of GEO C01 and C03 are larger than those of other satellites and also do not change much, which leads to a smaller multipath error. Meanwhile, the orbit accuracy of GEO C01 and C03 is better than that of GEO C04 and C05 [

We have presented static and kinematic PPP results in the modes of BeiDou-only, GPS-only and BeiDou/GPS systems, respectively. The visibility of the current BeiDou satellite constellation, multipath combinations and undifferenced phase and code observation residuals of BeiDou satellites are used in the analysis. The results are compared with the “ground truth of stations”. The following conclusions can be drawn:

The analysis of multipath combinations shows that the MPCs of BeiDou code measurements are higher than those of GPS code measurements at the testing stations;

The daily static PPP solutions using BeiDou code and phase measurements demonstrate that the horizontal precision is better than 1.0 cm while the vertical precision is better than 3.0 cm in the Asian-Pacific region. For the region having less observed BeiDou satellites, the horizontal precision of BeiDou-only PPP solutions reaches 3.0 cm. The horizontal precision of BeiDou-only kinematic PPP solutions is better than 3.0 cm and the vertical precision is better than 6.0 cm, which is close to that of GPS-only kinematic PPP. The convergence time of BeiDou-only kinematic PPP is longer than that of GPS-only kinematic PPP;

The daily static PPP solutions using BeiDou/GPS code and phase measurements demonstrate that the horizontal and vertical precisions are better than 1.0 cm, which is close to those of GPS-only static PPP. The horizontal precision of kinematic BeiDou/GPS PPP solutions is better than 2.0 cm while the vertical precision is better than 5.0 cm. The results improve significantly compared to that of BeiDou-only and GPS-only kinematic PPP. The convergence time of BeiDou/GPS kinematic PPP is also shorter than that of BeiDou-only and GPS-only kinematic PPP. The East and North components converge faster than the Up component. And less than 1 hour is used in all the components;

The analysis on the residuals shows that BeiDou undifferenced LC and PC residuals vary with orbital characteristics. The BeiDou code and phase residuals are higher than the GPS ones, which may be due to the multipath error.

Finally, it should be pointed out that the performance evaluation of BeiDou PPP is for preliminary results since the BeiDou constellation is not yet completed. Furthermore, as the number and proper distribution of the ground tracking stations increase, the accuracy of satellite orbit and clock biases will also improve greatly [

This work was supported by the GNSS Research Center at Wuhan University and the National Natural Science foundation of China (No. 41204029; No. 41231174), the Outstanding Youth Paper foundation of CSNC (CSNC2012-QY-1) and the “111 Project” of China (No. B07037). The authors are thankful to Xianglin Liu, who considerably revised the paper. In addition all the reviewers are appreciated for their comments and suggestions, which significantly improved our manuscript.

The authors declare no conflict of interest.

The distribution of “BETS” and the tracks of the sub-satellite points of four GEO, five IGSO and two MEO BeiDou Satellites.

Visibility of BeiDou satellites at CHDU on September 24, 2012 (the mask elevation is 7°).

Sky plots (azimuth

MPCs of the B1 and B2 codes, as well as the variation of the elevations of satellite C01 (GEO) at CHDU station on September 24, 2012.

Standard deviations of MPCs of B1 and B2 codes of BeiDou satellites at CHDU station on September 24, 2012.

Standard deviations of MPCs of C/A and P2 codes of GPS satellites at CHDU station on September 24, 2012.

RMS values of the differences between the BeiDou, GPS, and BeiDou/GPS static PPP results and the “ground truth” in the East, North and Up components from September 4 to September 30 in 2012.

Differences between BeiDou, GPS, and BeiDou/GPS kinematic PPP solutions with respect to the “ground truth” in the East, North and Up components of CHDU station, respectively on September 24, 2012.

Variations of satellite numbers used and PDOP of the BeiDou, GPS, and BeiDou/GPS of CHDU on September 24, 2012.

Daily RMS values of BeiDou, GPS, and BeiDou/GPS kinematic PPP solutions of CHDU against the “ground truth” in the East, North and Up components from September 24 to September 30 in 2012 (Day of year is from 268 to 274).

Undifferenced LC and PC residuals of BeiDou satellites.

RMS values of undifferenced LC and PC residuals for the BeiDou satellites of all individual sites.

RMS values of the undifferenced LC and PC residuals for GPS satellites of all individual sites.

The strategies for BeiDou PPP and BeiDou/GPS PPP.

Observables | Undifferenced ionosphere-free code and phase combination of B1 and B2 |

Elevation angle cutoff | 7° |

Sampling rate | 30 s |

Precise obit | GPS: IGS Final Ephemeris BeiDou: PANDA BeiDou Final Ephemeris |

Precise clock biases | GPS: IGS Precise Satellite Clock biases 30 s BeiDou: PANDA BeiDou Precise Satellite Clock biases 30 s |

Satellite Antenna PCO | Default values from manufacturer |

Satellite Antenna PCV | Only GPS |

Phase rotation correction | Phase polarization effects applied [ |

Receiver Antenna PCO and PCV | Not applied |

Troposphere model | Saastamoinen model for wet and dry hydrostatic delay with Global Mapping Function [ |

Ionosphere | 1st order effect eliminated by forming ionosphere-free linear combination |

Solid Earth tides | IERS Conventions 2010 |

Ocean tides | IERS Conventions 2010 |

Solid Earth pole tides | IERS Conventions 2010 |

Relativistic effects | IERS Conventions 2010 |

Time system | GPS Time |

Terrestrial frame | ITRF2008 |

Parameters estimation | Model & Constraint |

Coordinate | Static mode: constants, 10 m Kinematic mode: estimated as a random walk process for each epoch, 10 m, 10 m/sqrt (h) |

Receiver clock biases | Estimated as a random walk process for each epoch, 300 m/sqrt (h) |

Troposphere | Initial model and piece-wise constant in 2 h interval, 20 cm, 2 cm/sqrt (h) |

Integer ambiguity | Constant for each ambiguity arc |

System time difference | Estimated as a random walk process for each epoch, 300 m/sqrt (h) |

Biases of the results of the BeiDou, GPS, and BeiDou/GPS static PPP of the “BETS” against the “ground truth” in the East, North, and Up components on September 24, 2012.

| |||||||||
---|---|---|---|---|---|---|---|---|---|

BJF1 | –0.18 | –0.05 | –1.44 | 0.66 | –0.05 | –1.95 | –0.23 | –0.32 | –0.20 |

CHDU | 0.87 | 0.05 | 1.50 | 0.62 | –0.31 | –0.71 | 0.69 | –0.11 | 0.62 |

CWKJ | –0.22 | 0.51 | –3.27 | 0.43 | –0.31 | –0.87 | –0.24 | 0.10 | –0.88 |

HRBN | 0.86 | 0.41 | –1.37 | 0.55 | –0.36 | –-0.79 | 0.54 | –0.10 | –0.63 |

LASA | 1.60 | 0.44 | –2.14 | 1.23 | –0.26 | –0.16 | 0.92 | 0.16 | –1.19 |

WDKJ | 0.48 | 0.28 | –2.58 | 0.31 | –0.20 | 0.01 | –0.05 | 0.27 | –0.34 |

WUHN | –0.6 | 0.37 | –2.68 | 0.35 | –0.51 | 1.19 | 0.08 | 0.08 | –1.34 |

XIAN | 0.39 | 0.40 | –2.34 | –0.51 | –0.40 | –1.04 | –0.30 | 0.25 | –1.32 |

LEID | –0.97 | –1.78 | 0.81 | 0.03 | –0.07 | 0.01 | –0.25 | 0.03 | 0.31 |

GREECE | 1.04 | –0.27 | –6.22 | 0.29 | 0.07 | 1.10 | 0.58 | 0.14 | 0.63 |

RMS | 0.79 | 0.62 | 2.70 | 0.56 | 0.28 | 0.93 | 0.45 | 0.17 | 0.81 |

Average values of the RMS of undifferenced LC and PC residuals for all BeiDou satellites.

C01 | 0.71 | 1.29 |

C03 | 0.67 | 1.35 |

C04 | 0.89 | 2.02 |

C05 | 0.85 | 1.92 |

C06 | 0.84 | 1.33 |

C07 | 1.12 | 1.37 |

C08 | 0.85 | 1.24 |

C09 | 0.86 | 1.16 |

C10 | 0.89 | 1.25 |

C11 | 1.12 | 1.25 |

C12 | 1.62 | 1.42 |

Mean | 0.95 | 1.42 |