# Evaluation of Network RTK Positioning Performance Based on BDS-3 New Signal System

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## Abstract

**:**

## 1. Introduction

## 2. Network RTK Positioning Algorithm

#### 2.1. Ambiguity Resolution of Reference Stations

#### 2.2. Classification Modeling of Ionospheric and Tropospheric Delay

#### 2.3. Generation of Virtual Observations (VRS)

- The ambiguity of all satellite observations of the VRS is the same as that of the main reference station.
- The clock error between the virtual reference station and the main reference station is the same; that is, the capture time of the observation of the two stations is the same.
- The ionospheric and tropospheric delays of the reference satellite of the VRS are the same as those of the main reference station.

## 3. Datasets and Processing Strategy

#### 3.1. Datasets

#### 3.2. Processing Strategy

## 4. Experiment and Analysis

#### 4.1. Analysis of DD Atmospheric Correction at Reference Stations

#### 4.2. Accuracy Analysis of Regional Atmosphere Modeling and Interpolation

#### 4.3. Analysis of Positioning Performance of Network RTK Terminal

## 5. Discussion

- Firstly, in the long-distance baseline calculation between reference stations, tropospheric wet delay and ionospheric delay were estimated as parameters to assist the fixation of ambiguity. Although random walk was used to estimate parameters and a variance constraint was applied to accelerate the convergence of the baseline, the initial parameter values were set to zero. Theoretically, adding an external correction model to provide relatively accurate initial values would further shorten the baseline convergence time.
- Secondly, the experimental analysis results in Section 4.1 and Section 4.2 show that the ionospheric and troposphere atmospheric modeling and interpolation accuracy are negatively correlated with the satellite elevation angle. In Section 2.2 of atmospheric modeling strategy, this paper gives a preliminary method of ionospheric weighting based on elevation angle, but a more refined modeling weighting method considering the influence of elevation angle needs to be further studied.
- Finally, Section 4.3 of this paper takes the GPS system as reference and designs five schemes to preliminarily evaluate the positioning performance of network RTK of BDS-3. The horizontal error of each scheme is basically within 3 cm, and the elevation error is within 5 cm, which can meet the requirements of providing network RTK high-precision service independently. In addition, the terminal positioning effect statistics show that the positioning accuracy of BDS-2 is relatively poor, the positioning accuracy of BDS-3 is only slightly better than that of GPS, and the combined processing effect of BDS-2/3 using B1I+B3I transition signal is the best. The reason why the positioning performance of BDS-3 is slightly better than that of GPS may be attributed to the fact that the experimental data in this paper were collected in central China. Compared with GPS, the number of BDS-3 satellites and the distribution of DOP values in the Asia-Pacific region are obviously more advantageous. The number of satellites and the distribution of PDOP values of Station SC17, shown in Figure 9, can also be seen as related laws. Further comparative analysis requires further data collection of more regions for experimental demonstration.

## 6. Conclusions

- When the combination of B1C+B2a and B1I+B3I of a single BDS-3 constellation provides VRS service, the fixed rate of terminal RTK is above 95%, and the horizontal and elevation accuracy are within 1 cm and 2 cm, respectively. The single BDS-3 system is sufficient to meet the needs of providing network RTK high-precision positioning service in surveying and mapping operations. In addition, the terminal positioning effect statistics show that the positioning accuracy of BDS-2 is relatively poor, GPS is superior to BDS-2, the positioning accuracy of BDS-3 is better than that of GPS and BDS-2, BDS-2/3 combined processing of B1I+B3I transition signal has the best effect, and its accuracy in the E and N directions is better than 0.5 cm, and that in the U direction is better than 1.5 cm.
- Based on the analysis of atmospheric correction, regional atmospheric modeling, and network RTK terminal positioning accuracy, it can be seen that the new signal combination (B1C+B2a) of the BDS-3 system is slightly better than the transition signal combination (B1I+B3I). In addition, the double-difference atmospheric correction of the reference station and the accuracy of regional atmospheric modeling both show a positive correlation with elevation angle, so it is necessary to carry out reasonable weighting processing for the satellite according to elevation angle in regional atmospheric modeling.
- According to the above analysis, when a single BDS-3 constellation provides network RTK service, the combination of B1C+B2a is suggested to be adopted as the main frequency signals for calculation. When the BDS-2/3 combined solution provides network RTK service, it is recommended to adopt the B1I+B3I combination as the main frequency signals for the solution.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Distribution of the reference stations (red triangles) and rover stations (blue triangles).

**Figure 4.**(

**a**) Double-difference atmospheric correction for B1C+B2a combination of BDS-3 in WH04-HG02. (

**b**) Double-difference atmospheric correction for B1I+B3I combination of BDS-3 in WH04-HG02.

**Figure 5.**(

**a**) The residuals of pseudo-range and phase observations for B1C+B2a combination of BDS-3 in WH04-HG02. (

**b**) The residuals of pseudo-range and phase observations for B1I+B3I combination of BDS-3 in WH04-HG02.

**Figure 6.**Comparison of average RMS of the DD solutions from different combinations of BDS-3 in WH04-HG02.

**Figure 7.**Comparison of atmospheric modeling value and reference value of B33 satellite at SC17. Station (CZ modeling value/JX reference value/DIFF mutual difference of two values).

**Figure 8.**Comparison of mean RMS between atmospheric modeling values and reference values under different frequency signal combinations at Station SC17.

Signals | Frequency (MHz) | Wavelength (cm) | System |
---|---|---|---|

B1I | 1561.098 | 19.20 | BDS-2/3 |

B1C | 1575.420 | 19.03 | BDS-3 |

B2a | 1176.450 | 25.48 | BDS-3 |

B2b | 1207.140 | 24.83 | BDS-3 |

B3I | 1268.520 | 23.63 | BDS-2/3 |

Schemes | Items | Description |
---|---|---|

Observations | Double-difference non-combined model | |

Sampling interval | 1 s | |

Elevation mask | 10° | |

Weighting | Priori precision 0.003 m for phase and 0.3 m for code; Elevation-dependent weight: P/sin(el) | |

Relativistic effect | IERS Conventions 2010 | |

Satellite phase center | PCO and PCV for GPS and only PCO corrected for BDS using igs14.atx | |

Receiver phase center | PCO and PCV corrected for GPS and BDS using igs14.atx | |

Network RTK | Tropospheric dry delay | Saastamoinen model and GMF mapping function [31] |

Tropospheric wet delay | Random-walk process: zenith wet delay + GMF mapping functionVariance constraint: initial noise (0.0/m) + process noise (0.001*BL ^{1} m) | |

Ionospheric delay | Random-walk process: double-difference ionospheric delay on oblique pathVariance constraint: initial noise (0.0 m) + process noise (0.04*0.1*BL/sin(el) m) | |

Ambiguities | WL/NL joint estimation + partial ambiguity fixing strategy [32] + LAMBDA | |

Estimator | Kalman filtering | |

Observations | Double-difference non-combined model | |

Sampling interval | 1 s | |

Elevation mask | 10° | |

Weighting | Priori precision 0.003 m for phase and 0.3 m for code; Elevation-dependent weight: P/sin(el) | |

Relativistic effect | IERS Conventions 2010 | |

Terminal RTK | Satellite phase center | PCO and PCV for GPS and only PCO corrected for BDS using igs14.atx |

Receiver phase center | PCO and PCV corrected for GPS and BDS using igs14.atx | |

Tropospheric dry delay | Saastamoinen model and GMF mapping function | |

Coordinate (x/y/z) | Dynamic estimation + white noise | |

Ambiguities | Original frequency ambiguity + partial ambiguity fixing strategy + LAMBDA | |

Estimator | Kalman filtering |

^{1}BL represents the length of the baseline, unit: km.

**Table 3.**The RMS of double-difference solutions from different combinations of BDS-3 in WH04-HG02 (m).

B1C+B2a | B1I+B3I | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

PRN | ION | TRP | P-B1C | P-B2a | L-B1C | L-B2a | ION | TRP | P-B1I | P-B3I | L-B1I | L-B3I |

B24 | 0.012 | 0.016 | 0.526 | 0.541 | 0.006 | 0.003 | 0.019 | 0.015 | 0.703 | 0.643 | 0.004 | 0.002 |

B25 | 0.011 | 0.034 | 0.551 | 0.394 | 0.006 | 0.003 | 0.016 | 0.037 | 0.711 | 0.492 | 0.005 | 0.003 |

B26 | 0.024 | 0.039 | 0.831 | 0.708 | 0.006 | 0.003 | 0.019 | 0.051 | 0.994 | 0.833 | 0.006 | 0.003 |

B33 | 0.013 | 0.074 | 0.606 | 0.389 | 0.004 | 0.002 | 0.015 | 0.073 | 0.738 | 0.559 | 0.004 | 0.002 |

B34 | 0.017 | 0.024 | 0.796 | 0.692 | 0.004 | 0.002 | 0.019 | 0.04 | 1.118 | 0.844 | 0.005 | 0.003 |

B35 | 0.012 | 0.023 | 0.669 | 0.894 | 0.006 | 0.003 | 0.018 | 0.029 | 0.762 | 0.927 | 0.006 | 0.003 |

B39 | 0.01 | 0.01 | 0.752 | 0.568 | 0.003 | 0.001 | 0.012 | 0.015 | 0.86 | 0.521 | 0.003 | 0.002 |

B41 | 0.029 | 0.016 | 0.787 | 0.355 | 0.008 | 0.004 | 0.033 | 0.024 | 0.677 | 0.617 | 0.007 | 0.004 |

B42 | 0.017 | 0.078 | 0.958 | 0.671 | 0.007 | 0.003 | 0.021 | 0.068 | 1.355 | 0.761 | 0.006 | 0.004 |

B44 | 0.011 | 0.009 | 0.566 | 0.649 | 0.003 | 0.002 | 0.017 | 0.014 | 0.79 | 0.797 | 0.003 | 0.002 |

AVG | 0.016 | 0.032 | 0.704 | 0.586 | 0.0053 | 0.0026 | 0.019 | 0.037 | 0.871 | 0.699 | 0.0049 | 0.0028 |

Baseline | B1C+B2a | B1I+B3I |
---|---|---|

WH04-HG02 | 99.9% | 99.7% |

WH04-HG05 | 99.9% | 99.2% |

WH04-WH02 | 99.6% | 96.3% |

WH04-XN01 | 98.4% | 97.3% |

HG02-HG05 | 99.9% | 98.6% |

HG02-XN01 | 97.9% | 98.2% |

WH02-XN01 | 99.3% | 98.9% |

**Table 5.**RMS Statistics of atmospheric modeling values and reference values at Station SC17 under different frequency signal combinations (m).

B1C+B2a (ION) | B1C+B2a (TRP) | B1I+B3I (ION) | B1I+B3I (TRP) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

PRN | CZ | JX | DIFF | CZ | JX | DIFF | CZ | JX | DIFF | CZ | JX | DIFF |

B24 | 0.006 | 0.008 | 0.005 | 0.005 | 0.011 | 0.007 | 0.01 | 0.02 | 0.01 | 0.006 | 0.017 | 0.012 |

B25 | 0.006 | 0.01 | 0.006 | 0.011 | 0.011 | 0.009 | 0.007 | 0.013 | 0.008 | 0.014 | 0.025 | 0.012 |

B26 | 0.008 | 0.012 | 0.006 | 0.016 | 0.022 | 0.01 | 0.006 | 0.013 | 0.01 | 0.022 | 0.034 | 0.015 |

B33 | 0.007 | 0.01 | 0.005 | 0.029 | 0.022 | 0.011 | 0.009 | 0.016 | 0.009 | 0.028 | 0.02 | 0.017 |

B34 | 0.009 | 0.01 | 0.007 | 0.01 | 0.009 | 0.006 | 0.012 | 0.014 | 0.006 | 0.017 | 0.022 | 0.011 |

B35 | 0.006 | 0.014 | 0.01 | 0.028 | 0.027 | 0.012 | 0.008 | 0.015 | 0.012 | 0.014 | 0.019 | 0.016 |

B39 | 0.004 | 0.006 | 0.003 | 0.004 | 0.007 | 0.004 | 0.005 | 0.01 | 0.006 | 0.005 | 0.012 | 0.008 |

B41 | 0.01 | 0.018 | 0.011 | 0.015 | 0.016 | 0.013 | 0.013 | 0.022 | 0.015 | 0.017 | 0.024 | 0.013 |

B42 | 0.008 | 0.013 | 0.008 | 0.037 | 0.035 | 0.01 | 0.012 | 0.021 | 0.011 | 0.033 | 0.032 | 0.014 |

B44 | 0.005 | 0.011 | 0.008 | 0.005 | 0.015 | 0.013 | 0.007 | 0.015 | 0.01 | 0.006 | 0.018 | 0.014 |

AVG | 0.007 | 0.011 | 0.007 | 0.016 | 0.018 | 0.010 | 0.009 | 0.016 | 0.010 | 0.016 | 0.022 | 0.013 |

**Table 6.**The fixed rate of baseline and positioning RMS of fixed solution from different schemes for Station SC17.

Schemes | Fix Rate | E (m) | N (m) | U (m) |
---|---|---|---|---|

GPS | 98.6% | 0.0054 | 0.0062 | 0.0173 |

BDS-2 | 97.5% | 0.0063 | 0.0072 | 0.0202 |

BDS-3 [1I+3I] | 99.4% | 0.0055 | 0.0057 | 0.0170 |

BDS-3 [1C+2a] | 99.8% | 0.0049 | 0.0047 | 0.0162 |

BDS-2/3 | 100% | 0.0047 | 0.0040 | 0.0139 |

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**MDPI and ACS Style**

Wang, P.; Liu, H.; Yang, Z.; Shu, B.; Xu, X.; Nie, G.
Evaluation of Network RTK Positioning Performance Based on BDS-3 New Signal System. *Remote Sens.* **2022**, *14*, 2.
https://doi.org/10.3390/rs14010002

**AMA Style**

Wang P, Liu H, Yang Z, Shu B, Xu X, Nie G.
Evaluation of Network RTK Positioning Performance Based on BDS-3 New Signal System. *Remote Sensing*. 2022; 14(1):2.
https://doi.org/10.3390/rs14010002

**Chicago/Turabian Style**

Wang, Pengxu, Hui Liu, Zhixin Yang, Bao Shu, Xintong Xu, and Guigen Nie.
2022. "Evaluation of Network RTK Positioning Performance Based on BDS-3 New Signal System" *Remote Sensing* 14, no. 1: 2.
https://doi.org/10.3390/rs14010002