# A Single-Difference Multipath Hemispherical Map for Multipath Mitigation in BDS-2/BDS-3 Short Baseline Positioning

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## Abstract

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## 1. Introduction

## 2. BDS Multipath

#### 2.1. Multipath Extraction

**x**is a 3 × 1 order unknown baseline vector;

**y**is the n × 1 order integer ambiguity after double-difference;

**A**and

**B**are the design matrices of order n × 3 and n × n, respectively;

**L**is the n * 1 order the constant term of carrier phase; and

**V**is the double-difference residuals. In short baseline, the double-difference residuals are mainly the multipath and the noise.

**Q**is the variance-covariance matrix of the baseline vector and integer ambiguity;

**R**is the real value of the baseline vector; and

**Z**is the real value of the double-difference integer ambiguities.

#### 2.2. Single-Difference Multipath Modeling

## 3. Orbital Repeat Time of BDS Satellites

^{7}; and a is the square of the semimajor axis of the satellite orbit ellipse. Then, the operating period of the satellite can be obtained based on the angular velocity of the satellite. The time shifts of the GEO/IGSO and MEO satellite operating periods are:

## 4. Experiments and Results

#### 4.1. Data Collection

#### 4.2. Single-Difference Residual Analysis

#### 4.3. Results and Analysis

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**DOY 296/302/303 single-difference residuals series of C01/C11/C13/C29 and the elevation and azimuth angles.

**Figure 6.**RMS of the original single-difference series and their series with multipath mitigation for the DOY 303 observed satellite.

**Figure 7.**(

**a**) SD-MHM model established by DOY 296–302; and (

**b**) the distribution of DOY303 single-difference residuals.

**Figure 8.**(

**a**) DOY303 C29 single-difference residuals and ASF and SD-MHM multipath models and their mitigated series; and (

**b**) the power spectral density of the mitigated series and the single-difference residuals.

**Figure 9.**The original baseline series, ASF, and SD-MHM corrected series and C21 single-difference residuals at the adjacent periods.

**Figure 10.**(

**a**) HDOP, VDOP, and elevation of DOY303; and (

**b**) the corrected series by the SD-MHM in the east, north, and vertical directions.

**Figure 11.**The nine-day positioning accuracy in the east, north, and vertical directions and the baseline accuracy.

Orbit PRN | DOY 302–303 | DOY 296–303 | DOY 297–304 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Time Shift (s) | Correlation Coefficient | RMS (mm) | RMS_M (mm) | Time Shift (s) | Correlation Coefficient | RMS (mm) | RMS_M (mm) | Time Shift (s) | Correlation Coefficient | RMS (mm) | RMS_M (mm) | |

GEO C01 | 234 | 0.977 | 1.55 | 0.86 | 1645 | 0.983 | 1.54 | 0.75 | 1642 | 0.982 | 1.55 | 0.77 |

MEO-2 C11 | — | 0.097 | 1.69 | — | 1694 | 0.848 | 1.69 | 0.91 | 1696 | 0.948 | 1.37 | 0.44 |

IGSO C13 | 227 | 0.929 | 2.81 | 1.06 | 1603 | 0.928 | 2.81 | 1.05 | 1598 | 0.927 | 2.77 | 1.04 |

MEO-3 C29 | — | -0.086 | 1.89 | — | 1696 | 0.948 | 1.89 | 0.61 | 1698 | 0.898 | 1.71 | 0.8 |

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**MDPI and ACS Style**

Liu, C.; Tao, Y.; Xin, H.; Zhao, X.; Liu, C.; Hu, H.; Zhou, T.
A Single-Difference Multipath Hemispherical Map for Multipath Mitigation in BDS-2/BDS-3 Short Baseline Positioning. *Remote Sens.* **2021**, *13*, 304.
https://doi.org/10.3390/rs13020304

**AMA Style**

Liu C, Tao Y, Xin H, Zhao X, Liu C, Hu H, Zhou T.
A Single-Difference Multipath Hemispherical Map for Multipath Mitigation in BDS-2/BDS-3 Short Baseline Positioning. *Remote Sensing*. 2021; 13(2):304.
https://doi.org/10.3390/rs13020304

**Chicago/Turabian Style**

Liu, Chao, Yuan Tao, Haiqiang Xin, Xingwang Zhao, Chunyang Liu, Haojie Hu, and Tengfei Zhou.
2021. "A Single-Difference Multipath Hemispherical Map for Multipath Mitigation in BDS-2/BDS-3 Short Baseline Positioning" *Remote Sensing* 13, no. 2: 304.
https://doi.org/10.3390/rs13020304