# Analysis of BeiDou Satellite Measurements with Code Multipath and Geometry-Free Ionosphere-Free Combinations

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Models

#### 2.1. BDS Code Multipath Estimation

#### 2.2. GFIF Combination for Carrier Phase Bias Analysis

## 3. Experimental Analysis

Stations | Antenna Types | Receiver Types |
---|---|---|

CUT0 | TRM59800.00 SCIS | TRIMBLE NETR9 4.70 |

F711 | TRM57971.00 NONE | TRIMBLE NETR9 |

F713 | TRM55971.00 NONE | TRIMBLE NETR9 |

F714 | TRM55971.00 NONE | TRIMBLE NETR9 |

F721 | TRM57971.00 NONE | TRIMBLE NETR9 |

F783 | TRM57971.00 NONE | TRIMBLE NETR9 |

GMSD | TRM59800.00 SCIS | TRIMBLE NETR9 4.80 |

JFNG | TRM59800.00 NONE | TRIMBLE NETR9 4.70 |

JOG2 | JAV_RINGANT_G3T NONE | JAVAD TRE_G3TH DELTA3.4.7 |

NNOR | SEPCHOKE_MC NONE | SEPT POLARX4 2.3.4 |

#### 3.1. Comparing CNR and Code Multipath Combinations of Different Systems

**Figure 2.**The relationship between CNRs and satellite elevations for GPS, GLONASS, Galileo, and BDS satellites at GNSS station F713. (

**a**) G06; (

**b**) R01; (

**c**) E11; (

**d**) C11; (

**e**) C08; (

**f**) C03. Three frequencies are denoted as X1, X2, and X3 with the colors black, red and blue.

**Figure 3.**The multipath combinations (blue) and satellite elevations (red) for (

**a**) GPS satellite G06, (

**b**) GLONASS satellite R08, (

**c**) Galileo satellite E11 and (

**d**) BDS MEO satellite C14 at station F713.

#### 3.2. Bias in Code Multipath Combination of BDS

**Figure 4.**The relationship between multipath combination (blue) and satellite elevations (red) for BDS (

**a**) IGSO satellite C09 and (

**b**) GEO satellite C03 at station F713.

**Figure 5.**Cross-correlations between the code multipath combinations $M{P}_{1}$ and $M{P}_{2}$ (black), $M{P}_{1}$and $M{P}_{3}$ (red), $M{P}_{2}$ and $M{P}_{3}$ (blue) at stations (

**a**) F713, (

**b**) F783, (

**c**) GMSD, and (

**d**) JFNG.

**Figure 6.**Cross-correlations between the code multipath combinations $M{P}_{1}$ (black), $M{P}_{2}$ (red), $M{P}_{3}$ (blue) and the elevations at stations (

**a**) F713, (

**b**) F783, (

**c**) GMSD, and (

**d**) JFNG.

**Figure 7.**Cross-correlations between the code multipath combinations $M{P}_{1}$ (black), $M{P}_{2}$ (red), $M{P}_{3}$ (blue) and the azimuths at stations (

**a**) F713, (

**b**) F783, (

**c**) GMSD, and (

**d**) JFNG.

**Figure 8.**The systematic bias in multipath combination is eliminated through a between-station differencing. The single-station elevation-angle dependent troughs for satellites (

**a**) C07, (

**b**) C09, (

**c**) C13, and (

**d**) C14 vanish after the between-station differencing is performed.

**Figure 9.**The multipath combinations of BDS satellites (

**a**) C09 (IGSO) and (

**b**) C14 (MEO); after the elevation-dependent correction model is applied.

#### 3.3. Biases in Carrier Phase Geometry-Free and Ionosphere-Free Combination

**Figure 10.**GFIF combination (blue) and elevation (red) of BDS satellites at stations (

**a**) GMSD and (

**b,c**) CUT0.

**Figure 11.**GFIF combinations at station F783 (

**top**

**row**), station GMSD (

**middle**

**row**) and differencing result between the two stations (

**bottom**

**row**) for different BDS satellites, the red curve showing the satellite elevation.

**Figure 12.**Cross-correlations between the GFIF combination time series (ten days) of different GEO satellites at the stations GMSD (

**a**) and CUT0 (

**b**), with the red vertical line indicating the local time difference between the two satellites.

## 4. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Zhao, Q.; Wang, G.; Liu, Z.; Hu, Z.; Dai, Z.; Liu, J.
Analysis of BeiDou Satellite Measurements with Code Multipath and Geometry-Free Ionosphere-Free Combinations. *Sensors* **2016**, *16*, 123.
https://doi.org/10.3390/s16010123

**AMA Style**

Zhao Q, Wang G, Liu Z, Hu Z, Dai Z, Liu J.
Analysis of BeiDou Satellite Measurements with Code Multipath and Geometry-Free Ionosphere-Free Combinations. *Sensors*. 2016; 16(1):123.
https://doi.org/10.3390/s16010123

**Chicago/Turabian Style**

Zhao, Qile, Guangxing Wang, Zhizhao Liu, Zhigang Hu, Zhiqiang Dai, and Jingnan Liu.
2016. "Analysis of BeiDou Satellite Measurements with Code Multipath and Geometry-Free Ionosphere-Free Combinations" *Sensors* 16, no. 1: 123.
https://doi.org/10.3390/s16010123