# High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Global Navigation Satellite System (GNSS) Short Baseline Attitude Determination Using Multi-Antenna Receiver with Common Clock

#### 2.2. Theoretical Basis of Ambiguity Substitution Approach

#### 2.3. Single-Difference (SD) Observables with Single-Epoch Kalman Filter (KF) Model

## 3. The Assessment of SD Observables with a Common Clock in Static and Kinematic Mode

#### 3.1. Static Data Collection

#### 3.2. The Validation of Ambiguity Substitution Approach with a Common Clock

#### 3.3. Comparison of Single-Difference (SD) and Double-Difference (DD) Observables with a Common Clock in Static Mode

#### 3.4. Comparison of Single-Difference (SD) Observables and Double-Difference (DD) Observables with a Common Clock in Kinematic Mode

## 4. The Assessment of SD Observables with a Common Clock in a Vehicle Experiment

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Bar plots showing absolute baseline biases of SD-Float and SD-Fix solutions in east, north, and up directions for 6 days.

**Figure 4.**Repeatability of the baseline solutions in east, north, and up directions for SD-Float and SD-Fix solutions.

**Figure 6.**Waveform showing single-frequency and single-epoch kinematic attitude solutions between DD-Fix and SD-Fix before multipath mitigation.

**Figure 7.**Waveform showing single-frequency and single-epoch attitude solutions between DD-Fix and SD-Fix after multipath mitigation.

**Figure 8.**Photographs of the placement of two antennas (

**top**) and dynamic experimental trajectory (

**bottom**).

**Figure 11.**Comparison of attitude between fiber optic gyroscope inertial navigation system (FOG-INS) and SD-Fix.

**Table 1.**Processing strategy of global positioning system (GPS) carrier phase observations for PADS and Trimble BD982.

Contents | PADS | Trimble BD982 |
---|---|---|

Observables | raw GPS L1 | raw GPS L1 |

Weighting | elevation-dependent | elevation-dependent |

Elevation mask (deg) | 10 | 10 |

Sampling rate (s) | 1 | 1 |

Observable type | Single-difference (SD) | Double-difference (DD) |

Orbit type | broadcast | broadcast |

Process mode | Static | Static |

Adjustment method | Kalman filter | Kalman filter |

AR method | ambiguity substitution approach | unknown |

Estimated parameters | baseline vector, SD ambiguities, and uncalibrated phase delay (UPD) | baseline vector and DD ambiguities |

**Table 2.**Standard deviations (STDs) and root mean squared errors (RMSEs) of yaw, pitch angles, and baseline between DD-Fix and SD-Fix.

STDs | RMSEs | |||||
---|---|---|---|---|---|---|

Solutions | Yaw /° | Pitch /° | Baseline Length/mm | Yaw /° | Pitch /° | Baseline Length/mm |

DD-Fix | 0.02 | 0.06 | 4.4 | 0.02 | 0.06 | 5.05 |

SD-Fix | 0.004 | 0.004 | 0.52 | 0.004 | 0.004 | 1.1 |

Solution | Yaw | Pitch |
---|---|---|

DD-Fix | 0.04 | 0.06 |

SD-Fix | 0.04 | 0.05 |

Solution | Yaw | Pitch |
---|---|---|

DD-Fix | 0.02 | 0.04 |

SD-Fix | 0.02 | 0.02 |

Attitude Angles | Yaw Angle | Pitch Angle |
---|---|---|

RMSE | 0.74 | 0.47 |

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**MDPI and ACS Style**

Zhang, C.; Dong, D.; Chen, W.; Cai, M.; Peng, Y.; Yu, C.; Wu, J.
High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock. *Remote Sens.* **2021**, *13*, 3977.
https://doi.org/10.3390/rs13193977

**AMA Style**

Zhang C, Dong D, Chen W, Cai M, Peng Y, Yu C, Wu J.
High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock. *Remote Sensing*. 2021; 13(19):3977.
https://doi.org/10.3390/rs13193977

**Chicago/Turabian Style**

Zhang, Chenglong, Danan Dong, Wen Chen, Miaomiao Cai, Yu Peng, Chao Yu, and Jianping Wu.
2021. "High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock" *Remote Sensing* 13, no. 19: 3977.
https://doi.org/10.3390/rs13193977