# Research on Tightly Coupled Multi-Antenna GNSS/MEMS Single-Frequency Single-Epoch Attitude Determination in Urban Environment

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## Abstract

**:**

## 1. Introduction

## 2. GNSS/MEMS Coupled Attitude Determination

#### 2.1. MEMS Initial Alignment and Attitude Propagation

#### 2.2. Tightly Coupled Model

**DD**) operator; $i$ and $j$ represent the satellite numbers; $m$ and $k$ represent the antenna numbers; $\nabla \Delta \phi $ represents the DD carrier phase(unit: m); $\nabla \Delta P$ represents the DD pseudo-range (unit: m); $\nabla \Delta \rho $ represents the DD station–satellite distance; $\lambda $ represents carrier wavelength (unit: m); $\nabla \Delta N$ represents the carrier DD ambiguity (unit: cycle); ${\epsilon}_{\phi}$ and ${\epsilon}_{P}$ represent the noise of DD carrier phase and pseudo-range observation (unit: m), respectively. The DD station–satellite distance has the relationship with the attitude matrix ${C}_{b}^{e}$:

## 3. GNSS Observation Quality Control

- (1)
- Quickly eliminate bigger outliers in the data pre-processing step.

- (2)
- Ratio test and the posteriori residuals with integer ambiguity fixed.

Algorithm 1. MEMS Attitude aid Quality-Control (MAQC) |

Task: Eliminate observations that contain relatively large bias: |

Parameters: $\nabla \Delta {P}_{m,k}^{}$, $\nabla \Delta {\phi}_{m,k}^{}$, ${\mathit{l}}_{m,k}^{b}$, $\nabla {\mathit{e}}_{m}^{i,j}$,${C}_{b}^{e}$ |

Initialization: n1 = count ($\nabla \Delta {\phi}_{m,k}^{}$), n2 = count ($\nabla \Delta {\phi}_{m,j}^{}$) Fast Elimination: 1. calculate $\nabla \Delta {\rho}_{mems}$ by the Formula (12) 2. calculate detector ${D}_{p}$, ${D}_{\phi}$ by the Formula (21) 3. calculate ${T}_{P}$,${T}_{\phi}$ by the Formula (22) 4. eliminate the observations if ${D}_{p}>{T}_{p}$ or ${D}_{\phi}>{T}_{\phi}$ |

Iterative Elimination: 1. update the ratio, n1 and n2 While (ratio < 3 and (n1 > 3 or n2 > 3)), do: |

2. calculate measurement residuals $res$ of fixed solution by the Formula (23) |

3. eliminate the observation if its residual is the max one |

4. update the ratio, n1 and n2 |

End while |

Output: relatively high-quality observations |

## 4. Results

#### 4.1. Data Collection and Processing Strategy

#### 4.2. An Open Environment

#### 4.3. A Challenging Urban Environment

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Equipment setup for vehicle experiments: (

**a**) the experimental vehicle; (

**b**) equipment setup diagram.

**Figure 3.**First experiment in an open environment: (

**a**) trajectory of vehicle; (

**b**) number of visible satellites of the primary baseline; (

**c**) the GPS L1 “Satellite Lock—Cycle Slips” plot from IE; (

**d**) the BDS B1 “Satellite Lock—Cycle Slips” plot from IE.

**Figure 5.**Residuals of carrier phase in real experiment: (

**a**) prediction residuals of carrier phase; (

**b**) residuals of the retained carrier phase measurements by MAQC method. The rea lines symbolize threshold value. The blue lines symbolize the residuals.

**Figure 6.**Residuals of carrier phase in simulated experiment: (

**a**) prediction residuals of carrier phase; (

**b**) residuals of the retained carrier phase measurements by MAQC method. The rea lines symbolize the threshold value. The blue lines symbolize the residuals.

**Figure 9.**Second experiment in a challenged urban environment: (

**a**) trajectory of vehicle; (

**b**) the number of visible satellites of primary baseline; (

**c**) the GPS L1 “Satellite Lock—Cycle Slips” plot from IE; (

**d**) the BDS B1 “Satellite Lock—Cycle Slips” plot from IE.

**Figure 11.**Residuals of the carrier phase: (

**a**) residuals of the carrier phase measurements; (

**b**) residuals of the retained carrier phase measurements by MAQC method.

**Figure 12.**Success rates of ambiguity resolution: (

**a**) epoch counts for different numbers of available DD phase observations; (

**b**) success rates for different number of available DD phase observations; (

**c**) global success rates for all epochs in 4 attitude determination modes.

Specifications | ADIS16460 | SPAN-FSAS |
---|---|---|

MEMS Gyroscope | Fiber-Optical Gyroscope | |

Full Scale | ±100°/s | ±450°/s |

Bias | 750°/h | 0.75°/h |

Bias stability | 8°/h | 0.1°/h |

Random walk | 0.12°/$\sqrt{h}$ | 0.15°/$\sqrt{h}$ |

GNSS | GNSS/MEMS | ||||
---|---|---|---|---|---|

Types | All Solutions | Fixed Solutions | TC | TC-QC | |

Pitch | RMS | 2.196 | 0.251 | 0.170 | 0.168 |

STD | 2.196 | 0.247 | 0.170 | 0.118 | |

Roll | RMS | 4.035 | 0.290 | 0.212 | 0.211 |

STD | 4.035 | 0.289 | 0.212 | 0.212 | |

Yaw | RMS | 1.090 | 0.129 | 0.122 | 0.123 |

STD | 1.090 | 0.129 | 0.116 | 0.117 |

GNSS | GNSS/MEMS | ||||
---|---|---|---|---|---|

Fixed Solutions | TC | TC-QC | Reduce | ||

Pitch | RMS | 3.344 | 0.462 | 0.439 | 4.98% |

STD | 3.339 | 0.408 | 0.363 | 11.03% | |

Roll | RMS | 6.773 | 0.538 | 0.498 | 7.43% |

STD | 6.756 | 0.522 | 0.469 | 10.15% | |

Yaw | RMS | 3.167 | 0.321 | 0.196 | 38.94% |

STD | 3.168 | 0.298 | 0.156 | 47.65% |

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**MDPI and ACS Style**

Gao, M.; Liu, G.; Wang, S.; Xiao, G.; Zhao, W.; Lv, D.
Research on Tightly Coupled Multi-Antenna GNSS/MEMS Single-Frequency Single-Epoch Attitude Determination in Urban Environment. *Remote Sens.* **2021**, *13*, 2710.
https://doi.org/10.3390/rs13142710

**AMA Style**

Gao M, Liu G, Wang S, Xiao G, Zhao W, Lv D.
Research on Tightly Coupled Multi-Antenna GNSS/MEMS Single-Frequency Single-Epoch Attitude Determination in Urban Environment. *Remote Sensing*. 2021; 13(14):2710.
https://doi.org/10.3390/rs13142710

**Chicago/Turabian Style**

Gao, Ming, Genyou Liu, Shengliang Wang, Gongwei Xiao, Wenhao Zhao, and Dong Lv.
2021. "Research on Tightly Coupled Multi-Antenna GNSS/MEMS Single-Frequency Single-Epoch Attitude Determination in Urban Environment" *Remote Sensing* 13, no. 14: 2710.
https://doi.org/10.3390/rs13142710