# Interferometric Phase Error Analysis and Compensation in GNSS-InSAR: A Case Study of Structural Monitoring

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## Abstract

**:**

## 1. Introduction

## 2. Experimental System And Scene

## 3. Signal Processing for Deformation Retrieval

#### 3.1. Spatial Decorrelation Compensation

#### 3.2. Bistatic PS Selection and Multi-Angle Correlation

#### 3.3. Differential Interferometric Phase and Accurate Topological Phase Compensation

#### 3.4. Inter-Channel Phase Error Compensation

#### 3.5. Atmospheric Phase Compensation

#### 3.6. Deformation Retrieval And Evaluation

## 4. Structural Monitoring Experiment Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Experimental scene. Beijing Institute of Technology, Haidian District, Beijing (39°57′22.84″ N, 116°18′47.59″ E).

**Figure 5.**Spatial decoherence compensation results based on the proposed method: (

**a**) spatial coherence coefficient; (

**b**) phase noise.

**Figure 6.**Comparison of radar imaging results and optical images: (

**a**) the result of IGSO1 satellite; (

**b**) the result of IGSO2 satellite; (

**c**) the result of IGSO4 satellite.

**Figure 7.**PS points distribution under threshold 0.2 of three IGSO satellites. (

**a**–

**c**) are the PS points selection results of IGSO 1, 2 and 4 satellites.

**Figure 10.**Extracted inter-channel phase error and compensation results: (

**a**) interferometric phase at the origin point; (

**b**) interferometric phase of Gym before inter-channel phase error compensation; (

**c**) interferometric phase of Gym after inter-channel phase error compensation; (

**d**) interferometric phase of Building 1 before inter-channel phase error compensation; (

**e**) interferometric phase of Building 1 after inter-channel phase error compensation.

**Figure 11.**Residual phase of the transponder from three IGSO satellites and the average residual phase.

**Figure 12.**Interferometric phase after compensation of typical buildings: (

**a**) the compensation result of Gym; (

**b**) the compensation result of Building 1.

**Figure 13.**Estimated deformations with transponder displacement in all directions: (

**a**) the result along the upward direction; (

**b**) the result along east and north directions.

**Figure 14.**The residual phase error of the transponder: (

**a**) the result of the previous experiment; (

**b**) the result of the proposed experiment.

Type | IGSO | MEO |
---|---|---|

Nominal repeat-pass period | 23 h 56 min 0 s (1 sidereal day) | 6 d 23 h 32 min 0 s (7 sidereal days) |

Real repeat-pass period | 23 h 55 min 56–59 s | 6 d 23 h 31 min 40–44 s |

Parameter | Value |
---|---|

Nominal repeat-pass cycle | 1 sidereal day |

Carrier frequency | 1268.52 MHz (B3I) |

Wavelength | 0.2365 m |

Transmitted signal | C/A code |

Effective signal bandwidth | 10.23 MHz |

Equivalent PRT | 1 ms |

Orbit height | About 36,000 km |

Horn antenna gain | 11 dB |

Horn antenna main lobe width | ${47}^{\circ}$ |

Interference Pair | $\mathbf{\Delta}\mathit{T}$ | Interference Pair | $\mathbf{\Delta}\mathit{T}$ |
---|---|---|---|

M01, M02 | 7.636 s | M09, M10 | 3.681 s |

M02, M03 | −1.863 s | M10, M11 | 4.681 s |

M03, M04 | 2.335 s | M11, M12 | 8.354 s |

M04, M05 | 1.101 s | M12, M13 | 17.108 s |

M05, M06 | −7.873 s | M13, M14 | 11.199 s |

M06, M07 | 2.552 s | M14, M15 | 4.325 s |

M07, M08 | −6.231 s | M15, M16 | 5.432 s |

M08, M09 | 7.198 s | M16, M17 | 2.135 s |

Target | Transponder | Building 1 | Gym |
---|---|---|---|

$\Delta r$ | 172 m | 216 m | 410 m |

Building 1 | Gym | |
---|---|---|

Deformation value | 0.57 mm | 0.42 mm |

Accuracy | 1.33 mm | 1.32 mm |

Gym | |||
---|---|---|---|

IGSO1 | IGSO2 | IGSO4 | |

Traditional PS-InSAR processing | 20.94 mm | 18.34 mm | 28.11 mm |

Proposed PS-InSAR processing | 10.61 mm | 11.64 mm | 17.26 mm |

Building 1 | |||

IGSO1 | |||

Traditional PS-InSAR processing | 24.03 mm | ||

Proposed PS-InSAR processing | 15.82 mm |

IGSO1 | IGSO2 | IGSO4 | |
---|---|---|---|

Gym | −4.66 mm | −5.21 mm | −3.33 mm |

Building 1 | −1.23 mm |

Direction | RMSE (mm) |
---|---|

East | 1.68 |

North | 2.82 |

Up | 4.22 |

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**MDPI and ACS Style**

Wang, Z.; Liu, F.; Zeng, T.; Wang, C.
Interferometric Phase Error Analysis and Compensation in GNSS-InSAR: A Case Study of Structural Monitoring. *Remote Sens.* **2021**, *13*, 3041.
https://doi.org/10.3390/rs13153041

**AMA Style**

Wang Z, Liu F, Zeng T, Wang C.
Interferometric Phase Error Analysis and Compensation in GNSS-InSAR: A Case Study of Structural Monitoring. *Remote Sensing*. 2021; 13(15):3041.
https://doi.org/10.3390/rs13153041

**Chicago/Turabian Style**

Wang, Zhanze, Feifeng Liu, Tao Zeng, and Chenghao Wang.
2021. "Interferometric Phase Error Analysis and Compensation in GNSS-InSAR: A Case Study of Structural Monitoring" *Remote Sensing* 13, no. 15: 3041.
https://doi.org/10.3390/rs13153041