# Unmanned Airborne Bistatic Interferometric Synthetic Aperture Radar Data Processing Method Using Bi-Directional Synchronization Chain Signals

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## Abstract

**:**

## 1. Introduction

## 2. Bidirectional Synchronization Chain Scheme

## 3. Overall Processing Flow for Small UAV Bistatic InSAR

#### 3.1. Time and Phase Synchronization Error Compensation Methods

_{T}

_{0}is the central frequency of the first station, and φ

_{T}(·) is the time-varying phase of the first station.

_{R}

_{0}is the central frequency of the second station and φ

_{R}(·) is the time-varying phase of the second station. Taking the peak phase after compression of the direct wave pulse is equivalent to taking the phase at t = 0, with

_{0}= 2 us. In other words, the direct wave signal is produced by the receiver itself. The signal is as follows

_{0}= 2 μs, a crystal oscillator frequency error of 100 MHz can reach 10

^{−8}. Because the system operates at a central frequency of 1.5 GHz, this term is 0.0054 degrees and can be neglected. The second term ② represents the phase introduced by the baseline, and the baseline can be calculated based on this term. The third term ③ is the synchronous phase error term, which can be neglected as long as the phase remains stable at the microsecond level. Based on previous test data, this error term is less than 0.1 degrees. Through theoretical and experimental data analysis, both terms ① and ③ in the above equation can be ignored. Consequently, based on the second term, the calibration method for the baseline is given by

_{1}is the time difference between the transmission of the SAR signal and the synchronization signal, ${K}_{r}$ is the linear frequency modulation rate, and ${T}_{s}$ is the pulse width of the SAR signal. After reflection from the ground target, the signal received by the second station is given by

^{−7}orders of magnitude for the first and second stations for cost consideration. In order to avoid the impact of the time drift of the second station relative to the first station on the integrity of the echo acquisition, an echo recording window compensation mechanism with a period of 6.3 s and an offset of 1 us is pre-set in the actual system, which makes the echo data appear jagged. By analyzing the phase composition of the echo signal from the second station, it can be observed that the samples in the range direction are not aligned, and there is a term related to the azimuthal moment j, $j\frac{1}{PRF}\frac{{f}_{0T}-{f}_{0R}}{{f}_{0R}}$, which is exactly the time offset that needs to be compensated by means of envelope alignment. This is compensated by performing an FFT along the distance direction, multiplying the distance direction frequency domain by $\mathrm{exp}\left\{-j2\pi f\left(j\frac{1}{PRF}\frac{{f}_{0T}-{f}_{0R}}{{f}_{0R}}\right)\right\}$, and then changing back to the time domain.

- 1.
- Perform pulse compression and peak phase extraction on the direct wave signal received by the receiver at each ${\eta}_{j}$ moment to obtain ${\phi}_{RR}\left({\eta}_{j},t\right)$;
- 2.
- Perform pulse compression and peak phase extraction on the direct wave signal received at the transmitter at each ${\eta}_{j}$ moment to obtain ${\phi}_{TR}\left({\eta}_{j},t\right)$;
- 3.
- Calculate the baseline length inversion result $\left({\phi}_{RR}\left({\eta}_{j},t\right)+{\phi}_{TR}\left({\eta}_{j},t\right)\right)/2$ for subsequent interferometric processing;
- 4.
- Calculate the synchronization phase compensation term $\left({\phi}_{RR}\left({\eta}_{j},t\right)-{\phi}_{TR}\left({\eta}_{j},t\right)\right)/2$ and compensate for the received echo signals at each ${\eta}_{j}$ moment;
- 5.
- Perform envelope alignment, in which the echo is transformed by FFT along the range direction, multiplied by $\mathrm{exp}\left\{-j2\pi f\left(j\frac{1}{PRF}\frac{{f}_{0T}-{f}_{0R}}{{f}_{0R}}\right)\right\}$ in the range direction in the frequency domain, and then transformed back to the time domain to obtain the envelope aligned second echo for subsequent imaging.

#### 3.2. Trajectory Refinement Method Combining Synchronization Chain and POS Data

_{B}is the baseline length according to the two-way synchronization chain (Equation (9)), and (X

_{1},Y

_{1},Z

_{1}) and (X

_{2},Y

_{2},Z

_{2}) are the positions of the first and second station according to the POS data, respectively. $\overrightarrow{B}={\left({X}_{1}-{X}_{2},{Y}_{1}-{Y}_{2},{Z}_{1}-{Z}_{2}\right)}^{T}$ is the baseline vector from the POS data, ${\overrightarrow{B}}^{\prime}={\left({X}_{1}-{X}_{2}+\mathsf{\Delta}x,{Y}_{1}-{Y}_{2}+\mathsf{\Delta}y,{Z}_{1}-{Z}_{2}+\mathsf{\Delta}z\right)}^{T}$ is the optimized baseline vector, and (Δx, Δy, Δz) is the amount to be optimized. In the above equation, the first term is the baseline length constraint term, aiming to make the optimized trajectory’s baseline length as close as possible to the baseline length obtained from the two-way synchronous chain. The second term is the baseline direction constraint term, aligning the optimized baseline with the original baseline direction, where p is the weight (chosen as 0.2 in this study).

#### 3.3. High-Precision Bistatic InSAR Imaging Processing Methods

#### 3.3.1. One-Step Motion Compensation Algorithm Based on High-Precision Inertial Navigation

#### 3.3.2. Bistatic SAR Echo Azimuth Resampling

_{T}(nΔη)/V

_{T}and $n\mathsf{\Delta}\eta +\mathsf{\Delta}{Y}_{R}\left(n\mathsf{\Delta}\eta \right)/{V}_{R}$, respectively. Since transmitting and receiving should be regarded as simultaneous under the stop–go assumption, it is assumed that the n pulse under the motion error along flight direction is transmitted and received, respectively, at this moment.

#### 3.3.3. Highly Accurate Motion Compensation Method Based on Doppler Bandwidth Segmentation and Sub-Aperture Image Superposition

#### 3.4. Interferometric Processing and Elevation Inversion

#### 3.4.1. Interferometric Calibration

- 1.
- Slant range calibration

- 2.
- Baseline length and baseline angle calibration

#### 3.4.2. Interferometric Processing

- 1.
- Complex image registration and generation of the interference phase

- 2.
- Flat-earth phase removal

- 3.
- Phase filtering

- 4.
- Phase unwrapping

- 5.
- Elevation inversion

## 4. Experiment

#### 4.1. Bistatic SAR Ground Test

#### 4.2. Bistatic SAR Flight Experiment

#### 4.2.1. Synchronization Error Compensation

#### 4.2.2. Results of the Second Station Trajectory Refinement

#### 4.2.3. Bistatic InSAR Imaging Results

#### 4.2.4. Interference Processing and Elevation Inversion Results

#### 4.3. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Measurement results of second radar after time and phase synchronization. (

**a**) envelope of the synchronization signal after pulse compression; (

**b**) the phase of the peak of the synchronization pulse after compression.

**Figure 10.**(

**Top**) Baseline as extracted from the synchronization signal and as calculated using GPS. (

**Bottom**) Difference between the two baselines.

**Figure 13.**The difference between the refined baseline and the baseline extracted from the synchronization signal.

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

Flight altitude (relative to ground) | 2 km |

Incident angle | 45° |

Baseline angle | 0° |

Effective baseline length | 30 m |

Horizontal baseline length | 42.43 m |

Frequency of carrier wave | 1.5 GHz |

Bandwidths | 400 MHz |

Sampling rate | 625 MHz |

Azimuthal beamwidth | 10° |

Parameter | the First Station | the Second Station |
---|---|---|

Azimuth resolution | 0.45 m | 0.49 m |

Range resolution | 0.37 m | 0.37 m |

Corner Reflector | Measured Height (m) | Height Error before Refinement (m) | Height Error after Refinement (m) | Copernicus DEM Error (m) |
---|---|---|---|---|

C1 | 1385.71 | 0.18 | 0.02 | 0.24 |

C2 | 1383.23 | 0.17 | 0.27 | −0.36 |

C3 | 1384.38 | −0.56 | −0.03 | 1.87 |

C4 | 1382.11 | 0.29 | 0.57 | 0.20 |

C5 | 1387.05 | 0.55 | 0.58 | 0.11 |

C6 | 1383.61 | −0.35 | 0.03 | 1.78 |

C7 | 1382.98 | 0.31 | 0.70 | 1.09 |

C8 | 1386.03 | −0.09 | 0.19 | 0.16 |

C9 | 1387.79 | −1 | 0.55 | 0.47 |

C10 | 1387.68 | 0.32 | −0.05 | 0.52 |

C11 | 1387.25 | −1.99 | −0.27 | 0.86 |

C12 | 1386.65 | −0.17 | −0.50 | 0.73 |

C13 | 1386.09 | −0.27 | −0.62 | 0.22 |

C14 | 1385.57 | −0.18 | −0.41 | 0.78 |

RMS | 0.66 | 0.42 | 0.87 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, J.; Lin, B.; Pan, J.; Cheng, Y.; Qiu, X.; Jiang, W.; Liu, Y.; Liu, M.
Unmanned Airborne Bistatic Interferometric Synthetic Aperture Radar Data Processing Method Using Bi-Directional Synchronization Chain Signals. *Remote Sens.* **2024**, *16*, 769.
https://doi.org/10.3390/rs16050769

**AMA Style**

Zhu J, Lin B, Pan J, Cheng Y, Qiu X, Jiang W, Liu Y, Liu M.
Unmanned Airborne Bistatic Interferometric Synthetic Aperture Radar Data Processing Method Using Bi-Directional Synchronization Chain Signals. *Remote Sensing*. 2024; 16(5):769.
https://doi.org/10.3390/rs16050769

**Chicago/Turabian Style**

Zhu, Jinbiao, Bei Lin, Jie Pan, Yao Cheng, Xiaolan Qiu, Wen Jiang, Yuquan Liu, and Mingqian Liu.
2024. "Unmanned Airborne Bistatic Interferometric Synthetic Aperture Radar Data Processing Method Using Bi-Directional Synchronization Chain Signals" *Remote Sensing* 16, no. 5: 769.
https://doi.org/10.3390/rs16050769