# A Hybrid SAR/ISAR Approach for Refocusing Maritime Moving Targets with the GF-3 SAR Satellite

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## Abstract

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## 1. Introduction

- We use the DCT algorithm in the IROPE method to improve the SNR of the data and render the subsequent estimation more accurate, which also makes the data more consistent with the model of the ROPE method.
- We avoid the averaging of phase vectors with different linear components and maximize the accuracy of the phase compensation by using the circular shift of the prominent point in each range bin to zero frequency to rationalize the initialization of the Doppler center.
- Moreover, better estimates are obtained through iteration. Multiple iterative algorithms improve the SNR, which further improves the accuracy of the Doppler circular shift and the estimation of phase error.
- The proposed method focuses the blurred images well and exhibits the superiority of robustness, reduced sidelobes, and suitability for various phase errors, which does not require time-consuming parameter adjustment procedures to achieve improved performance and allows a long coherent processing interval.

## 2. Moving Signal Model

#### 2.1. SAR Signal Model

#### 2.1.1. Analysis of Moving Echo Characteristics

#### 2.1.2. Analysis of Moving Target Response

#### 2.2. ISAR Signal Model

## 3. Improved Rank-One Phase Estimation Algorithm

#### 3.1. Problems of the Rank-One Phase Estimation Algorithm

#### 3.2. Principle of IROPE

**I. Preliminary Phase Compensation**

**II. Two-step Convergence**

**III. Circular Shifting**

**IV. Iteration**

Algorithm 1: The IROPE algorithm for phase compensation |

Input: The range-aligned echo $e\left(r\right)$, $[Nr,Na]=size\left(e\right(r\left)\right)$, $p=0$, number of iterations l, threshold value T |

1: I. Preliminary Phase Compensation |

2: for $i=1:Na-1$ |

3: ${e}_{i+1}\left(r\right)={e}_{i+1}\left(r\right).\ast {e}^{j\phi}$ |

4: end |

5: IV. Iteration |

6: for $l=1:l$ (Image entropy is further applied to control the iteration process) |

7: II. Two-step Convergence |

8: III. Circular Shifting |

9: while ${\widehat{\epsilon}}_{k}^{\left(p\right)}-{\widehat{\epsilon}}_{k}^{(p-1)}$> T |

10: for $k=1:Na-1$ |

11: Update ${\widehat{\epsilon}}_{k}^{\left(p\right)}$ calculated by Equation (19) |

12: end |

13: for $j=1:{N}_{r}$ |

14: Update ${\omega}_{j}^{\left(p\right)}$ calculated by Equation (19) |

15: end |

16: $p=p+1$ |

17: end while |

18: $\widehat{\epsilon}={\sum}_{k=1}^{K}{\widehat{\epsilon}}_{k}^{\left(p\right)}$ |

19: $e\left(r\right)=e\left(r\right).\ast exp(-1i\ast \widehat{\epsilon})$ |

20: end |

Output: Compensated range-Doppler echo $e\left(r\right)$, phase error $\widehat{\epsilon}$ |

#### 3.3. Performance of IROPE

#### 3.4. The Whole Process of the Refocusing Method

## 4. Experiments and Performance Comparisons

#### 4.1. Results of Spotlight Simulation

#### 4.1.1. Ship Target with Velocity and Acceleration

#### 4.1.2. Ship target with Translation and Rotation

#### 4.2. Spaceborne SAR Data Experiments

#### 4.2.1. Real Data Corrupted by Phase Error

#### 4.2.2. Intrinsically Corrupted Real Data

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**The interpolated contour and azimuth profile. (

**a**,

**d**) Conventional SAR processing; (

**b**,

**e**) ROPE; (

**c**,

**f**) IROPE.

**Figure 8.**Recovered images of defocused ship target with velocity and acceleration. (

**a,b**) Conventional SAR processing system; (

**c,d**) MD method; (

**e,f**) ROPE method; (

**g,h**) The proposed method.

**Figure 9.**Variations in the magnitudes of PSLR and ISLR in terms of the linear acceleration based on the proposed method. (

**a**) PSLR; (

**b**) ISLR.

**Figure 10.**Recovered images of defocused ship target with translation and rotation speed. (

**a**,

**b**) Conventional SAR processing system; (

**c**,

**d**) MD method; (

**e**,

**f**) ROPE method; (

**g**,

**h**) The proposed method.

**Figure 11.**Variation in the magnitudes of PSLR and ISLR in terms of the rotational angular velocity based on the proposed method. (

**a**) PSLR; (

**b**) ISLR.

**Figure 12.**Nominal, corrupted, and recovered images. (

**a**) Nominal; (

**b**) Corrupted by phase error; (

**c**) Image recovered with MD method; (

**d**) Image recovered with ROPE method; (

**e**) Image recovered with the proposed method.

**Figure 14.**GF-3 SAR image of the Port of Singapore. The yellow rectangles are the enlarged defocused sub-images. (

**a**) (E104.0, N1.3); (

**b**) (E104.1, N1.3).

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

Mode | Spotlight |

Radar Center Frequency (GHz) | 5.4 |

Wavelength (m) | 0.0555 |

Bandwidth (MHz) | 50 |

Azimuth Resolution (m) | 1.5 |

Range Resolution (m) | 2.6562 |

PRF (Hz) | 3125 |

Upsampled PRF (Hz) | 9950.2398 |

Upsampled Doppler Bandwidth (Hz) | 6188.7356 |

Slant-Range (m) | 1,067,731.2395 |

Synthetic Aperture Time (s) | 2.3342 |

SAR Velocity (m/s) | 7500 |

squint angle () | 0 |

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

Mode | Spotlight |

Radar Center Frequency (GHz) | 5.400012 |

Bandwidth (MHz) | 240.000000 |

Azimuth Resolution (m) | 1 |

Range Resolution (m) | 0.6 |

PRF (Hz) | 3125.164062 |

Synthetic Aperture Time (s) | 8.58 |

Satellite Velocity (m/s) | 7570.962970 |

IQEMs | Corrupted image | MD | ROPE | IROPE |
---|---|---|---|---|

Contrast increase | −4.08 | −3.86 | −0.47 | −0.09 |

Entropy reduction | −1.69 | −1.58 | −0.21 | 0.08 |

IP increase | −20.01 | −16.82 | −2.58 | 0.77 |

Ship | Ship1 | Ship2 | Ship3 | ||||||
---|---|---|---|---|---|---|---|---|---|

IQEMs | MD | ROPE | IROPE | MD | ROPE | IROPE | MD | ROPE | IROPE |

Contrast increase | 0.42 | 0.23 | 0.49 | 0.01 | 0.01 | 0.02 | 0.23 | −0.12 | 0.93 |

Entropy reduction | 0.40 | 0.25 | 0.47 | 0.16 | 0.15 | 0.24 | 0.20 | −0.02 | 0.47 |

IP increase | 6.08 | 5.21 | 6.78 | 3.05 | 2.60 | 4.82 | 4.18 | 1.53 | 4.69 |

Works | Schemes | Application | Phase Error Estimation | Accuracy |
---|---|---|---|---|

MD | Sub-aperture correlation | Limited | Unsatisfactory | Unsatisfactory |

ROPE | Two-step convergence | Limited | Unsatisfactory | Unsatisfactory |

IROPE | Preprocessing+ Circular Shifting +Two-step convergence+Iteration | Wide | Good | Good |

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## Share and Cite

**MDPI and ACS Style**

Yan, Z.; Zhang, Y.; Zhang, H.
A Hybrid SAR/ISAR Approach for Refocusing Maritime Moving Targets with the GF-3 SAR Satellite. *Sensors* **2020**, *20*, 2037.
https://doi.org/10.3390/s20072037

**AMA Style**

Yan Z, Zhang Y, Zhang H.
A Hybrid SAR/ISAR Approach for Refocusing Maritime Moving Targets with the GF-3 SAR Satellite. *Sensors*. 2020; 20(7):2037.
https://doi.org/10.3390/s20072037

**Chicago/Turabian Style**

Yan, Zhishuo, Yi Zhang, and Heng Zhang.
2020. "A Hybrid SAR/ISAR Approach for Refocusing Maritime Moving Targets with the GF-3 SAR Satellite" *Sensors* 20, no. 7: 2037.
https://doi.org/10.3390/s20072037