# Focusing High-Resolution Highly-Squinted Airborne SAR Data with Maneuvers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling and Motivation

#### 2.1. Modeling

#### 2.2. Motivation

## 3. Imaging Approach

#### 3.1. 2-D Cross-Coupling Spatial Variation Elimination

#### 3.2. Range and Azimuth Spatial Variation Elimination

#### 3.3. Flowchart of Imaging Algorithm

## 4. Implementation and Discussion

#### 4.1. Simplified Processing

#### 4.2. Constraint on Scene Extent

## 5. Simulation Results

#### 5.1. Experiment 1

^{2}, $\mathit{b}=\left(0.32,-0.56,-0.17\right)$ m/s

^{3}, and $\mathit{c}=\left(-0.032,-0.037,0.024\right)$ m/s

^{4}. The ideal azimuth resolution is 0.364 m, the height of target PT9 is set to 300 m with respect to the reference target PT5, and other simulation parameters are listed in Table 1.

#### 5.2. Experiment 2

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

## References

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**Figure 2.**Impacts of motion parameter vectors $\mathit{b}$ , $\mathit{c}$, and $\mathit{d}$ on imaging results. (

**a**) Phase errors and (

**b**) spatially variant errors.

**Figure 3.**Spatial variations brought by motion parameter vectors, $\mathit{b}$ , $\mathit{c}$, and $\mathit{d}$. (

**a**) Range spatial variations with respect to range distance and resolution. (

**b**) Azimuth spatially variant errors with respect to range distance and resolution.

**Figure 4.**Spatial variations brought by motion parameter vectors $\mathit{b}$ , $\mathit{c}$, and $\mathit{d}$. (

**a**) Range spatial variations with respect to range distance and squint angle. (

**b**) Azimuth spatially variant errors with respect to range distance and squint angle.

**Figure 5.**Spatial variations distribution. (

**a**) Spatial variations distributed in ground scene. (

**b**) TFDs of targets T0, T1, T2, and T3.

**Figure 6.**Illustration of cross-coupling spatial variation elimination by TFDs of three targets with different positions. (

**a**,

**b**) TFDs before and after bulk compensation, respectively; (

**c**,

**d**) TFDs before and after polynomial phase filtering.

**Figure 7.**Illustration of proposed algorithm by 2-D spectra of a target and impulse response after compression. (

**a**–

**c**) in top row are 2-D spectra after phase decomposition, while (

**d**–

**f**) in the second row illustrate 2-D spectra after corresponding processing, and (

**g**–

**i**) in the bottom row are imaging results. The solid lines in the first two rows represent phase contours.

**Figure 10.**Phase errors in (

**a**) range and azimuth, (

**b**) range and height, and (

**c**) azimuth and height planes.

**Figure 12.**Comparative results of target PT1, PT5, and PT9. (

**a**) Proposed method, (

**b**)

**c**not considered, (

**c**)

**b**not considered, and (

**d**) FDA.

**Figure 13.**Comparative results of azimuth point impulse responses processed by proposed method [17], and BPA. (

**a**) Target PT1. (

**b**) Target PT5. (

**c**) Target PT9.

Motion Parameter | Value | System Parameter | Value |
---|---|---|---|

Radar Position at ACM | (0, 0, 10) km | Carrier Frequency | 17 GHz |

Reference Position | (12.68, 26, 0) km | Pulse Bandwidth | 500 MHz |

Velocity $\mathit{v}$ | (0, 170, −10) m/s | Sampling Frequency | 620 MHz |

Acceleration $\mathit{a}$ | (1.2, 1.73, −1.4) m/s^{2} | Squint Angle | 60° |

Third-order Parameter $\mathit{b}$ | (−0.09, 0.11, −0.14) m/s^{3} | Azimuth Resolution | 0.242 m |

Fourth-order Parameter $\mathit{c}$ | (0.005, 0.007, 0.003) m/s^{4} | Scene Size (Range×Azimuth) | 1.6 × 1.6 km |

Range | Azimuth | ||||||
---|---|---|---|---|---|---|---|

Method | Target | IRW (m) | PSLR (dB) | ISLR (dB) | IRW (m) | PSLR (dB) | ISLR (dB) |

Proposed | PT1 | 0.266 | −13.21 | −9.99 | 0.247 | −13.17 | −9.92 |

PT5 | 0.265 | −13.23 | −10.01 | 0.243 | −13.22 | −10.03 | |

PT9 | 0.266 | −13.19 | −9.98 | 0.241 | −13.15 | −9.95 | |

FDA | PT1 | 0.266 | −13.24 | −9.96 | 0.893 | −6.02 | −4.49 |

PT5 | 0.266 | −13.25 | −10.09 | 0.242 | −13.23 | −10.07 | |

PT9 | 0.267 | −13.17 | −10.01 | 1.302 | −4.74 | −3.56 |

Method | Target | IRW (m) | PSLR (dB) | ISLR (dB) |
---|---|---|---|---|

Proposed | PT1 | 0.367 | −13.16 | −9.87 |

PT5 | 0.365 | −13.21 | −10.02 | |

PT9 | 0.362 | −13.14 | −9.94 | |

[17] | PT1 | 1.031 | −6.11 | −4.56 |

PT5 | 0.364 | −13.24 | −10.06 | |

PT9 | 1.135 | −5.78 | −4.12 | |

BPA | PT1 | 0.365 | −13.24 | −10.04 |

PT5 | 0.364 | −13.27 | −10.08 | |

PT9 | 0.361 | −13.25 | −10.05 |

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

Velocity $\mathit{v}$ | (0, 110, −10) m/s |

Acceleration $\mathit{a}$ | (1.21, 1.43, −0.74) m/s^{2} |

3rd-order Paramater $\mathit{b}$ | (−0.1, 0.2, 0.2) m/s^{3} |

4th-order Paramater $\mathit{c}$ | (0.007, −0.015, 0.004) m/s^{4} |

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**MDPI and ACS Style**

Tang, S.; Zhang, L.; So, H.C.
Focusing High-Resolution Highly-Squinted Airborne SAR Data with Maneuvers. *Remote Sens.* **2018**, *10*, 862.
https://doi.org/10.3390/rs10060862

**AMA Style**

Tang S, Zhang L, So HC.
Focusing High-Resolution Highly-Squinted Airborne SAR Data with Maneuvers. *Remote Sensing*. 2018; 10(6):862.
https://doi.org/10.3390/rs10060862

**Chicago/Turabian Style**

Tang, Shiyang, Linrang Zhang, and Hing Cheung So.
2018. "Focusing High-Resolution Highly-Squinted Airborne SAR Data with Maneuvers" *Remote Sensing* 10, no. 6: 862.
https://doi.org/10.3390/rs10060862