# Impact of SAR Azimuth Ambiguities on Doppler Velocity Estimation Performance: Modeling and Analysis

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## Abstract

**:**

## 1. Introduction

- (1)
- A model for ocean surface Doppler velocity estimation affected by azimuth ambiguities is developed to investigate how the azimuth ambiguities impact the ocean surface Doppler velocity estimation performance.
- (2)
- Based on the developed model, the estimated bias and standard deviation are derived, and how significant the azimuth ambiguities affect the Doppler velocity estimation performance is quantitatively analyzed.

## 2. Model for Ocean Surface Doppler Velocity Estimation Affected by Azimuth Ambiguities

## 3. Statistic of Doppler Velocity Estimation Affected by Azimuth Ambiguities

#### 3.1. Doppler Velocity Estimation Bias Affected by Azimuth Ambiguities

#### 3.2. Standard Deviation of Doppler Velocity Estimates Affected by Azimuth Ambiguities

## 4. Validation

#### 4.1. Validation with Simulation

#### 4.2. Validation with Chinese GF-3 SAR Data

#### 4.2.1. GF-3 SAR Data Affected by the Right Azimuth Ambiguity

#### 4.2.2. GF-3 SAR Data Affected by the Left and Right Azimuth Ambiguities

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Doppler centroid estimation bias as a function of AASR, and the phase difference of the auto-correlation function of the ambiguity signal and the main signal. (

**a**) $-5\mathrm{dB}\u2a7dAASR\u2a7d5\mathrm{dB}$. (

**b**) Several given values of $AASR$.

**Figure 2.**Standard deviation of the Doppler centroid estimates as a function of AASR, and the phase difference of the auto-correlation function of the ambiguity signal and the main signal. (

**a**) $-5\mathrm{dB}\u2a7dAASR\u2a7d5\mathrm{dB}$. (

**b**) Several given values of $AASR$.

**Figure 3.**Comparison of simulated and theoretical results for (left panels) ocean surface Doppler velocity estimation bias and (right panels) the standard deviation of ocean surface Doppler velocity estimates for different AASR. (

**a**,

**b**) $AASR$ = −5 dB. (

**c**,

**d**) $AASR$ = 0 dB. (

**e**,

**f**) $AASR$ = 5 dB. The solid blue lines indicate the results obtained by Monte Carlo simulations, the solid red lines indicate the theoretical results.

**Figure 4.**Ocean surface Doppler velocity estimation results. (

**a**) GF-3 SAR image with the “ghost target” of the land due to the right azimuth ambiguity. The azimuth (Azi) and range (Rg) directions are indicated by arrows. (

**b**) Estimated AASR. (

**c**) Estimated ocean surface Doppler velocity affected by azimuth ambiguities, where the black frames refer to the regions of interest that will be quantitatively analyed below. (

**d**) Estimated ocean surface Doppler velocity without azimuth ambiguities.

**Figure 5.**Statistical histograms of ocean surface Doppler velocity estimates (

**a**) before and (

**b**) after azimuth ambiguity suppression. The solid red lines indicate the theoretical distributions of ocean surface Doppler velocity estimates.

**Figure 6.**Ocean surface Doppler velocity estimation results. (

**a**) GF-3 SAR image affected by ghosts due to left and right azimuth ambiguities. The azimuth (Azi) and range (Rg) directions are indicated by arrows. (

**b**) Estimated AASR due to the left ambiguity. (

**c**) Estimated AASR due to the right ambiguity. (

**d**) Estimated ocean surface Doppler velocity affected by azimuth ambiguities, where the black frames refer to the regions of interest that will be quantitatively analyed below. (

**e**) Estimated ocean surface Doppler velocity without azimuth ambiguities.

**Figure 7.**Statistical histograms of ocean surface Doppler velocity estimates (

**a**) before and (

**b**) after azimuth ambiguity suppression. The solid red lines indicate the theoretical distributions of ocean surface Doppler velocity estimates.

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

Pulse Repetition Frequency | $PRF$ | 1000 Hz |

Electromagnetic Wavenumber | ${k}_{e}$ | 118 rad/m |

Incidence Angle | ${\theta}_{I}$ | 45${}^{\circ}$ |

Power of Main Signal | ${P}_{m}$ | 1 J |

Azimuth Ambiguity-to-Signal Ratio | $AASR$ | −5 dB, 0 dB, 5 dB |

**Table 2.**The simulated and theoretical results for ocean surface Doppler velocity estimation bias (BIAS) and the standard deviation (STD) of the ocean surface Doppler velocity estimates.

MAE | RMSE | PCC | ||
---|---|---|---|---|

$AASR$ = −5 dB | BIAS | 0.05 m/s | 0.06 m/s | 0.99 |

STD | 0.01 m/s | 0.01 m/s | 0.99 | |

$AASR$ = 0 dB | BIAS | 0.13 m/s | 0.22 m/s | 0.99 |

STD | 0.04 m/s | 0.19 m/s | 0.81 | |

$AASR$ = 5 dB | BIAS | 0.12 m/s | 0.18 m/s | 0.99 |

STD | 0.01 m/s | 0.01 m/s | 0.99 |

**Table 3.**Doppler velocity estimation bias and the standard deviations of the Doppler velocity estimates within ROI1–ROI4.

AASR | Method | Bias | Standard Deviation | |||
---|---|---|---|---|---|---|

Theoretical Value | Measured Value | Theoretical Value | Measured Value | |||

ROI1 | −3.03 | OE | −0.56 m/s | −0.55 m/s | 0.23 m/s | 0.20 m/s |

CDE | −0.56 m/s | −0.54 m/s | 0.23 m/s | 0.18 m/s | ||

ROI2 | −1.22 | OE | −0.88 m/s | −0.87 m/s | 0.22 m/s | 0.18 m/s |

CDE | −0.88 m/s | −0.84 m/s | 0.22 m/s | 0.16 m/s | ||

ROI3 | 0.60 | OE | −1.80 m/s | −1.85 m/s | 0.25 m/s | 0.29 m/s |

CDE | −1.80 m/s | −1.83 m/s | 0.25 m/s | 0.27 m/s | ||

ROI4 | −2.53 | OE | −0.50 m/s | −0.52 m/s | 0.22 m/s | 0.24 m/s |

CDE | −0.50 m/s | −0.51 m/s | 0.22 m/s | 0.23 m/s |

**Table 4.**Doppler velocity estimation bias and the standard deviations of the Doppler velocity estimates within ROI5 and ROI6.

AASR | Method | Bias | Standard Deviation | |||
---|---|---|---|---|---|---|

Theoretical Value | Measured Value | Theoretical Value | Measured Value | |||

ROI5 | −5.60 | OE | −3.00 m/s | −3.05 m/s | 0.77 m/s | 0.79 m/s |

CDE | −3.00 m/s | −3.07 m/s | 0.77 m/s | 0.78 m/s | ||

ROI6 | −5.66 | OE | 2.74 m/s | 2.73 m/s | 0.73 m/s | 0.78 m/s |

CDE | 2.74 m/s | 2.75 m/s | 0.73 m/s | 0.78 m/s |

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**MDPI and ACS Style**

Sun, K.; Diao, L.; Zhao, Y.; Zhao, W.; Xu, Y.; Chong, J.
Impact of SAR Azimuth Ambiguities on Doppler Velocity Estimation Performance: Modeling and Analysis. *Remote Sens.* **2023**, *15*, 1198.
https://doi.org/10.3390/rs15051198

**AMA Style**

Sun K, Diao L, Zhao Y, Zhao W, Xu Y, Chong J.
Impact of SAR Azimuth Ambiguities on Doppler Velocity Estimation Performance: Modeling and Analysis. *Remote Sensing*. 2023; 15(5):1198.
https://doi.org/10.3390/rs15051198

**Chicago/Turabian Style**

Sun, Kai, Lijie Diao, Yawei Zhao, Wenjia Zhao, Yongsheng Xu, and Jinsong Chong.
2023. "Impact of SAR Azimuth Ambiguities on Doppler Velocity Estimation Performance: Modeling and Analysis" *Remote Sensing* 15, no. 5: 1198.
https://doi.org/10.3390/rs15051198