# Above Ground Level Estimation of Airborne Synthetic Aperture Radar Altimeter by a Fully Supervised Altimetry Enhancement Network

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- The proposition of a novel label generation algorithm based on a semi-analytical model to implement a fully supervised network for parameter estimation, so that clean and accurate DDMs can be produced by discretizing landforms in the domain of range and Doppler together with empirical scattering theory;
- Accordingly, the estimation is designed by a novel, fully supervised network, which is capable of accessing the AGL parameters for airborne SARAL on complicated landforms;
- The raw data of landscapes are employed in this paper to validate the generalizability and accuracy of the proposed approach.

## 2. Airborne SARAL Geometry and Signal Model

#### 2.1. Airborne SARAL Geometry

#### 2.2. Airborne SARAL Signal Model

## 3. Methodology

#### 3.1. Clean Label Generation

Algorithm 1: Generation process of the clean label. | |

Input: The coordinates of each scatter: ${\mathit{p}}_{S}^{\left(i\right)}={\left({x}^{\left(i\right)},{y}^{\left(i\right)},{z}^{\left(i\right)}\right)}^{T},i\in \mathcal{S}$, where $\mathcal{S}$ is the total set of scatters. Current location and velocity of the platform: ${\mathit{p}}_{0}={\left({x}_{0},{y}_{0},{z}_{0}\right)}^{T}$ and ${\mathit{v}}_{0}={\left({\dot{x}}_{0},{\dot{y}}_{0},{\dot{z}}_{0}\right)}^{T}$. The wavelength of radar is $\lambda $. The resolution of range gates and Doppler channels as $\Delta r$ and $\Delta d$, respectively. | |

- 1.
- Substitute ${\mathit{p}}_{S}^{\left(i\right)}$, ${\mathit{p}}_{0}$ and ${\mathit{v}}_{0}$ into the following equations to calculate the relative ranges ${R}^{\left(i\right)}$, location vectors ${\mathit{r}}^{\left(i\right)}$ and Doppler frequency ${D}^{\left(i\right)}$ of each scatter.
| |

$${R}^{\left(i\right)}={\Vert {\mathit{p}}_{S}^{\left(i\right)}-{\mathit{p}}_{0}\Vert}_{2}$$
| |

$${\mathit{r}}^{\left(i\right)}=\left({\mathit{p}}_{S}^{\left(i\right)}-{\mathit{p}}_{0}\right)/{\Vert {\mathit{p}}_{S}^{\left(i\right)}-{\mathit{p}}_{0}\Vert}_{2}$$
| |

$${D}^{\left(i\right)}=2{\mathit{v}}_{0}^{T}{\mathit{r}}^{\left(i\right)}/\lambda $$
| |

- 2.
- Compute the scatter coefficients as
| |

$${\sigma}^{\left(i\right)}={p}_{1}+{p}_{2}\mathrm{exp}\left(-{p}_{3}{\theta}^{\left(i\right)}\right)+{p}_{4}\mathrm{cos}\left({p}_{5}{\theta}^{\left(i\right)}+{p}_{6}\right)$$
| |

where $\theta =\mathrm{arccos}\left(\left|{z}^{\left(i\right)}-{z}_{0}\right|\right)$ and ${p}_{1}~{p}_{6}$ depend on the type of land cover medium.- 3.
- Calculate the reflection of individual scatter as
| |

$${s}^{\left(i\right)}=\sqrt{\frac{{\lambda}^{2}}{{\left(4\pi \right)}^{3}}{\sigma}^{\left(i\right)}\frac{1}{{\left({R}^{\left(i\right)}\right)}^{4}}}$$
| |

- 4.
- Accumulate each element of the DDM matrix according to the sets of range and Doppler indexes as
| |

$${\mathit{D}}_{mn}=\left|{\displaystyle {\sum}_{i\in {\mathcal{R}}_{m}\cup {\mathcal{D}}_{n}}{s}^{\left(i\right)}}\right|$$
| |

where ${\mathcal{R}}_{m}$ and ${\mathcal{D}}_{n}$ are the index sets with respect to the mth range gate, and nth Doppler channels, correspondingly. | |

Output: A clean DDM power matrix as $\mathit{D}\in {\mathbb{R}}^{M\times N}$, where $M$ is the number of pulses and $N$ is the number of range gates. |

#### 3.2. FuSAE-Net

#### 3.2.1. A Lightweight DDM Enhancement Module

- A. Architecture Designation

- B. Training

^{−4}. The lr means learning rate. The network was developed using Python 3.9, and the network was tested and trained using Pytorch.

#### 3.2.2. AGL Estimation Module

## 4. Experiments

#### 4.1. Data Set Description

#### 4.1.1. Flight Route

#### 4.1.2. Data Collection and Preprocessing

#### 4.2. Evaluation Indicators

#### 4.3. Performance Analysis and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Raney, R.K. The delay/Doppler radar altimeter. IEEE Trans. Geosci. Remote Sens.
**1998**, 36, 1578–1588. [Google Scholar] [CrossRef] - Halimi, A. From conventional to delay/doppler altimetry. Ph.D. dissertation, INP Toulouse, Toulouse, France, 2013. [Google Scholar]
- Ray, C.; Martin-Puig, C.; Clarizia, M.P.; Ruffini, G.; Dinardo, S.; Gommenginger, C.; Benveniste, J. SAR altimeter backscattered waveform model. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 911–919. [Google Scholar] [CrossRef] - Yang, S.; Zhai, Z.; Xu, K.; Zhisen, W.; Lingwei, S.; Lei, W. The ground process segment of SAR altimeter. Remote Sens. Technol. Appl.
**2017**, 32, 1083–1092. [Google Scholar] - Brown, G.S. The average impulse response of a rough surface and its applications. IEEE Trans. Antennas Propag.
**1977**, 25, 67–74. [Google Scholar] [CrossRef] - Dinardo, S.; Fenoglio-Marc, L.; Buchhaupt, C.; Becker, M.; Scharroo, R.; Fernandes, M.J.; Benveniste, J. Coastal SAR and PLRM altimetry in German Bight and West Baltic Sea. Adv. Space Res.
**2018**, 62, 1371–1404. [Google Scholar] [CrossRef] - Buchhaupt, C.; Fenoglio-Marc, L.; Dinardo, S.; Scharroo, S.; Becker, M. A fast convolution based waveform model for conventional and unfocused SAR altimetry. Adv. Space Res.
**2018**, 62, 1445–1463. [Google Scholar] [CrossRef] - Idris, N.H.; Vignudelli, S.; Deng, X. Assessment of retracked sea levels from Sentinel-3A Synthetic Aperture Radar (SAR) mode altimetry over the marginal seas at Southeast Asia. Int. J. Remote Sens.
**2021**, 42, 1535–1555. [Google Scholar] [CrossRef] - Dumont, J.P. Estimation optimale des paramètres altimétriques des signaux radar Poséidon. Ph.D. dissertation, INP Toulouse, Toulouse, France, 1985. [Google Scholar]
- Yang, L.; Zhou, H.; Huang, B.; Liao, X.; Xia, Y. Elevation Estimation for Airborne Synthetic Aperture Radar Altimetry Based on Parameterized Bayesian Learning. J. Electron. Inf. Technol.
**2023**, 45, 1254–1264. [Google Scholar] - Halimi, A.; Mailhes, C.; Tourneret, J.Y.; Snoussi, H. Bayesian Estimation of Smooth Altimetric Parameters: Application to Conventional and Delay/Doppler Altimetry. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 2207–2219. [Google Scholar] [CrossRef] - Liao, X.; Zhang, Z.; Jiang, G. Mutant Altimetric Parameter Estimation Using a Gradient-Based Bayesian Method. IEEE Geosci. Remote Sens. Lett.
**2022**, 19, 1–5. [Google Scholar] [CrossRef] - Zhan, Y. Study on the Coastal Echo Processing Method for Satellite Radar Altimeter. Master’s Thesis, University of Chinese Academy of Sciences, Beijing, China, 2021. [Google Scholar]
- Wingham, D.J.; Rapley, C.G.; Griffiths, H. New techniques in satellite altimeter tracking systems. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Zurich, Switzerland, 8–11 September 1986. [Google Scholar]
- Davis, C.H. Growth of the Greenland ice sheet: A performance assessment of altimeter retracking algorithms. IEEE Trans. Geosci. Remote Sens.
**1995**, 33, 1108–1116. [Google Scholar] [CrossRef] - Hwang, C.; Guo, J.; Deng, X.; Hsu, H.Y.; Liu, Y. Coastal gravity anomalies from retracked Geosat/GM altimetry: Improvement, limitation and the role of airborne gravity data. J. Geodesy.
**2006**, 80, 204–216. [Google Scholar] [CrossRef] - Lee, H.; Shum, C.K.; Emery, W.; Calmant, S.; Deng, X.; Kuo, C.; Roesler, C.; Yi, Y. Validation of Jason-2 altimeter data by waveform retracking over California coastal ocean. Mar. Geodesy.
**2010**, 33, 304–316. [Google Scholar] [CrossRef] - Huang, Z.; Wang, H.; Luo, Z.; Shum, C.K.; Tseng, K.-H.; Zhong, B. Improving Jason-2 Sea Surface Heights within 10 km Offshore by Retracking Decontaminated Waveforms. Remote Sens.
**2017**, 9, 1077. [Google Scholar] [CrossRef] - Wang, H.; Huang, Z. Waveform Decontamination for Improving Satellite Radar Altimeter Data Over Nearshore Area: Upgraded Algorithm and Validation. Front. Earth Sci.
**2021**, 9, 748401. [Google Scholar] [CrossRef] - Shu, S.; Liu, H.; Beck, R.A.; Frappart, F.; Korhonen, J.; Xu, M.; Yu, B.; Hinkel, K.M.; Huang, Y.; Yu, B. Analysis of Sentinel-3 SAR altimetry waveform retracking algorithms for deriving temporally consistent water levels over ice-covered lakes. Remote Sens. Environ.
**2020**, 239, 111643. [Google Scholar] [CrossRef] - Agar, P.; Roohi, S.; Voosoghi, B.; Amini, A.; Poreh, D. Sea Surface Height Estimation from Improved Modified, and Decontaminated Sub-Waveform Retracking Methods over Coastal Areas. Remote Sens.
**2023**, 15, 804. [Google Scholar] [CrossRef] - Molini, A.B.; Valsesia, D.; Fracastoro, G.; Magli, E. DeepSUM: Deep Neural Network for Super-Resolution of Unregistered Multitemporal Images. IEEE Trans. Geosci. Remote Sens.
**2020**, 58, 3644–3656. [Google Scholar] [CrossRef] - Xing, D.; Hou, J.; Huang, C.; Zhang, W. Spatiotemporal Reconstruction of MODIS Normalized Difference Snow Index Products Using U-Net with Partial Convolutions. Remote Sens.
**2022**, 14, 1795. [Google Scholar] [CrossRef] - Perera, M.V.; Bandara, W.G.C.; Valanarasu, J.M.J.; Patel, V.M. SAR Despeckling Using Overcomplete Convolutional Networks. In Proceedings of the IGARSS 2022 - 2022 IEEE International Geoscience and Remote Sensing Symposium, Kuala Lumpur, Malaysia, 17–22 July 2022. [Google Scholar]
- Wang, P.; Zhang, H.; Patel, V.M. SAR Image Despeckling Using a Convolutional Neural Network. IEEE Signal Process. Lett.
**2017**, 24, 1763–1767. [Google Scholar] [CrossRef] - Zhang, Q.; Yuan, Q.; Li, J.; Yang, Z.; Ma, X. Learning a Dilated Residual Network for SAR Image Despeckling. Remote Sens.
**2018**, 10, 196. [Google Scholar] [CrossRef] - Lattari, F.; Leon, B.G.; Asaro, F.; Rucci, A.; Prati, C.; Matteucci, M. Deep Learning for SAR Image Despeckling. Remote Sens.
**2019**, 11, 1532. [Google Scholar] [CrossRef] - Ko, J.; Lee, S. SAR Image Despeckling Using Continuous Attention Module. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2022**, 15, 3–19. [Google Scholar] [CrossRef] - Pongrac, B.; Gleich, D. Despeckling of SAR Images Using Residual Twin CNN and Multi-Resolution Attention Mechanism. Remote Sens.
**2023**, 15, 3698. [Google Scholar] [CrossRef] - Chierchia, G.; Gheche, M.E.; Scarpa, G.; Verdoliva, L. Multitemporal SAR Image Despeckling Based on Block-Matching and Collaborative Filtering. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 5467–5480. [Google Scholar] [CrossRef] - Lehtinen, J.; Munkberg, J.; Hasselgren, J.; Laine, S.; Karras, T.; Aittala, M.; Aila, T. Noise2Noise: Learning Image Restoration without Clean Data. arXiv
**2018**, arXiv:1803.04189. [Google Scholar] - Lin, H.; Zhuang, Y.; Huang, Y.; Ding, X. Unpaired Speckle Extraction for SAR Despeckling. IEEE Trans. Geosci. Remote Sens.
**2023**, 60, 1–14. [Google Scholar] [CrossRef] - Molini, A.B.; Valsesia, D.; Fracastoro, G.; Magli, E. Speckle2Void: Deep Self-Supervised SAR Despeckling With Blind-Spot Convolutional Neural Networks. IEEE Trans. Geosci. Remote Sens.
**2022**, 60, 1–17. [Google Scholar] [CrossRef] - Laine, S.; Karras, T.; Lehtinen, J.; Aila, T. High-Quality Self-Supervised Deep Image Denoising. arXiv
**2019**, arXiv:1901.10277. [Google Scholar] - Tan, S.; Zhang, X.; Wang, H.; Yu, L.; Du, Y.; Yin, J.; Wu, B. A CNN-Based Self-Supervised Synthetic Aperture Radar Image Denoising Approach. IEEE Trans. Geosci. Remote Sens.
**2022**, 60, 1–15. [Google Scholar] [CrossRef] - Moore, R.K.; Williams, C.S. Radar Terrain Return at Near-Vertical Incidence. Proc. IRE
**1957**, 45, 228–238. [Google Scholar] [CrossRef] - Dobson, M.C.; Ulaby, F.T.; Hallikainen, M.T.; El-rayes, M.A. Microwave Dielectric Behavior of Wet Soil-Part II: Dielectric Mixing Models. IEEE Trans. Geosci. Remote Sens.
**1985**, GE-23, 35–46. [Google Scholar] [CrossRef] - Landy, J.C.; Tsamados, M.; Scharien, R.K. A Facet-Based Numerical Model for Simulating SAR Altimeter Echoes From Heterogeneous Sea Ice Surfaces. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 4164–4180. [Google Scholar] [CrossRef] - Zhu, Z.; Zhang, H.; Xu, F. Raw signal simulation of synthetic aperture radar altimeter over complex terrain surfaces. Radio Sci.
**2020**, 55, 1–17. [Google Scholar] [CrossRef] - Geng, X.; Wang, L.; Wang, X.; Qin, B.; Liu, T.; Tu, Z. Learning to Refine Source Representations for Neural Machine Translation. arXiv
**2018**, arXiv:1812.10230. [Google Scholar] [CrossRef] - Tewari, A.; Zollhoefer, M.; Bernard, F.; Garrido, P.; Kim, H.; Perez, P.; Theobalt, C. High-Fidelity Monocular Face Reconstruction Based on an Unsupervised Model-Based Face Autoencoder. IEEE. Trans. Pattern Anal. Mach. Intell.
**2020**, 42, 357–370. [Google Scholar] [CrossRef] [PubMed] - Etten, A.V.; Lindenbaum, D.; Bacastow, T.M. SpaceNet: A remote sensing dataset and challenge series. arXiv
**2018**, arXiv:1807.01232. [Google Scholar] - de Rijk, P.; Schneider, L.; Cordts, M.; Gavrila, D.M. Structural Knowledge Distillation for Object Detection. arXiv
**2022**, arXiv:2211.13133. [Google Scholar] - He, K.; Zhang, X.; Ren, S.; Sun, J. Deep residual learning for image recognition. In Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA, 27–30 June 2016. [Google Scholar]

**Figure 1.**Schematic diagrams of the working principle of SARAL: (

**a**) airborne SARAL geometry; (

**b**) footprint of the pulse signals.

**Figure 7.**From (

**left**) to (

**right**): raw DDMs, labels, enhanced DDMs by teacher network, enhanced DDMs by student network.

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

Altitude | 2.06 km | Bandwidth | 20 MHz |

Speed | 20 m/s | PRT | 200 μs |

Band | X | Pulses of each burst | 125 |

Component | PSNR (dB) | MAE (m) | RMSE (m) | Time (ms) |
---|---|---|---|---|

AGL-E-M (Raw data) | 12.7356 | 30.1383 | 25.7765 | 0.4883 |

Teacher + AGL-E-M | 24.3585 | 6.6338 | 9.2215 | 11.4566 |

KD + AGL-E-M (Proposed method) | 21.8368 | 6.9163 | 10.3378 | 6.0065 |

Method | MAE (m) | RMSE (m) | Time (ms) |
---|---|---|---|

LS | 23.3591 | 29.3692 | 56,968.2 |

MAP-smooth | 12.5811 | 23.2932 | 37,782.0 |

MAP-mutant | 11.0306 | 21.8112 | 36,144.3 |

Proposed method | 6.9163 | 10.3378 | 6.0065 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Duan, M.; Lu, Y.; Wang, Y.; Liu, G.; Tan, L.; Gao, Y.; Li, F.; Jiang, G.
Above Ground Level Estimation of Airborne Synthetic Aperture Radar Altimeter by a Fully Supervised Altimetry Enhancement Network. *Remote Sens.* **2023**, *15*, 5404.
https://doi.org/10.3390/rs15225404

**AMA Style**

Duan M, Lu Y, Wang Y, Liu G, Tan L, Gao Y, Li F, Jiang G.
Above Ground Level Estimation of Airborne Synthetic Aperture Radar Altimeter by a Fully Supervised Altimetry Enhancement Network. *Remote Sensing*. 2023; 15(22):5404.
https://doi.org/10.3390/rs15225404

**Chicago/Turabian Style**

Duan, Mengmeng, Yanxi Lu, Yao Wang, Gaozheng Liu, Longlong Tan, Yi Gao, Fang Li, and Ge Jiang.
2023. "Above Ground Level Estimation of Airborne Synthetic Aperture Radar Altimeter by a Fully Supervised Altimetry Enhancement Network" *Remote Sensing* 15, no. 22: 5404.
https://doi.org/10.3390/rs15225404