# On-Ground Retracking to Correct Distorted Waveform in Spaceborne Global Navigation Satellite System-Reflectometry

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## Abstract

**:**

## 1. Introduction

## 2. Simulation Scenario and Models

#### 2.1. Scenario

#### 2.2. GNSS-R Scattering Models

#### 2.3. Noise Models

## 3. Speckle Noise vs. Incoherent Averaging

## 4. Influence of Dynamic on Waveform

#### 4.1. Delay Change Rate

## 5. Influence on Feature Parameter

#### 5.1. Sea Surface Height

#### 5.2. Wind Speed

## 6. Methodology of Retracking

- using estimated Doppler difference between direct and reflected signals to produce the DDCR and PSF;
- developing model of the distorted waveform using convolution Equation (18) and the initial coefficients of the Model (20);
- fitting the distorted model above with the measured waveform using nonlinear least square to obtain the optimal coefficients of (20);
- reconstructing the pure waveform using the Model (20) and the estimated coefficients above.

## 7. Results and Discussion

#### 7.1. Validation Using UK-DMC Data

#### 7.2. Validation Using UK-TDS-1 Data

#### 7.3. Validation Using Simulation

#### 7.4. Comparison with CLS and TSVD Result

#### 7.5. Influence of DCR Accuracy

## 8. Retrieval Performance

- generating randomly 1000 sets of wind speed, incident angle, the moving direction of LEO and GNSS satellites as the input parameters of the models in Section 2;
- using scattering scenario and models in Section 2 to produce 1000 delay waveform corrupted by the noises and the dynamic of GNSS-R geometry;
- retracking above delay waveforms to obtain pure ones through proposed methods in Section 6 and estimating the retracked and non-retracked waveforms’ features defined by (11)∼(14);
- developing retrieval approaches and evaluating the root mean square error (RMSE) of sea surface height and wind speed measured using retracked and non-retracked waveforms.

#### 8.1. Sea Surface Height

#### 8.2. Wind Speed

- case 1: the single observable of the delay waveform, such as PW, is the input of neural network;
- case 2: the three observable are all considered as the input of the neural network.

#### 8.3. Performance vs. SNR

## 9. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Derivation of Delay Difference Change Rate

## References

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**Figure 2.**Exponential distribution of (

**a**) reflected GNSS signals for UK-TDS-1 satellite and (

**b**) simulated data using scattering and noise models. The dotted lines are the best least squares fit using exponential function.

**Figure 3.**Standard deviation vs. number of incoherent averaging for the UK-TDS-1 data. The dotted line shows the expected decrease as Equation (8).

**Figure 4.**Change of the delay difference between direct and reflected signals with $\theta $ being ${30}^{\circ}$, (

**a**) ${\alpha}_{\mathrm{r}}$ being ${45}^{\circ}$, ${\alpha}_{\mathrm{t}}$ being ${45}^{\circ}$; (

**b**) ${\alpha}_{\mathrm{r}}$ being ${225}^{\circ}$, ${\alpha}_{\mathrm{t}}$ being ${225}^{\circ}$.

**Figure 5.**Incoherently averaged delay waveform with $\theta $ being ${30}^{\circ}$, (

**a**) ${\alpha}_{\mathrm{r}}$ being ${45}^{\circ}$, ${\alpha}_{\mathrm{t}}$ being ${45}^{\circ}$; (

**b**) ${\alpha}_{\mathrm{r}}$ being ${225}^{\circ}$, ${\alpha}_{\mathrm{t}}$ being ${225}^{\circ}$.

**Figure 6.**Simulated and computed DDCR with $\theta $ being ${30}^{\circ}$, (

**a**) ${\alpha}_{\mathrm{r}}$ being ${45}^{\circ}$, ${\alpha}_{\mathrm{t}}$ being ${45}^{\circ}$; (

**b**) ${\alpha}_{\mathrm{r}}$ being ${225}^{\circ}$, ${\alpha}_{\mathrm{t}}$ being ${225}^{\circ}$.

**Figure 7.**Sensitivity of (

**a**) peak waveform; (

**b**) leading edge slope; and (

**c**) trailing edge slope on wind speed before and after retracking under the condition of the moving direction of LEO and GNSS satellite are both ${45}^{\circ}$; and the incidence angle is ${30}^{\circ}$.

**Figure 10.**Delay waveform with the tracking refresh period of 1 ms, (

**a**) 1 s; (

**b**) 3 s; and corresponding waveform after retracking using Equation (21) for UK-DMC.

**Figure 11.**Delay waveform with the tracking refresh period of 1 ms, (

**a**) 1 s; (

**b**) 3 s; and corresponding waveform after retracking using Equation (19) for UK-TDS-1.

**Figure 13.**MSE between the retracked waveform and the one compensated on each correlation integration time period as the function of the DCR for (

**a**) UK-DMC and (

**b**) UK-TDS.

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

GNSS Satellite Height ${h}_{\mathrm{t}}$ | km | 20,200 |

LEO Satellite Height ${h}_{\mathrm{r}}$ | km | 659 |

GNSS Satellite speed ${v}_{\mathrm{t}}$ | km | 3.07 |

LEO Satellite speed ${v}_{\mathrm{r}}$ | km | 7.60 |

Earth Radius ${R}_{\mathrm{e}}$ | km | 6371 |

Maximum Gain ${G}_{0}$ | dB | 12 |

3 dB Beam Width $\phi $ | deg | 25 |

incident angle $\theta $ | deg | [0:50] |

Moving direction of GNSS Satellite ${\alpha}_{\mathrm{t}}$ | deg | [0:360] |

Moving direction of LEO Satellite ${\alpha}_{\mathrm{r}}$ | deg | [0:360] |

Coherent integration time ${T}_{\mathrm{coh}}$ | ms | 1 |

Incoherent Integration time ${T}_{\mathrm{incoh}}$ | s | 16 |

Tracking Refresh Period ${T}_{\mathrm{TR}}$ | ms | [1, 1000, 3000] |

Wind Speed W | m/s | [1:20] |

**Table 2.**Comparison of MSE between retracked waveform and the one with the TRP of 1 ms using proposed and CSL and TSVD for UK-DMC and UK-TDS-1 data.

Methods | 1 s | 3 s | |||
---|---|---|---|---|---|

UK-DMC | UK-TDS-1 | UK-DMC | UK-TDS-1 | ||

proposed | 0.026 | 70.10 | 0.044 | 61.80 | |

CLS | $\gamma =0.050$ | 0.041 | 85.82 | 0.078 | 89.94 |

$\gamma =0.005$ | 0.103 | 111.90 | 0.115 | 202.57 | |

TSVD | $p=400$ | 0.044 | 88.75 | 0.130 | 95.43 |

$p=1000$ | 0.116 | 86.79 | 0.329 | 202.74 |

**Table 3.**Standard Deviations of Estimated sea surface height for Retracked and Non-Retracked Waveform. re. and non-re. is the Shorthand of Retracking and Non-Retracking.

Parameter | 1 ms [m] | 1 s [m] | 3 s [m] | ||
---|---|---|---|---|---|

re. | non-re. | re. | non-re. | ||

std | 4.66 | 6.19 | 40.98 | 11.49 | 125.45 |

Observable | 1 ms [m/s] | 1 s [m/s] | 3 s [m/s] | ||
---|---|---|---|---|---|

re. | non-re. | re. | non-re. | ||

PW | 2.24 | 2.25 | 2.55 | 2.43 | 3.37 |

LES | 1.48 | 1.92 | 2.88 | 2.42 | 4.42 |

TES | 1.59 | 1.84 | 2.33 | 2.51 | 4.95 |

combined | 1.27 | 1.37 | 1.73 | 1.45 | 1.88 |

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## Share and Cite

**MDPI and ACS Style**

Wang, F.; Yang, D.; Li, W.; Yang, W.
On-Ground Retracking to Correct Distorted Waveform in Spaceborne Global Navigation Satellite System-Reflectometry. *Remote Sens.* **2017**, *9*, 643.
https://doi.org/10.3390/rs9070643

**AMA Style**

Wang F, Yang D, Li W, Yang W.
On-Ground Retracking to Correct Distorted Waveform in Spaceborne Global Navigation Satellite System-Reflectometry. *Remote Sensing*. 2017; 9(7):643.
https://doi.org/10.3390/rs9070643

**Chicago/Turabian Style**

Wang, Feng, Dongkai Yang, Weiqiang Li, and Wei Yang.
2017. "On-Ground Retracking to Correct Distorted Waveform in Spaceborne Global Navigation Satellite System-Reflectometry" *Remote Sensing* 9, no. 7: 643.
https://doi.org/10.3390/rs9070643