# A Modified Dual-Baseline PolInSAR Method for Forest Height Estimation

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## Abstract

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## 1. Introduction

## 2. Methods for Model-Based PolInSAR Forest Height Inversion

#### 2.1. PolInSAR Coherence

#### 2.2. RVoG Model

#### 2.3. SBPI Method

#### 2.4. S-RVoG Model

#### 2.5. Cloude’s DBPI Method

#### 2.6. Modified DBPI Method

## 3. Test Site and PolInSAR Data Set Description

## 4. Results and Analysis

#### 4.1. SBPI vs. Cloude’s DBPI

^{2}were chosen for the statistical analysis of the inversion’s performance. The colour of each dot represents the mean range terrain slope of the corresponding stand, scaled from −15° to 15°. From Figure 3a,b, it can be seen that the SBPI results from baseline 1-2 and baseline 1-3 are similar, with a high RMSE of 7.88 m and 8.63 m, respectively. The reason for such a high bias is the significant ground scattering contribution in all polarization channels at the P-band. The assumed volume-only polarization channel (e.g., PDHigh) is not a reasonable assumption with this configuration. However, Figure 3c,d shows that the DBPI results present significant improvements, with RMSEs of 4.65 m and 4.79 m, respectively. The average accuracy of the DBPI results has been improved by a mean value of 42.86%. The reason is explained as follows. As seen in Figure 4, in the two SBPI cases, the point corresponding to ${\gamma}_{PDHigh}$ coherence is chosen as the volume-only coherence, indicated by the red hexagrams. However, in the DBPI cases, the estimated volume-only coherences are the dark crosses for the second baseline and the blue crosses for the first baseline marked inside the red circles. It is obvious that after the constraint of an additional baseline, the positions of the volume-only coherence in the DBPI cases are further than the ${\gamma}_{PDHigh}$ point chosen in SBPI cases, and hence improve the final estimated results of forest height. It indicates that the DBPI method can compensate for the GVR estimation bias with respect to the SBPI method. As a result, it can estimate more accurately pure volume-only coherence, which is critical for forest height inversion.

#### 4.2. Cloude’s DBPI vs. Modified DBPI

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Geometrical reference frame for the sloped random volume over ground (S-RVoG) model. (

**a**) Positive terrain slope; (

**b**) Negative terrain slope. ${B}_{\perp}$ is the perpendicular baseline, $\theta $ is the incidence angle, $R$ is the slant range, $\alpha $ is the range terrain slope, and ${\theta}^{\prime}$ is the incidence angle in the new geometric reference frame.

**Figure 2.**Forest height inversion results from four cases of inversion configurations. (

**a**) Image 1-2 with single baseline PolInSAR (SBPI); (

**b**) Image 1-3 with SBPI; (

**c**) Image 1-2 as the first baseline ${B}_{1}$ with dual-baseline PolInSAR (DBPI); (

**d**) Image 1-3 as the first baseline ${B}_{1}$ with DBPI.

**Figure 3.**Validation plots of inversion results from four cases of inversion configurations; PolInSAR forest height estimates versus LIDAR forest height. (

**a**) Image 1-2 with SBPI; (

**b**) Image 1-3 with SBPI; (

**c**) Image 1-2 as the first baseline ${B}_{1}$ with DBPI; (

**d**) Image 1-3 as the first baseline ${B}_{1}$ with DBPI. The color of the stand dots represents the range terrain slope, scaled from −15° to 15°. RMSE, root mean square error.

**Figure 4.**One example of inversion scenario for the SBPI and DBPI methods in the unit complex plane. (

**a**) Image 1-2 as the first baseline ${B}_{1}$ with DBPI; (

**b**) Image 1-3 as the first baseline ${B}_{1}$ with DBPI.

**Figure 5.**Forest height inversion results from the modified DBPI method. (

**a**) Image 1-2 as the first baseline with modified DBPI; (

**b**) Image 1-3 as the first baseline with modified DBPI. (

**c**) Difference values of forest height between the modified DBPI and DBPI results with image 1-2 as the first baseline, scaled from −5 m to 5 m; (

**d**) Difference values of forest height between the modified DBPI and DBPI results with image 1-3 as the first baseline, scaled from −5 m to 5 m; (

**e**) The range terrain slope map, scaled from −20° to 20°.

**Figure 6.**Validation plots of the inversion results from different inversion configurations; PolInSAR forest height estimates versus LIDAR forest height. (

**a**) Image 1-2 as the first baseline ${B}_{1}$ with modified DBPI; (

**b**) Image 1-3 as the first baseline ${B}_{1}$ with modified DBPI. (

**c**) Image 1-2 as the first baseline ${B}_{1}$ with DBPI (slope $\left|\alpha \right|>{10}^{\circ}$); (

**d**) Image 1-3 as the first baseline ${B}_{1}$ with DBPI (slope $\left|\alpha \right|>{10}^{\circ}$). (

**e**) Image 1-2 as the first baseline ${B}_{1}$ with modified DBPI (slope $\left|\alpha \right|>{10}^{\circ}$); (

**f**) Image 1-3 as the first baseline ${B}_{1}$ with modified DBPI (slope $\left|\alpha \right|>{10}^{\circ}$). The color of the stand dots represents the range terrain slope, scaled from −15° to 15°.

Image | Temporal Baseline (min) | Baseline (m) | Kz Interval |
---|---|---|---|

1 | 0 | 0 | master |

2 | 53 | 24 | 0.024–0.135 |

3 | 70 | 32 | 0.051–0.181 |

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## Share and Cite

**MDPI and ACS Style**

Xie, Q.; Zhu, J.; Wang, C.; Fu, H.; Lopez-Sanchez, J.M.; Ballester-Berman, J.D. A Modified Dual-Baseline PolInSAR Method for Forest Height Estimation. *Remote Sens.* **2017**, *9*, 819.
https://doi.org/10.3390/rs9080819

**AMA Style**

Xie Q, Zhu J, Wang C, Fu H, Lopez-Sanchez JM, Ballester-Berman JD. A Modified Dual-Baseline PolInSAR Method for Forest Height Estimation. *Remote Sensing*. 2017; 9(8):819.
https://doi.org/10.3390/rs9080819

**Chicago/Turabian Style**

Xie, Qinghua, Jianjun Zhu, Changcheng Wang, Haiqiang Fu, Juan M. Lopez-Sanchez, and J. David Ballester-Berman. 2017. "A Modified Dual-Baseline PolInSAR Method for Forest Height Estimation" *Remote Sensing* 9, no. 8: 819.
https://doi.org/10.3390/rs9080819