# Geocoding Error Correction for InSAR Point Clouds

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## Abstract

**:**

## 1. Introduction

## 2. InSAR Geocoding: Principle and Error Sources

#### 2.1. Errors in Azimuth and Range Times

- satellite dynamic effects such as incorrect annotation of ${t}_{az}$ in the time of radar pulse reception or incorrect annotation of ${\tau}_{rg}$ due to instrument cable delays in the satellite [9].

#### 2.2. Error in the Height of PS

## 3. Methodology

#### 3.1. PSI Processing

#### 3.2. Master Scene Corrections

#### 3.3. GCP Generation

#### 3.4. Height Offset Estimation and Updated Geocoding

- Coordinate differences are calculated in range and azimuth of the GCPs and their assumed corresponding bright point in the PSI point cloud.
- Points with coordinate differences larger than two times the standard deviation of differences (2$\sigma $ rule) are discarded first in range and then in azimuth.

#### 3.5. Cross-Comparison with LiDAR

- 2D horizontal accuracy: For a number of test sites, a line is robustly fitted to each side of the building footprint in the LiDAR point cloud in the East–North plane. The mean distance of the façade PS in the PSI point clouds are evaluated with respect to the corresponding footprint line in the LiDAR data. The average of all the deviations for corrected and non-corrected PSI point clouds are separately calculated, which demonstrates the closeness of each point cloud to the reference LiDAR data.
- 1D vertical accuracy: For an identical area in the LiDAR data and both corrected and non-corrected PSI point clouds, the façade points are excluded. Then for each of the three point clouds, ellipsoidal height histograms are formed containing two peaks which respectively represent ground and building roofs from the selected test site. The difference between the height values for which the ground peaks, in the PSI point cloud and in the LiDAR point cloud occur, indicates the vertical accuracy.

## 4. Area of Interest and Data Set

## 5. Results and Discussion

#### 5.1. Berlin InSAR and PSI Processing

#### 5.2. Geodetic Corrections, GCP Generation and Height Offset Estimation

#### 5.3. Cross-Comparison with LiDAR

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ADI | Amplitude Dispersion Index |

DEM | Digital Elevation Model |

DLR | German Aerospace Center |

DSM | Digital Surface Model |

ECMWF | European Centre for Medium-Range Weather Forecasts |

GCP | Ground Control Point |

GNSS | Global Navigation Satellite Systems |

IERS | International Earth Rotation and Reference Systems Service |

IGS | International GNSS Service |

InSAR | Interferometric SAR |

LiDAR | Light Detection and Ranging |

MAD | Median Absolute Deviation |

PSI | Persistent Scatterer Interferometry |

PS | Persistent Scatterer |

PTA | Point Target Analysis |

SAR | Synthetic Aperture Radar |

SCR | Signal-to-Clutter-Ratio |

SGP | SAR Geodesy Processor |

SLC | Single Look Complex |

SRTM | Shuttle Radar Topography Mission |

TEC | Total Electron Content |

UTM | Universal Transverse Mercator |

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**Figure 1.**Timing bias in azimuth and its effect on the geocoded coordinates. (

**a**) azimuth timing error causing a displacement on the ground $\delta {l}_{az}$; (

**b**) projection of $\delta {l}_{az}$ onto the East $\delta {l}_{az}^{E}$ and North $\delta {l}_{az}^{N}$ components using satellite heading angle $\alpha $.

**Figure 2.**Timing bias in range and its effect on the geocoded coordinates. (

**a**) range timing error and its impact on geocoding in the ground range $\delta {l}_{gr}$; (

**b**) projection of $\delta {l}_{gr}$ onto the East $\delta {l}_{gr}^{E}$ and North $\delta {l}_{gr}^{N}$ components using satellite heading angle $\alpha $.

**Figure 3.**Depiction of height error $\delta H$ due to unknown DEM error at the reference point and its effect on geocoded coordinates. It can be seen that this error causes a shift in the cross-range direction $\delta {l}_{H}^{s}$, which is decomposed into an offset in ground range $\delta {l}_{H}^{gr}$ and a vertical component $\delta H$.

**Figure 4.**Workflow of the utilized geocoding error correction method. The processing steps, included in the big rectangles, are carried out independently and their results are shown by the parallelograms. The double shapes indicate that each processing is carried out for two or more SAR image stacks, which is the necessary condition for GCP generation.

**Figure 5.**Optical image of Berlin taken from Google Earth. The mean scene coverage of the TerraSAR-X images as well as the extent of the LiDAR data are marked with colored rectangles. The small yellow rectangle shows the test site within which the vertical localization accuracy of PSI point clouds has been analyzed. The cyan arrows indicate the three test sites used for horizontal accuracy analysis.

**Figure 6.**Temporal-perpendicular baseline distribution of the SAR image stacks in Berlin. (

**a**,

**b**) correspond to the data stacks of Beam57 and Beam42, respectively.

**Figure 7.**Geocoded PSI point cloud of Berlin, reconstructed from Beam57, in UTM coordinates. The ellipsoidal height is colorcoded. The x- and y-axis correspond to the UTM East and North, respectively. The test sites used for vertical and horizontal accuracy analysis are marked with black rectangle and black arrows, respectively.

**Figure 8.**Geocoded PSI point cloud of Berlin, reconstructed from Beam42, in UTM coordinates. The ellipsoidal height is colorcoded. The x- and y-axis correspond to the UTM East and North, respectively. The test sites used for vertical and horizontal accuracy analysis are marked with black rectangle and black arrows, respectively.

**Figure 9.**Range and azimuth error in the radar coordinate system (x-axis: range, y-axis: azimuth) of the master scenes of both investigated beams, which were acquired on 24 December 2011 (Beam57) and on 7 March 2012 (Beam42). Note that the scale of the colorbars for range error is in meters while the one for azimuth errors is in centimeters. The test sites used for vertical and horizontal accuracy analysis are marked with black rectangle and black arrows, respectively.

**Figure 10.**Histogram of GCP precision values in East ${\sigma}_{E}$, North ${\sigma}_{N}$ and height ${\sigma}_{H}$.

**Figure 11.**Distribution of the GCPs within the PSI point clouds of both beams. The test sites used for vertical and horizontal accuracy analysis are marked with black rectangle and black arrows, respectively.

**Figure 12.**Restriction of the DEM error estimation to the true correspondences among GCPs and PS. (

**a**,

**b**) demonstrate the scatterplots of GCP-PS pairs before outlier removal, for Beam57 and Beam42, respectively; (

**c**,

**d**) show the scatterplots of the GCP-PS pairs after outlier removal. This causes a decrease in the bias and the standard deviation of the coordinate differences; (

**e**,

**f**) depict the robust height offset estimation after removal of the height differences in accordance with the $2\sigma $ rule. The peak of the smoothed histogram indicates the DEM error for each beam. Note that, for all the figures, the coordinate differences are defined as the GCP coordinates subtracted from their corresponding PS coordinates.

**Figure 13.**2D horizontal localization accuracy analysis of PSI point clouds of the test sites marked with cyan arrows in Figure 5 (top: non-corrected, bottom: corrected). The x- and y-axes correspond to the Easting and Northing in UTM. Green and red dots show the ascending and descending point clouds while white dots show the extracted LiDAR footprints. The scale of figures is not identical meaning that the degree of zoom-in is higher in subfigures (

**c**,

**f**).

**Figure 14.**1D vertical localization accuracy analysis of PSI point clouds, before and after applying geodetic corrections and height offset compensation, in comparison with LiDAR. The x- and y-axes correspond to the Easting in UTM and ellipsoidal height, respectively. Green and red dots show the ascending (Beam57) and descending (Beam42) point clouds while white dots show the LiDAR data. (

**a**,

**c**) depict the non-corrected point clouds while (

**b**,

**d**) correspond to the corrected ones. The height shifts, caused by the unknown DEM error of the reference points are easily recognizable in non-corrected point clouds while the offsets are compensated for in the corrected results. Note that the Easting and the height are differently scaled in order to emphasize the vertical effect.

**Figure 15.**Ellipsoidal height histograms of non-façade points in LiDAR (red), non-corrected PSI (green) and corrected PSI point clouds (blue) corresponding to the yellow bounding box in Figure 5. (

**a**,

**b**) show the results for Beam57 and Beam42, respectively. For both beams, the height shifts are compensated for after correction, using SAR-GCPs, as the ground peaks of PSI point clouds and LiDAR data become aligned.

Beam Nr. | Center θ (Degree) | Average α (Degree) | Orbit Direction | Area (km^{2}) | Polarization | Nr. of Images |
---|---|---|---|---|---|---|

42 | 36.1 | 350.3 | descending | 40.94 | VV | 107 |

57 | 41.9 | 190.6 | ascending | 42.52 | VV | 107 |

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## Share and Cite

**MDPI and ACS Style**

Montazeri, S.; Rodríguez González, F.; Zhu, X.X. Geocoding Error Correction for InSAR Point Clouds. *Remote Sens.* **2018**, *10*, 1523.
https://doi.org/10.3390/rs10101523

**AMA Style**

Montazeri S, Rodríguez González F, Zhu XX. Geocoding Error Correction for InSAR Point Clouds. *Remote Sensing*. 2018; 10(10):1523.
https://doi.org/10.3390/rs10101523

**Chicago/Turabian Style**

Montazeri, Sina, Fernando Rodríguez González, and Xiao Xiang Zhu. 2018. "Geocoding Error Correction for InSAR Point Clouds" *Remote Sensing* 10, no. 10: 1523.
https://doi.org/10.3390/rs10101523