# Geocoding Error Correction for InSAR Point Clouds

^{1}

^{2}

^{*}

## 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 |

## References

- Ferretti, A.; Prati, C.; Rocca, F. Permanent scatterers in SAR interferometry. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 8–20. [Google Scholar] [CrossRef] [Green Version] - Kampes, B.M. Radar Interferometry: Persistent Scatterer Technique. In Number v. 12 in Remote Sensing and Digital Image Processing; Springer: Dordrecht, The Netherlands, 2006. [Google Scholar]
- Zebker, H.; Villasenor, J. Decorrelation in interferometric radar echoes. IEEE Trans. Geosci. Remote Sens.
**1992**, 30, 950–959. [Google Scholar] [CrossRef] [Green Version] - Gernhardt, S.; Bamler, R. Deformation monitoring of single buildings using meter-resolution SAR data in PSI. ISPRS J. Photogramm. Remote Sens.
**2012**, 73, 68–79. [Google Scholar] [CrossRef] - Gernhardt, S.; Adam, N.; Eineder, M.; Bamler, R. Potential of very high resolution SAR for persistent scatterer interferometry in urban areas. Ann. GIS
**2010**, 16, 103–111. [Google Scholar] [CrossRef] - Schwabisch, M. A fast and efficient technique for SAR interferogram geocoding. In Proceedings of the 1998 IEEE International Geoscience and Remote Sensing (IGARSS), Seattle, WA, USA, USA, 6–10 July 1998; Volume 2, pp. 1100–1102. [Google Scholar] [CrossRef]
- Hanssen, R.F. Radar Interferometry: Data Interpretation and Error Analysis. In Number v. 2 in Remote Sensing and Digital Image Processing; Kluwer Academic: Dordrecht, The Netherlands; Boston, MA, USA, 2001. [Google Scholar]
- Eineder, M. Efficient simulation of SAR interferograms of large areas and of rugged terrain. IEEE Trans. Geosci. Remote Sens.
**2003**, 41, 1415–1427. [Google Scholar] [CrossRef] - Eineder, M.; Minet, C.; Steigenberger, P.; Cong, X.Y.; Fritz, T. Imaging Geodesy—Toward Centimeter-Level Ranging Accuracy With TerraSAR-X. IEEE Trans. Geosci. Remote Sens.
**2011**, 49, 661–671. [Google Scholar] [CrossRef] - Chang, L.; Hanssen, R.F. Detection of cavity migration and sinkhole risk using radar interferometric time series. Remote Sens. Environ.
**2014**, 147, 56–64. [Google Scholar] [CrossRef] - Yang, M.; Dheenathayalan, P.; Chang, L.; Wang, J.; Lindenbergh, R.; Liao, M.; Hanssen, R. High-precision 3D geolocation of persistent scatterers with one single-Epoch GCP and LIDAR DSM data. In Proceedings of the Living Planet Symposium; European Space Agency: Paris, France, 2016; Volume 740, p. 398. [Google Scholar]
- Bateson, L.; Novali, F.; Cooksley, G. Terrafirma User Guide: A Guide to the Use and Understanding of Persistent Scatterer Interferometry in the Detection and Monitoring of Terrain-Motion; Technical Report 19366/05/I-EC; ESA: Paris, France, 2010. [Google Scholar]
- Gernhardt, S.; Cong, X.Y.; Eineder, M.; Hinz, S.; Bamler, R. Geometrical Fusion of Multitrack PS Point Clouds. IEEE Geosci. Remote Sens. Lett.
**2012**, 9, 38–42. [Google Scholar] [CrossRef] - Gernhardt, S. High Precision 3D Localization and Motion Analysis of Persistent Scatterers Using Meter-Resolution Radar Satellite Data. Ph.D. Thesis, Technische Universität München, München, Germany, 2012. [Google Scholar]
- Cong, X. SAR Interferometry for Volcano Monitoring: 3D-PSI Analysis and Mitigation of Atmospheric Refractivity. Ph.D. Thesis, Technische Universität München, München, Germany, 2014. [Google Scholar]
- Besl, P.; McKay, N.D. A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell.
**1992**, 14, 239–256. [Google Scholar] [CrossRef] - Zhu, X.X.; Montazeri, S.; Gisinger, C.; Hanssen, R.F.; Bamler, R. Geodetic SAR Tomography. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 18–35. [Google Scholar] [CrossRef] - Gisinger, C.; Balss, U.; Pail, R.; Zhu, X.X.; Montazeri, S.; Gernhardt, S.; Eineder, M. Precise Three-Dimensional Stereo Localization of Corner Reflectors and Persistent Scatterers With TerraSAR-X. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 1782–1802. [Google Scholar] [CrossRef] - Zhu, X.X.; Bamler, R. Very high resolution spaceborne SAR tomography in urban environment. IEEE Trans. Geosci. Remote Sens.
**2010**, 48, 4296–4308. [Google Scholar] [CrossRef] [Green Version] - Balss, U.; Runge, H.; Suchandt, S.; Cong, X.Y. Automated extraction of 3-D Ground Control Points from SAR images—An upcoming novel data product. In Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China, 10–15 July 2016; pp. 5023–5026. [Google Scholar] [CrossRef]
- Montazeri, S.; Gisinger, C.; Eineder, M.; Zhu, X.X. Automatic Detection and Positioning of Ground Control Points Using TerraSAR-X Multiaspect Acquisitions. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 2613–2632. [Google Scholar] [CrossRef] - Van Leijen, F. Persistent Scatterer Interferometry Based on Geodetic Estimation Theory. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 2014. [Google Scholar]
- Cumming, I.G.; Wong, F.H.C. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation; Artech House Remote Sensing Library, Artech House: Boston, MA, USA, 2005. [Google Scholar]
- Yoon, Y.; Eineder, M.; Yague-Martinez, N.; Montenbruck, O. TerraSAR-X Precise Trajectory Estimation and Quality Assessment. IEEE Trans. Geosci. Remote Sens.
**2009**, 47, 1859–1868. [Google Scholar] [CrossRef] - Hackel, S.; Montenbruck, O.; Steigenberger, P.; Balss, U.; Gisinger, C.; Eineder, M. Model improvements and validation of TerraSAR-X precise orbit determination. J. Geod.
**2017**, 91, 547–562. [Google Scholar] [CrossRef] - Cong, X.Y.; Balss, U.; Eineder, M.; Fritz, T. Imaging Geodesy—Centimeter-Level Ranging Accuracy with TerraSAR-X: An Update. IEEE Geosci. Remote Sens. Lett.
**2012**, 9, 948–952. [Google Scholar] [CrossRef] - Balss, U.; Cong, X.Y.; Brcic, R.; Rexer, M.; Minet, C.; Breit, H.; Eineder, M.; Fritz, T. High precision measurement on the absolute localization accuracy of TerraSAR-X. In Proceedings of the 2012 IEEE International Geoscience and Remote Sensing Symposium, Munich, Germany, 22–27 July 2012; pp. 1625–1628. [Google Scholar] [CrossRef]
- Balss, U.; Gisinger, C.; Cong, X.Y.; Brcic, R.; Hackel, S.; Eineder, M. Precise measurements on the absolute localization accuracy of TerraSAR-X on the base of far-distributed test sites. In Proceeding of the 10th European Conference on Synthetic Aperture Radar (EUSAR), Berlin, Germany, 3–5 June 2014. [Google Scholar]
- Balss, U.; Breit, H.; Fritz, T.; Steinbrecher, U.; Gisinger, C.; Eineder, M. Analysis of internal timings and clock rates of TerraSAR-X. In Proceedings of the 2014 IEEE International Geoscience and Remote Sensing Symposium, Quebec City, QC, Canada, 13–18 July 2014; pp. 2671–2674. [Google Scholar] [CrossRef]
- Misra, P.; Enge, P. Global Positioning System: Signals, Measurements, and Performance; Misra, P., Enge, P., Eds.; Jamuna Press: Warsaw, Poland, 2006. [Google Scholar]
- Gisinger, C. Atmospheric Corrections for TerraSAR-X Derived from GNSS Observations. Master’s Thesis, Technische Universität München, München, Germany, 2012. [Google Scholar]
- Balss, U.; Gisinger, C.; Cong, X.Y.; Brcic, R.; Steigenberger, P.; Eineder, M.; Pail, R.; Hugentobler, U. High resolution geodetic earth observation with TerraSAR-X: Correction schemes and validation. In Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium, Melbourne, VIC, Australia, 21–26 July 2013; pp. 4499–4502. [Google Scholar] [CrossRef]
- Petit, G.; Luzum, B. IERS Conventions; IERS Technical Note No. 36; Verlag des Bundesamts für Kartographie und Geodäsie: Frankfurt am Main, Germany, 2010. [Google Scholar]
- Balss, U.; Gisinger, C.; Eineder, M. Measurements on the Absolute 2-D and 3-D Localization Accuracy of TerraSAR-X. Remote Sens.
**2018**, 10, 656. [Google Scholar] [CrossRef] - Eineder, M.; Balss, U.; Suchandt, S.; Gisinger, C.; Cong, X.; Runge, H. A definition of next-generation SAR products for geodetic applications. In Proceedings of the 2015 IEEE International Geoscience and Remote Sensing Symposium, Milan, Italy, 26–31 July 2015; pp. 1638–1641. [Google Scholar] [CrossRef]
- OpenStreetMap Contributors. Planet Dump. 2017. Available online: https://www.openstreetmap.org (accessed on 18 August 2018).
- Rousseeuw, P.J.; Hubert, M. Anomaly detection by robust statistics. Wiley Interdiscip. Rev. Data Min. Knowl. Discov.
**2018**, 8, 1–14. [Google Scholar] [CrossRef] - Adam, N.; Kampes, B.M.; Eineder, M. The development of a scientific persistent scatterer system: Modifications for mixed ERS/ENVISAT time series. In Proceedings of the Envisat and ERS Symposium, Salzburg, Austria, 6–10 September 2004; pp. 1–9. [Google Scholar]
- Adam, N.; Gonzalez, F.R.; Parizzi, A.; Brcic, R. Wide area Persistent Scatterer Interferometry: Current developments, algorithms and examples. In Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium, Melbourne, VIC, Australia, 21–26 July 2013; pp. 1857–1860. [Google Scholar] [CrossRef]
- Rodriguez Gonzalez, F.; Bhutani, A.; Adam, N. L1 network inversion for robust outlier rejection in persistent Scatterer Interferometry. In Proceedings of the 2011 IEEE International Geoscience and Remote Sensing Symposium, Vancouver, BC, Canada, 24–29 July 2011; pp. 75–78. [Google Scholar] [CrossRef]
- Rodriguez Gonzalez, F.; Adam, N.; Parizzi, A.; Brcic, R. The Integrated Wide Area Processor (IWAP): A Processor for Wide Area Persistent Scatterer Interferometry. In Proceedings of the ESA Living Planet Symposium 2013; ESA: Edinburgh, UK, 2013; pp. 1–4. [Google Scholar]
- Adam, N.; Kampes, B.M.; Eineder, M.; Worawattanamateekul, J.; Kircher, M. The Development of a Scientific Permanent Scatterer System. In Proceedings of the Joint ISPRS/EARSeL Workshop on High Resolution Mapping from Space 2003, Edinburgh, UK, 9–13 September 2003. [Google Scholar]
- Montazeri, S. The Fusion of SAR Tomography and Stereo-SAR for 3D Absolute Scatterer Positioning. Master’s Thesis, Delft University of Technology, Delft, The Netherlands, 2014. [Google Scholar]
- Montazeri, S.; Zhu, X.X.; Eineder, M.; Bamler, R. Three-Dimensional Deformation Monitoring of Urban Infrastructure by Tomographic SAR Using Multitrack TerraSAR-X Data Stacks. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 6868–6878. [Google Scholar] [CrossRef]

**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 |

© 2018 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 (http://creativecommons.org/licenses/by/4.0/).

## 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