# Monitoring Deformation along Railway Systems Combining Multi-Temporal InSAR and LiDAR Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Mt-Insar Process

#### 2.2. Attribution of the Insar Observations

#### 2.2.1. Absolute Height Correction

#### 2.2.2. Generating the Positioning Error Ellipsoid

#### 2.2.3. Snapping to the Point Cloud

#### 2.3. Quality Metrics

#### 2.3.1. Temporal Coherence

#### 2.3.2. Dilution of Precision

**One track.**If only one LOS observation is available, we may decide to evaluate only the projection of the deformation vector onto the normal direction, assuming that the longitudinal and transversal directions may be negligible. Here, we introduce pseudo-observations ${d}_{L}$ and ${d}_{T}$, which are set to zero. Supposing that ${\mathbf{R}}_{\mathrm{trans}}$ denote the transformation matrix from local coordinate to ground coordinate [43], the relationship between the displacement vector and LOS observation is defined as$$\left[\begin{array}{c}{d}_{LOS}\\ {d}_{T}\\ {d}_{L}\end{array}\right]=\left[\begin{array}{ccc}0& 0& cos\theta \\ 0& 1& 0\\ 0& 0& 1\end{array}\right]{\mathbf{R}}_{\mathrm{trans}}\left[\begin{array}{c}{d}_{T}\\ {d}_{L}\\ {d}_{N}\end{array}\right]=\mathbf{A}\phantom{\rule{0.166667em}{0ex}}{\mathbf{d}}_{\mathrm{asset}}.$$**Two tracks.**If two LOS observations are available, we may decide to assume that deformation in the longitudinal direction is negligible, by using a pseudo-observation ${d}_{L}$ to be equal to zero. Then, the relationship between the displacement vector and LOS observations is defined as$$\left[\begin{array}{c}{d}_{LO{S}_{1}}\\ {d}_{LO{S}_{2}}\\ {d}_{L}\end{array}\right]=\left[\begin{array}{ccc}-sin{\theta}_{1}cos{\alpha}_{1}& 0& cos{\theta}_{1}\\ -sin{\theta}_{2}cos{\alpha}_{2}& 0& cos{\theta}_{2}\\ 0& 1& 0\end{array}\right]{\mathbf{R}}_{\mathrm{trans}}\left[\begin{array}{c}{d}_{T}\\ {d}_{L}\\ {d}_{N}\end{array}\right]=\mathbf{A}\phantom{\rule{0.166667em}{0ex}}{\mathbf{d}}_{\mathrm{asset}},$$**Three or more tracks.**If at least three LOS observations are available, the LOS decomposition can be solved directly, as long as the viewing geometries are significantly different. The relationship between the displacement vector and LOS observations is defined as$$\left[\begin{array}{c}{d}_{LO{S}_{1}}\\ {d}_{LO{S}_{2}}\\ \vdots \\ {d}_{LO{S}_{n}}\end{array}\right]=\left[\begin{array}{ccc}-sin{\theta}_{1}cos{\alpha}_{1}& sin{\theta}_{1}sin{\alpha}_{1}& cos{\theta}_{1}\\ -sin{\theta}_{2}cos{\alpha}_{2}& sin{\theta}_{2}sin{\alpha}_{2}& cos{\theta}_{2}\\ \vdots & \vdots & \vdots \\ -sin{\theta}_{n}cos{\alpha}_{n}& sin{\theta}_{n}sin{\alpha}_{n}& \mathrm{cos}{\theta}_{n}\end{array}\right]{\mathbf{R}}_{\mathrm{trans}}\left[\begin{array}{c}{d}_{T}\\ {d}_{L}\\ {d}_{N}\end{array}\right]=\mathbf{A}{\mathbf{d}}_{\mathrm{asset}}.$$

#### 2.3.3. Sensitivity

## 3. Results and Discussion

#### 3.1. Data Resources

#### 3.2. Radar Observations along the Railway

#### 3.3. Coordinate Correction and Classification

#### 3.4. Comparison and Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Hanssen, R.F. Radar Interferometry: Data Interpretation and Error Analysis; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2001. [Google Scholar] [CrossRef]
- Ferretti, A.; Prati, C.; Rocca, F. Permanent Scatterers in SAR Interferometry. In Proceedings of the International Geoscience and Remote Sensing Symposium, Hamburg, Germany, 28 June–2 July 1999; pp. 1–3. [Google Scholar]
- Ferretti, A.; Prati, C.; Rocca, F. Permanent Scatterers in SAR Interferometry. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 8–20. [Google Scholar] [CrossRef] - Kampes, B.M.; Hanssen, R.F. Ambiguity Resolution for Permanent Scatterer Interferometry. IEEE Trans. Geosci. Remote Sens.
**2004**, 42, 2446–2453. [Google Scholar] [CrossRef] - Hooper, A.; Zebker, H.; Segall, P.; Kampes, B. A new method for measuring deformation on volcanoes and other non-urban areas using InSAR persistent scatterers. Geophys. Res. Lett.
**2004**, 31, L23611. [Google Scholar] [CrossRef] - Van Leijen, F.J. Persistent Scatterer Interferometry Based on Geodetic Estimation Theory; NCG: Amersfoort, The Netherlands, 2014. [Google Scholar]
- Özer, I.E.; Rikkert, S.J.; van Leijen, F.J.; Jonkman, S.N.; Hanssen, R.F. sub-seasonal Levee Deformation observed Using satellite Radar Interferometry to enhance Flood protection. Sci. Rep.
**2019**, 9, 2646. [Google Scholar] [CrossRef] [PubMed] - Özer, I.E.; van Leijen, F.J.; Jonkman, S.N.; Hanssen, R.F. Applicability of satellite radar imaging to monitor the conditions of levees. J. Flood Risk Manag.
**2018**, 12509, 1–16. [Google Scholar] [CrossRef] - Perissin, D.; Wang, T. Time-series InSAR applications over urban areas in China. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2011**, 4, 92–100. [Google Scholar] [CrossRef] - Costantini, M.; Falco, S.; Malvarosa, F.; Minati, F.; Trillo, F.; Vecchioli, F. Persistent scatterer pair interferometry: Approach and application to COSMO-SkyMed SAR data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2014**, 7, 2869–2879. [Google Scholar] [CrossRef] - Wu, J.; Hu, F. Monitoring ground subsidence along the Shanghai Maglev zone using TerraSAR-X images. IEEE Geosci. Remote Sens. Lett.
**2017**, 14, 117–121. [Google Scholar] [CrossRef] - Chang, L.; Dollevoet, R.P.; Hanssen, R.F. Nationwide railway monitoring using satellite SAR interferometry. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2017**, 10, 596–604. [Google Scholar] [CrossRef] - Wang, H.; Chang, L.; Markine, V. Structural health monitoring of railway transition zones using satellite radar data. Sensors
**2018**, 18, 413. [Google Scholar] [CrossRef] - Ribeiro, D.; Calçada, R.; Ferreira, J.; Martins, T. Non-contact measurement of the dynamic displacement of railway bridges using an advanced video-based system. Eng. Struct.
**2014**, 75, 164–180. [Google Scholar] [CrossRef] - Bowness, D.; Lock, A.; Powrie, W.; Priest, J.; Richards, D. Monitoring the dynamic displacements of railway track. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit
**2007**, 221, 13–22. [Google Scholar] [CrossRef] - Iryani, L.; Setiawan, H.; Dirgantara, T.; Putra, I.S. Development of a railway track displacement monitoring by using digital image correlation technique. Appl. Mech. Mater.
**2014**, 548, 683–687. [Google Scholar] [CrossRef] - Dheenathayalan, P.; Small, D.; Schubert, A.; Hanssen, R.F. High-precision positioning of radar scatterers. J. Geod.
**2016**, 90, 403–422. [Google Scholar] [CrossRef] [Green Version] - Yang, M.; Dheenathayalan, P.; Chang, L.; Wang, J.; Lindenbergh, R.C.; Liao, M.; Hanssen, R.F. High-precision 3D geolocation of persistent scatterers with one single-Epoch GCP and LIDAR DSM data. In Proceedings of the ESA Living Planet Symposium 2016, Prague, Czech Republic, 9–13 May 2016. [Google Scholar]
- Mahapatra, P.; van der Marel, H.; van Leijen, F.; Samiei-Esfahany, S.; Klees, R.; Hanssen, R. InSAR datum connection using GNSS-augmented radar transponders. J. Geod.
**2018**, 92, 21–32. [Google Scholar] [CrossRef] - Van Natijne, A. Locating PS-InSAR Derived Deformation Using LiDAR Point Clouds. Master’s Thesis, Delft University of Technology, Delft, The Netherlands, 2018. [Google Scholar]
- Van Natijne, A.; Lindenbergh, R.C.; Hanssen, R.F. Massive linking of PS-InSAR deformations to a national airborne laser point cloud. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2018**, 42, 2. [Google Scholar] [CrossRef] - Dheenathayalan, P.; Small, D.; Hanssen, R.F. 3-D Positioning and Target Association for Medium-Resolution SAR Sensors. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 6841–6853. [Google Scholar] [CrossRef] - Dheenathayalan, P.; Cuenca, M.C.; Hoogeboom, P.; Hanssen, R.F. Small reflectors for ground motion monitoring with InSAR. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 6703–6712. [Google Scholar] [CrossRef] - Ferretti, A.; Colesanti, C.; Perissin, D.; Prati, C.; Rocca, F. Evaluating the effect of the observation time on the distribution of SAR Permanent Scatterers. In Proceedings of the Third International Workshop on ERS SAR Interferometry, ‘FRINGE03’, Frascati, Italy, 1–5 December 2003; pp. 1–5. [Google Scholar]
- Perissin, D.; Ferretti, A. Urban-Target Recognition by Means of Repeated Spaceborne SAR Images. IEEE Trans. Geosci. Remote Sens.
**2007**, 45, 4043–4058. [Google Scholar] [CrossRef] - Zhang, L. Temporarily Coherent Point SAR Interferometry. Ph.D. Thesis, The Hong Kong Polytechnic University, Hong Kong, China, 2012. [Google Scholar]
- Hu, F.; Wu, J.; Chang, L.; Hanssen, R.F. Incorporating Temporary Coherent Scatterers in Multi-Temporal InSAR Using Adaptive Temporal Subsets. IEEE Trans. Geosc. Remote Sens.
**2019**, 57, 7658–7670. [Google Scholar] [CrossRef] [Green Version] - Crosetto, M.; Monserrat, O.; Cuevas-González, M.; Devanthéry, N.; Luzi, G.; Crippa, B. Measuring thermal expansion using X-band persistent scatterer interferometry. ISPRS J. Photogramm. Remote Sens.
**2015**, 100, 84–91. [Google Scholar] [CrossRef] [Green Version] - Chang, L.; Hanssen, R.F. A probabilistic approach for InSAR time-series postprocessing. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 421–430. [Google Scholar] [CrossRef] - Monserrat, O.; Crosetto, M.; Cuevas, M.; Crippa, B. The thermal expansion component of persistent scatterer interferometry observations. IEEE Geosci. Remote Sens. Lett.
**2011**, 8, 864–868. [Google Scholar] [CrossRef] - Verhagen, S.; Teunissen, P.J. New global navigation satellite system ambiguity resolution method compared to existing approaches. J. Guid. Control Dyn.
**2006**, 29, 981–991. [Google Scholar] [CrossRef] - Ferretti, A.; Prati, C.; Rocca, F. Nonlinear Subsidence Rate Estimation using Permanent Scatterers in Differential SAR Interferometry. IEEE Trans. Geosci. Remote Sens.
**2000**, 38, 2202–2212. [Google Scholar] [CrossRef] - Baarda, W. S-Transformations and Criterion Matrices, 2nd ed.; Publications on Geodesy, New Series; Netherlands Geodetic Commission: Delft, The Netherlands, 1981; Volume 5, p. 168. [Google Scholar]
- Kampes, B.M. Radar Interferometry; Springer: Houten, The Netherlands, 2006. [Google Scholar]
- Ataei, A. Improved Qrginv algorithm for computing Moore-Penrose inverse matrices. ISRN Appl. Math.
**2014**, 2014, 1–5. [Google Scholar] [CrossRef] - Johnson, R.A.; Wichern, D.W. Applied Multivariate Statistical Analysis; Prentice Hall: Upper Saddle River, NJ, USA, 2002; Volume 5. [Google Scholar]
- Montazeri, S.; Rodríguez González, F.; Zhu, X. Geocoding Error Correction for InSAR Point Clouds. Remote Sens.
**2018**, 10, 1523. [Google Scholar] [CrossRef] - Schreier, G. SAR Geocoding: Data and Systems; Wichmann Verlag: Karlsruhe, Germany, 1993. [Google Scholar]
- Ahlgren, P.; Jarneving, B.; Rousseau, R. Requirements for a cocitation similarity measure, with special reference to Pearson’s correlation coefficient. J. Am. Soc. Inf. Sci. Technol.
**2003**, 54, 550–560. [Google Scholar] [CrossRef] - Adam, N.; Kampes, B.M.; Eineder, M. Development of a scientific Persistent Scatterer System: Modifications for mixed ERS/ENVISAT time series. In Proceedings of the ENVISAT & ERS Symposium, Salzburg, Austria, 6–10 September 2004; p. 9. [Google Scholar]
- Stansbury, D. The Statistical Whitening Transform. Available online: https://theclevermachine.wordpress.com/tag/eigenvalue decomposition (accessed on 30 March 2019).
- Finkel, R.; Friedman, J.; Bentley, J. An algorithm for finding best matches in logarithmic expected time. ACM Trans. Math. Softw.
**1977**, 3, 209–226. [Google Scholar] - Chang, L.; Dollevoet, R.P.; Hanssen, R.F. Monitoring line-infrastructure with multisensor SAR interferometry: Products and performance assessment metrics. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2018**, 11, 1593–1605. [Google Scholar] [CrossRef] - KNMI. Available online: http://projects.knmi.nl/klimatologie/uurgegevens (accessed on 30 October 2018).
- Kadaster; Geonovum. Publieke Dienstverlening Op de Kaart (PDOK). Available online: https://www.pdok.nl/ (accessed on 30 November 2018).
- De Bruijne, A.; van Buren, J.; Kösters, A.; van der Marel, H. Geodetic Reference Frames in The Netherlands. Definition and Specification of ETRS89, RD and NAP, and Their Mutual Relationships; Netherlands Geodetic Commission: Delft, The Netherlands, 2005. [Google Scholar]

**Figure 1.**Flowchart of the attribution of the InSAR observations using LiDAR data. There are three main steps: (1) absolute height correction; (2) error ellipsoid estimation; and (3) snapping to the LiDAR point cloud.

**Figure 2.**(

**a**) AHN3 point cloud along the railway and its buffer zone with classifications. Estimated parameters on both CCS and TCS: (

**b**) velocity map; (

**c**) height map; (

**d**) thermal dilation; and map. (

**e**) Location of the railway (green line).

**Figure 4.**Displacement time series of two selected scatterers with strong thermal dilation: (

**a**) the RMS of the displacement drops from 4.2 to 1.0 mm; and (

**b**) the RMS of the displacement drops from 5.2 to 2.3 mm. Green dot line, temperature per acquisition; red line, linear deformation time series; blue line, deformation time series without temperature correction including linear deformation, nonlinear deformation, temperature motion and noise; black line, temperature-corrected deformation time series including linear deformation, nonlinear deformation and noise.

**Figure 5.**Distribution of the radar scatterers (red dots) relative to the LiDAR data (height-colored dots): (

**a**) coordinates of radar scatterers before height offset correction; and (

**b**) coordinates of radar scatterers after height offset correction.

**Figure 6.**3D map of radar scatterers (

**a**) without and (

**b**) with coordinate correction by LiDAR, showing a better separability of high and low objects.

**Figure 7.**Classification of the radar scatterers with corrected coordinates based on their attribute to the LiDAR points, which are already classified.

**Figure 8.**Parameters of the scatterers with corrected coordinates: (

**a**) deformation velocity, demonstrating the instability of the north area; and (

**b**) thermal dilation, showing the strong thermal dilation of the bridge structure.

**Figure 9.**DoP values of radar scatterers with correct coordinates, showing the qualities of different scatterers.

**Figure 10.**Deformation velocity of the scatterers with selected classifications (bridge and ground), indicating the deformation related to the railway.

**Figure 11.**Histograms of the deformation velocity within different classes, showing a better interpretation of deformation signals with classified scatterers.

**Figure 12.**(

**a**–

**f**) Comparison of the height model between LiDAR data and radar scatterers. The first column corresponds to the LiDAR data and the second column corresponds to the radar scatterers. Each row corresponds to a selected segment of the railway.

**Figure 13.**Parameters of the selected bridge: (

**a**) velocity map, showing the transitions of velocity between bridge and ground; and (

**b**) thermal dilation map, showing the strong thermal dilation on the bridge structure.

**Figure 14.**Comparison of classification map: (

**a**,

**c**) classification maps of LiDAR; (

**b**,

**d**) classification maps of radar scatterers; (

**a**,

**b**) classification maps without unclassified one; and (

**c**,

**d**) classification maps with unclassified one.

**Figure 15.**Classification maps of two selected areas: (

**a**,

**c**) classification maps of LiDAR; and (

**b**,

**d**) classification maps of radar scatterers, showing the importance of including the unclassified group.

© 2019 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**

Hu, F.; Leijen, F.J.v.; Chang, L.; Wu, J.; Hanssen, R.F.
Monitoring Deformation along Railway Systems Combining Multi-Temporal InSAR and LiDAR Data. *Remote Sens.* **2019**, *11*, 2298.
https://doi.org/10.3390/rs11192298

**AMA Style**

Hu F, Leijen FJv, Chang L, Wu J, Hanssen RF.
Monitoring Deformation along Railway Systems Combining Multi-Temporal InSAR and LiDAR Data. *Remote Sensing*. 2019; 11(19):2298.
https://doi.org/10.3390/rs11192298

**Chicago/Turabian Style**

Hu, Fengming, Freek J. van Leijen, Ling Chang, Jicang Wu, and Ramon F. Hanssen.
2019. "Monitoring Deformation along Railway Systems Combining Multi-Temporal InSAR and LiDAR Data" *Remote Sensing* 11, no. 19: 2298.
https://doi.org/10.3390/rs11192298