Document Type : Original Research Paper
Authors
School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran ,Iran
Abstract
Background and Objectives: Monitoring the displacement of the ground surface and structures is an important topic in deformation studies. Ground-Based Synthetic Aperture Radar (GBSAR) offers considerable potential for deformation monitoring due to its ability to acquire images independently of lighting conditions and measure submillimeter displacements along the line of sight (LOS). One of the essential steps in extracting displacement information from radar data is phase unwrapping, because the restriction of the measured phase to a specific interval introduces ambiguity in determining the number of complete phase cycles. On the other hand, the performance of conventional phase unwrapping methods may be associated with reduced accuracy in the presence of significant displacements, abrupt changes, and measurement errors. Therefore, the aim of the present study is to investigate the performance of a combined approach based on temporal and spatial information to improve phase unwrapping and increase displacement estimation accuracy. For this purpose, two displacement models, linear and step-like, were investigated.
Methods: In this study, time-series data corresponding to two displacement models, linear and step-like, were acquired using a GBSAR sensor, and the radar images were processed to extract amplitude and phase information. Permanent scatterers (PSs) were then selected based on their amplitude behavior throughout the time series, with 42 points selected for the linear model and 18 points for the step-like model. Following the selection of the points, the phase of each point was extracted over time, and temporal phase unwrapping was performed using Itoh's algorithm. In the next step, the selected points were connected using a Delaunay triangulation network, and a system of equations was established based on spatial relationships by calculating the phase differences between neighboring points. Subsequently, the unwrapped phase values at the points were estimated using the least-squares method and converted into displacements along the line of sight (LOS). Finally, to evaluate the performance of the two methods, the estimated displacements were compared with the reference values, and the root mean square error (RMSE) was calculated. The processing times of the temporal and combined temporal–spatial methods were also measured.
Findings: The results showed that the combined temporal–spatial method improved displacement estimation accuracy compared with temporal phase unwrapping alone. In the linear model, the final displacement estimated by the combined method was 31.563 mm, and the RMSE decreased from 0.3317 to 0.0406 mm, representing an improvement of 87.8%. In the step-like model, the final displacement was 3.748 mm, and the RMSE decreased from 0.1432 to 0.1203 mm. Analysis of the displacement time series also showed that the combined method was able to reconstruct the overall displacement trend and its abrupt changes with good agreement with the reference values. Furthermore, the processing times of the temporal and combined temporal–spatial methods were 0.0005 and 0.0132 s, respectively, for the linear model, and 0.0004 and 0.0051 s, respectively, for the step-like model.
Conclusion: The findings of this study showed that combining temporal and spatial phase unwrapping using permanent scatterers (PSs) improves displacement estimation accuracy and reduces residual errors remaining after temporal phase unwrapping. This improvement was observed in both displacement models, with the greatest error reduction occurring in the linear model. In the step-like model, the combined method also demonstrated more accurate performance than the temporal method despite abrupt displacement changes. It is recommended that future studies investigate the performance of the method under more complex displacement models and examine the effects of the number and distribution of permanent scatterers on displacement estimation accuracy.
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