# Joint SAR Image Time Series and PSInSAR Data Analytics: An LDA Based Approach
## 4 Experimental Setup
### Comparative Analysis of Parameter's Influence  
Characteristic parameters of both datasets are synthesized in Table 3.  
Sentinel-1 dataset's acquisition timespan is less than half that of ERS dataset's timespan. Considering the launch date of the former mission, April 2014, is not possible yet to create a Sentinel-1 dataset which has a timespan equal to one of the ERS images. Therefore, the temporal signature of the pixels is analyzed in a larger time interval in case of ERS dataset, which should lead to more accurate results in this case. Also, both amplitude and spectral characteristics of the targets, studied for PS identification, are analyzed, in case of the two datasets, in temporal intervals with different lengths. This should not affect the PS detection process, since the stability characteristics of the persistent scatterers should be identifiable independently of the acquisition timespan of the analyzed multitemporal dataset; representing the idea behind PS-InSAR development. The spatial dimensions of a resolution cell are lower in the case of the ERS dataset--53.46 m compared to 70.37 m for Sentinel-1 images. This decreases the probability of occurrence of the speckle phenomenon--interference between response of targets present within the same resolution cell, therefore, from this point of view, the PS detection process is slightly aided in the case of the ERS images. The radar frequency of the two SAR datasets is similar; both sensors operated in the C band. Therefore, the additive noise has a similar influence on both datasets [25]. Furthermore, the vegetation penetrating capabilities of both sensors are identical, so the corresponding areas should present similar behavior in case of both ERS and Sentinel-1 images. Due to the different incidence angles of the sensors, the gap between the ground range resolutions of the two dataset's images increases, being equal to 25.38 m for ERS and 4.92 m for Sentinel-1 set. Therefore, Sentinel-1 has a much lower value of resolution in the ground range direction, but this feature is partially annulled by its higher the azimuth resolution value. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **ERS Dataset** & **Sentinel-1 Dataset** \\ \hline acquisition timespan & 5 years 1 month & 2 years 3 months \\ range resolution & 9.9 m & 3.1 m \\ azimuth resolution & 5.4 m & 22.7 m \\ radar frequency & 5.3 GHz & 5.4 GHz \\ chirp bandwidth & 15.5 MHz & 48.3 MHz \\ incidence angle & 23.2\({}^{\circ}\) & 39.1\({}^{\circ}\) \\ critical baseline & 1041 m & 6350 m \\ baselines standard dev & 553.44 m & 53.39 m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative synthetization of the dataset’s acquisition parameters. Figure 6: Flattened interferometric phase corresponding to the Constanta test region, interferometric pair: 20 December 2015–28 August 2015. The difference between satellite positions during image acquisition induces a shift between target spectral responses. This shift is proportional with the perpendicular baseline value. In order to be able to extract common information from a target's response along the dataset's multiple acquisitions, the spectrum supports of target responses across the dataset's images must overlap, therefore the induced shift must be below a certain value. The maximum perpendicular baseline which allows common information extraction is called the critical baseline \(B_{cr}\), and is dependent on sensor to scene distance \(R\), radar frequency \(f_{0}\) chirp bandwidth \(BW\), and incidence angle \(\theta\):  
\[B_{cr}=\frac{R\cdot BW\cdot\tan\theta}{f_{0}} \tag{9}\]  
The ERS dataset presents a much higher critical baseline, equal to 1041 m, compared to the Senintel-1 set, equal to 635 m. In both sets, the perpendicular baseline values are situated below the critical one, with a maximum absolute value equal to 985.2 m in case of ERS and 125 m for the Sentinel-1 set. This aspect is mostly important for LDA classification.