## 3 Experimental Results  
The experiments of this work were conducted in indoor conditions, in a building's pavilion of approximate size 8 m \(\times\) 10 m. The two radars were set up on a table of 1 m high, 2.5 m distant from each other and connected with a computer that was running the program. Numerous experiments were run with different scenarios, namely with 1, 2, 3 and 5 persons, to prove the consistent efficiency of the proposed method. In all these scenarios, the targets were moving with an average velocity of 10 m/12 s.  
While running the experiment with online processing, the raw signal frames were saved in order to be able to process the same scenario later with other methods for a better comparison. Figure 7 shows the results of the respective clutter rejection methods.  
As discussed in the sections above, the raw frames recorded by each radar are processed separately for the background removal. The first and second rows of Figure 7 present the clutter-free signals of the two radar modules using different clutter removal algorithms. It is clear that the reflected waves from farther targets are very weak, henceforth the need of path loss compensation.  
The estimated clutter-free signals of both radar modules are submitted to the target-detection algorithm and the results of both datasets are plotted in the third line of Figure 7. At this stage, the results are already elaborated for comparison. If we compare these methods, we can see the weaknesses of PCA and Exponential Averaging in separating the two subspaces, which results in many false alarms in the detection step. The detection results from the two radars will then be used for the target-localization task, and the results are shown in the last row of Figure 7.  
Figure 6: Overlapping windows method flowchart.  
The results in Figure 7 present the outcome of the target detection and localization steps based on the clutter removal results of every method. We can clearly see the good performance of the first two methods, RPCA in both live and batched data processing, and this can also be proved by the numeric results presented in Table 1. For a better comparison, we use the following metrics to explain the differences in performance of these methods:  
* RMSE (Root Mean Square Error): the commonly used metric to measure the differences between two data sets, one predicted by a model or an estimator and the actually observed one. In here, it is the average of the individual RMSEs between each radar's estimated clutter and the true clutter. The true clutter is approximated by recording a relatively large number of frames in a target-free space, and these frames are averaged to minimize the effect of the noise. \[RMSE=\frac{1}{M}\sum_{i=1}^{M}\left(\sqrt{\frac{1}{N}\sum_{J=1}^{N}\left(\rm A _{(i,j)}-\hat{A}_{(i,j)}\right)^{2}}\right)\,,\] (12) where A is the estimated clutter and A is the true clutter.
* Localization error: the average distance-error (the Euclidean distances) between the estimated target position and the approximated the true path of the target. We assume the target was moving following straight lines.  
Figure 7: Clutter-free signals of the 2 radars, their respective detection results and the resulting 2D positioning given by different clutter removal techniques: Column (**a**) O-W processing RPCA; Column (**b**) Batch Processing RPCA; Column (**c**) EAM; Column (**d**) PCA.  
Other experiments, of which the results are shown in Figure 8, were run with 2, 3 and 5 moving targets, and the processing procedure took the same flow as in a one-person scenario. The presented results show the detection results from one radar's data, and are numerically compared based only on RMSE as it is presented in Table 2.