5.3.4. The Influence of The Time Window Size *w*

The size of time window directly affects whether all moving objects can be found in each window. In the experiment, we set *ρ* = 0.1, *ξ* = 2, *ϕ* = 90◦ , *N* = 200, and the experimental results under different *w* sizes are compared in Table 6.


**Table 6.** The influence of the time window size *w* on the experimental results.

It can be seen from Table 6 that, as compared with the other two methods (BC and PF + BC), our proposed method (PCC + PF + BC) integrates Pearson correlation coefficient into the update stage of particle filter, and matches the laser cluster-based radial velocity and the phase-based radial velocity in each window has the least localization error and the highest matching rate. In addition, if the window is too small (e.g., *w* = 5), when the object is occluded during the experiment, the algorithm cannot find all objects in a period time, which will cause the failure of radial velocity matching. Consequently, we obtain the error up to 0.71 m, and the matching rate reduces to 81.8%. A suitable window size (e.g., *w* = 25) can ensure that all moving objects can be found in each time window, the matching rate can be 90.2%, and the localization error is only 0.33 m. If the window is too large (e.g., *w* = 50), the algorithm can always filter out the appropriate cluster to match with RFID tag in each window, which has little impact on the experimental results, but redundant information may occupy the computing resources of the system, and affect the real-time performance of localization and identification. Besides, as compared with *w* = 25, the average time-consuming is increased to 62.24 ms. Therefore, it is very important to choose an appropriate window size. This paper uses the window size *w* = 25 in order to ensure that the experiment has small positioning error and high matching rate. Figure 5a–c shows the localization error at different locations with *w* = 25.

**Figure 5.** The positioning error at different locations with *w*=25. (**a**) The first object; (**b**) The second object; (**c**) The third object.

#### *5.4. Evaluation of the Approach with a Complex Path and a Different Environment*

We expand the original experimental scene to an area of 8 m × 4 m and move it to the area closer to the wall in order to verify the robustness of the whole system. The specific experimental scenario is shown in Figure 6. The experimental parameters are set to be the same as the original experimental parameters, and the result is shown in Figure 7. As can be seen from Figure 7c, as compared with Figure 7a,b, the object's estimated paths are basically consistent to the ground truth, and the average localization error of all humans is 0.52 m, which is only 0.19 m worse than the original experiment. The BC-based approach (BC) cannot locate the moving objects very well, the localization error is 0.90 m. Although the particle filter-based approach (PF + BC) improves the accuracy when compared to the BC-based approach, the result is still not good enough: the localization error is 0.76 m. The experimental results show that our approach is able to achieve identification and localization of multiple objects with good positioning accuracy.

**Figure 6.** Complex paths experimental setup.

We conducted experiments in the lobby of our campus building in order to verify the actual use of our system in an indoor environment. In this experiment scene, the ceiling is about 2.3 m above the ground, and there are several walls in the environment. The experimental scenario is shown in Figure 8, the results are shown in Figure 9 and Table 7. As can be seen from Figure 9, the object's paths estimated by our method (PCC + PF + BC) are basically consistent to the ground truth, and the average localization error is 0.44 m, which is similar to our previous experiments. Similarly, we also compare the localization error of the other two methods (the BC-based approach (BC), and the particle filter-based approach (PF + BC)), as shown in Table 7.

The experimental results show that our approach is able to achieve identification and localization of multiple objects with a similar localization accuracy when compared to our previous experiments. In practical applications, we can deploy this system in such an environment to identify and locate the passing pedestrians.

**Figure 7.** Complex paths results. (**a**) BC; (**b**) PF + BC; (**c**) PCC + PF + BC; (**d**) CDFs.

**Figure 8.** Experimental setup of complex path in indoor environment.

**Figure 9.** Experimental results of complex path in indoor environment.

**Table 7.** Comparison of experimental results of complex path in indoor environment based on different methods.


#### **6. Conclusions**

This paper proposed an approach for fusing the RFID and laser data in order to achieve dynamic multi-objects identification and localization by combining Pearson correlation coefficients and particle filter. The Pearson correlation coefficient and particle filter are combined to find out the historical path of each cluster, and then the radial velocity is estimated based on the cluster's position at adjacent times. At the same time, the radial velocity of the moving object is estimated using the phase difference between the adjacent moments of RFID, and those two are matched by the similarity algorithm based on the sliding time window to realize the identification and localization of multiple dynamic objects. The experiments show that the method that is proposed in this paper can achieve a matching rate of 90.2% in an environment with obstacles and a localization error of 0.33 m. In the future, we will overcome the problem of phase ambiguity, and further improve the matching rate and localization accuracy. Another research direction is visual sensors to overcome the problem of positioning failure of moving objects after long-term occlusion.

**Author Contributions:** W.F. analyzed the data and wrote the paper; R.L. proposed the idea and designed the experiments; R.A. revised the paper; Y.H. and Z.Q. conducted the experiments; H.W. and Z.C. reviewed the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This work is supported by Sichuan Science and Technology Program 2019YFH0161, 2019JDTD0019, National Natural Science Foundation 61601381, 61701421 and 61471306, and partially by China's 13th Five-Year Plan in the Development of Nuclear Energy under the grant number of 2016[1295].

**Conflicts of Interest:** The author declare no conflict of interest.
