# Robust and Accurate Wi-Fi Fingerprint Location Recognition Method Based on Deep Neural Network
## 4 Experience and Analysis
### Experiments of China University of Mining and Technology
#### 4.2.2 Analysis of Dynamic Positioning Results  
Currently, KNN (RADAR) [16], weighted KNN (WKNN) [18] and Clustering-WKNN (CWKNN) (Horus) [17] are the gold standards of Wi-Fi positioning methods. Our evaluation of the DNN performance in dynamic Wi-Fi positioning can be seen in Figure 10, which illustrates the average error of the DNN as well as that of classic methods in dynamic motion. Further, the figure also shows the changes in the positioning accuracy of different methods two months after the establishment of the fingerprint database. Without the influence of device heterogeneity, the difference between the positioning results based on the DNN and traditional methods becomes smaller, but DNN still offers better performance. Compared with KNN, WKNN and CWKNN, the average errors of DNN are reduced as follows: 20.49%, 15.68% and 13.62%, respectively. As time goes by, the positioning errors of these methods increase to varying degrees, but the DNN still has the best positioning accuracy, with an error of 2.25 m. Figure 11 shows the average time consumption of these methods for each positioning. The DNN-based Wi-Fi positioning method has the least time consumption since there is no need to cluster and calculate the Euclidean distance of signal strength between unknown and all fingerprint points. Accordingly, experiments demonstrate that the DNN can not only offer better  
Figure 9: Layout of the experimental site. positioning accuracy and better real-time performance than the traditional methods, but also have a good time robustness. In order to test the effectiveness of constrained KF in dynamic positioning results, the following calculation schemes were conducted:  
* Scheme 1: No use of Kalman filter. * Scheme 2: Use of constrained Kalman filter. * Scheme 3: Use of adaptive constrained Kalman filter. Figure 12 shows the dynamic positioning results of the three schemes. It can be seen from the details of location trajectories that Scheme 1 without constraint inevitably suffers from typical overlapping and jumping due to the influence of multipath interference and \(RSS\) fluctuation. In Schemes 2 and 3, the accuracy of the positioning trajectory improved significantly with constrained KF. Further, Scheme 3 further adjusted the measurement noise adaptively to make trajectory smoother and reduce the occurrence of overlapping and jumping, so it estimated the location of the user very well. The trajectories show that the proposed adaptive constrained KF enhances the robustness of the localization results when gross errors of Wi-Fi appear. Figure 10: Positioning errors with different Wi-Fi positioning methods. Figure 11: Average time consumption with different methods. Figure 12: Positioning results of dynamic Wi-Fi positioning with different schemes: (**a**) Scheme 1; (**b**) Scheme 2; (**c**) Scheme 3. Figures 13 and 14 show in detail the positioning errors and corresponding cumulative distribution functions (CDFs). The positioning result of Scheme 1 is not stable, and there is a large error. Schemes 2 and 3 can effectively suppress the error after using the constrained KF, and the maximum error is obviously decreased. Compared with Scheme 2, the main contribution of Scheme 3 is that the adaptive mechanism can recognize the gross error when it appears and reduce its influence on the positioning results by adjusting measurement noise. The probabilities of positioning errors of less than 3.5 m for the three schemes are 80.25%, 83.95% and 90.12% respectively. Table 4 shows the average error, RMSE, circular-error-probability (CEP) and maximum error of the three schemes. Constrained KF improves the accuracy of dynamic positioning. Scheme 3, which uses the adaptive mechanism, offers the best performance. Compared with Schemes 1 and 2, Scheme 3 shows reduced errors as follows: (a) 19.25% and 7.03% for average error; (b) 29.47% and 8.97% for RMSE; (c) 39.07% and 5.86%for CEP; (d) 50.28% and 14.33%for maximum error. The positioning errors of Scheme 3 using adaptive constraint KF greatly reduce.