# Fingerprinting Indoor Positioning Based on Improved Sequential Deep Learning
## 4 Experimental Results and Discussion
### Results Based on Experimental Data  
We first apply a sequential classification algorithm to identify the building and floor of a test point. Based on the estimated location (building and floor number), the training data are filtered and normalized. The filtered data are then used to train the proposed DNN model. If the DNN model achieves accuracy above the required threshold, the corresponding weight vector for the test point is output. Otherwise, the proposed WKNN algorithm is employed to generate the weight vector, which is subsequently used to estimate the specific coordinates of the test point. Several DNN models were trained using data collected from different regions, with the loss function values reported in Table 3. The loss function threshold was set to 0.15. For any test point where the DNN model's loss function for the estimated region exceeds this threshold, the proposed WKNN algorithm was applied instead. However, as illustrated in Figure 4, the DNN model demonstrated suboptimal performance on floors 0 and 1 of Building 1, as well as on floor 4 of Building 2. This performance deficiency can be attributed to the uneven distribution of training data across these floors and the scarcity of data in certain areas. For example, the lack of training data on the lower right part of floor 4 in Building 2 negatively impacted the positioning accuracy. To assess the practicality of our algorithm in real-time localization applications, we analyzed the time required to obtain the first position estimation from the moment a test data point is input. After all networks were trained, our results indicated that the time-to-first estimation is approximately 0.23 s when using MATLAB 2024a for simulation on hardware with the following specifications: an Intel Core i7-13700 KF CPU and an NVIDIA GeForce RTX 4060 Ti GPU. This processing time satisfies real-time positioning requirements, demonstrating the feasibility of our algorithm for real-time indoor localization scenarios. Therefore, our method can be effectively utilized in settings where timely location information is critical. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Distinct buildings & 3 \\ Distinct floors & 13 \\ Traing samples & 19,937 \\ Traing points & 933 \\ Traing device & 16 \\ Test samples & 1111 \\ Test device & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of information about the experimental tested. Figure 5 provides a visual comparison between the actual positions of the validation dataset and the predicted positions generated by our method. To accurately assess the prediction error, discrepancies in building and floor estimates were also considered with a uniform floor height of 4 m assumed during the evaluation. Figure 6 displays the positioning errors for test points across different floors, while Table 4 summarizes the mean positioning error for each floor across different buildings. From these results, we observed that the proposed method consistently performed well in Building 0 which is attributed to the reasonable and balanced distribution of the training points collected in this region. Notably, the test set was collected three months after the training set, during which environmental changes--such as the movement of large furniture and the presence of moving people--might have occurred. Despite these potential changes, our method demonstrated robust localization performance in the test, indicating a degree of resilience to typical environmental dynamics within indoor settings. However, we acknowledge that significant layout modifications involving extensive changes, such as major furniture rearrangements or structural alterations, may lead to outdated fingerprint data and ultimately degrade positioning accuracy. This limitation could also explain the lower positioning performance observed on certain floors in our simulations.