# Utilizing Ensemble Learning to Improve the Distance Information for UWB Positioning
## 4 Experimental Results  
Here, we detail our experiments, and all relevant settings are listed as follows:  
* In the experiments, three scenarios were considered, i.e., classroom, parking garage, and parking lot (shown in Figure 5);
* Four anchors were set at fixed positions (red points);
* Twenty-seven points were utilized to collect the data: training data (blue points) and testing data (green points);
* For every point, 100 continuing distance values were collected;
* The complete location information is shown in Figure 6;
* The UWB transceiver device utilized in the experiments was DWM1000 [16]. * The DWM1000 integrated the antenna, the Radio Frequency (RF), clock circuitries, and the power management module. It used the Time Difference of Arrival (TDOA) method to obtain the raw distance data between each pair of UWB devices [17]. * Google Colab [18] allowed us to write and execute Python 3 in the browser with the power of a Graphics Processing Unit (GPU). * The tools, scikit-learn [19] and Keras [20], were used to realize all the machine learning algorithms in this paper. Figure 4: Our second refinement for UWB positioning. Figure 5: Three scenarios are considered in this paper: (**a**) classroom, (**b**) parking garage, and (**c**) parking lot. Figure 3: Our first refinement for UWB positioning. Next, different prefilters and machine learning models were applied in our experiment accordingly:  
* MaxAve: We removed the largest 10% and smallest 10% and then only considered the average of the cluster with the most elements for \(k\)-means clustering (\(k=3\)) as the training data;
* MaxCen: We removed the largest 10% and smallest 10% and then only considered the median of the cluster with the most elements for \(k\)-means clustering (\(k=3\)) as the training data;
* CenAve: We removed the largest 10% and smallest 10% and then only considered the average of the central cluster for \(k\)-means clustering (\(k=3\)) as the training data;
* CenCen: We removed the largest 10% and smallest 10% and then only considered the median of the central cluster for \(k\)-means clustering (\(k=3\)) as the training data;
* 10%: We removed the largest 10% and smallest 10% and then only considered the average of the residual part as the training data;
* Machine learning approaches:
* LR: Linear Regression;
* Third order PR: Third order Polynomial Regression;
* Fifth order PR: Fifth order Polynomial Regression;
* Tenth order PR: Tenth order Polynomial Regression;
* Model: sequential model;
* Activation function: rectified linear unit;
* Optimizer: adam;
* Loss function: mean absolute error;
* The architecture is shown in Figure 7.  
Next, the experimental results are shown in the following tables. First, the higher order polynomial regression, i.e., the tenth order polynomial regression, caused overfitting for all the experiments, which was consistent with that in [5]. Hence, we will not discuss this in this paper. Figure 6: The complete location information. According to Tables 1 and 2, we considered our methods with these new prefilters to work well. More specifically, we observed that if the experimental space had a higher density of obstacles (classroom), using the ANN refinement with the MaxCen prefilter was better for accuracy (error) and stability (standard deviation). Then, for the space with a lower density of obstacles (parking lot), using the ANN refinement was also better. Note that since all standard deviation values were lower in the parking lot, we merely considered the viewpoint of error. These results met all three declarations in the beginning of this paper. Namely, in [5], all training data were refined first by sorting the data from large to small and then removing the largest and smallest 10% of data; the authors claimed that this filtering method helped them to remove some extreme unreasoned data and worked well. However, they were not the best threshold values.