## 5 Detection in UWB Positioning Algorithms
### MI-Algorithms for UWB IPS  
As mentioned, various types of ML algorithms have been proposed and used in a large range of applications for improving the IPS, especially for NLoS detection and error correction. Among the existing successive development of ML algorithms mentioned above, SVM, DT, NB, and NN have gradually improved the positioning accuracy and significant usefulness of IPSs. These algorithms are discussed in detail in this section. * **k-Nearest Neighbors (k-NN):** k-NN is a type of the non-parametric-based supervised learning classifier that can be applied to both regression and classification. It typically uses the assumption of the data feature similarity that the data points can be found near one to another. The new data can be assigned a value based on how similarly the data match the points trained in the training set [91; 92]. The advantages of k-NN algorithm can be summarized: Firstly, it is easy to implement and achieve high-accuracy results. Secondly, it is suitable for multi-label classification cation issues. In contrast, the disadvantage is that the algorithm requires large calculations, which can increase the memory overhead. Moreover, it provides relatively low-accuracy results when the sample is imbalanced [93; 94; 95]. * **Support Vector Machine (SVM):** SVM is a typical classic supervised ML algorithm that adopts the structural risk minimization principle to solve both classification and regression problems under high-dimensional space substitution [96]. It provides robust and superior performance without tuning several parameters due to it being based on the framework of statistical learning theory compared with other ML algorithms [97]. The main principle of the algorithm consists in estimating a hyperplane that can maximize the distance between the values of interest in each class. As shown in Figure 14, for a linearly separable dataset, there is only one separating hyper-plane with the largest geometric interval. Let us consider that a training dataset contains n points of the form \(T=(x_{1},y_{1}),...,(x_{n},y_{n})\), where the \(y_{i}\) is labeled as 1 or \(-1\). \(x_{i}\) is the p-dimensional real feature vector and \(x_{i}\in\mathbb{R}^{n}\). The hyper-plane is the maximum margin determined to divide the group of points \(x_{i}\) into group \(y_{i}=1\) and group \(y_{i}=-1\). The hyper-plane can be described by the following linear equation: \[w^{T}x+b=0\] (14) The advantages of SVM are as follows: firstly, strict mathematical theory support and strong interpretability due to the algorithm not requiring typical statistical methods, thus simplifying the usual classification and regression problems; secondly, it is easy to find key samples (i.e., support vectors) that are critical to the algorithm which can handle nonlinear classification and regression tasks; and thirdly, the calculation complexity of the algorithm depends on the number of support vectors instead of the dimensionality of the sample space, which can simplify the calculation process. In contrast, the disadvantage is that the training time is long due to the prediction running time being proportional to the number of support vectors. * **Decision Tree (DT):** The DT algorithm is very suitable for large datasets with complex different features due to its ability to mimic human-like thinking for interpreting the data [98; 99]. The advantage of DT is that it can break down the dataset into smaller subsets to operate the classification, which can minimize the classification error. In addition, DT can decide which attribute is the best at each tree node to ensure the high accuracy of the classification. The main advantage of decision tree learning is that it can minimize the error at the tree root due to it creating a single outcome by creating the tree at every leaf. Meanwhile, each tree root will also take a longer running time, which is the main disadvantage; therefore, it is not suitable for the application, which requires a fast response.