## 2 Related Method and Work
### Decision Tree  
In the key identification part of the indoor sensor system, the DT model is relatively intuitive, easy to transplant, and a widely used graphical method with a probability analysis process. In the real-world situation, its core process is to analyze the relationship between each attribute and its value according to the concept of entropy theory. In its graph structure, the analysis process is often implemented as a \"tree\" structure by researchers, hence the name is obtained. At the same time, it is also a supervised learning method and suitable for our research situations. To make the indoor localization system complete the NLOS identification better, the classifier in the system is supposed to be absorbed into the difference between LOS and NLOS acoustic signals. Based on the conditions and experimental results in [11,20,21,31,32,33, 20], it can be inferred that the LOS acoustic signal in the system will be more easily affected by the position of the acoustic anchors according to their eigenvalues. Furthermore, LOS acoustic signals will appear more frequently in the transmission path. However, due to the exceptional nature of the binary and non-linear classifier's shortcomings, the solutions to the identification ability of NLOS signals will also bring more positive effects to the system. In this paper, the algorithm in [20] is used to complete the feature extraction process. It is clear to find out that when not normalized, the eigenvalues of each dimension between the features of the acoustic signals are greatly different. The overall dimensions of the acoustic  
Figure 3: Different kinds of acoustic anchors. (**a**) Single receiving acoustic anchor; (**b**) Dual-receiving acoustic anchor. signal feature set are not too high, and the correlation between the features is strong enough. Combining multiple factors and situations, the fitness function can be constructed based on the maximum entropy principle and the DT model. For the entropy-increasing and independent process in this system, the fitness function value can be regarded as the numerical reference for feature set recombination, adaptive optimization, re-adjustment process, and the basis for the DT model. In our system, information entropy can be used to express the chaos degree, that is, the uncertainty of the system itself caused by the acoustic signal communication process or the cognitive IoT networks. The weighted calculation set can be considered as the mathematical expectation calculation of it. This paper combines the maximum entropy principle with the DT model to build the fitness function. For an indoor localization system, if the probability of the NLOS acoustic signal in the sample set \(D\) is \(p_{k}\) and there are \(N\) samples in total, the information entropy can be written as follows:  
\[\text{Ent}\big{(}\text{NLOS Signals}\big{)}=-\sum_{k=1}^{N}p_{k}\log_{2}p_{k} \tag{1}\]  
Meanwhile, according to the LOS signal set and (1), we can obtain:  
\[\text{Ent}\big{(}\text{LOS Signals}\big{)}=-\sum_{k=1}^{N}\big{(}1-p_{k}\big{)} \log_{2}(1-p_{k}) \tag{2}\]  
\(M\) conditions should be considered. We can also obtain the conditional entropy of the NLOS acoustic signal, which can be written as:  
\[\text{Con}(\text{NLOS Signals})=-\sum_{i=1}^{M}\frac{|D_{i}|}{|D|}\sum_{k=1}^{ N}\left|\frac{|D_{i,k}|}{|D_{i}|}\cdot\log(\frac{|D_{i,k}|}{|D_{i}|})\right| \tag{3}\]  
Then, the information gain can be obtained. The system should finish the classification tasks with assignable differences on information gain. It can be written as:  
\[\text{Gain}(\text{D})=\text{Ent}(\text{D})-\text{Con}(\text{D}) \tag{4}\]  
The DT model constructed based on the principle of information gain rules is chosen, which can guarantee that the model is not too complex, and is also conducive to using the CTGSA method proposed in this paper to optimize the system.