## 3 Analysis of Data Features
### Analysis of Feature Discriminability  
In rescue operations within confined or obstructed spaces, personnel engage in various activities such as crawling, crouch-walking, jumping, and running. The inertial data collected from different body parts during these movements exhibit significant variations in feature discriminability and extraction difficulty, directly impacting the accuracy of motion mode and step length recognition. To quantitatively analyze the feature discriminability across different motion states, multi-source data were collected, and a feature discriminability evaluation model was developed to assess the significance of key features under each motion state.  
To achieve this goal, multi-source sensors are installed on key body parts, including the chest, the outer side of the left thigh, the outer side of the left calf, and the top of the left foot. These sensors collect three-axis acceleration, three-axis angular velocity, and three-axis magnetometer data across a range of movements, including normal walking, running, jumping, squatting, moving while squatting, crawling, bending, side-stepping, going upstairs, going downstairs, turning in a circle to the right in place, turning in a circle  
Figure 1: Framework of the proposed localization system.  
to the left in place. The data of the motion states mentioned above are labeled as S\({}_{1}\) to S\({}_{12}\), respectively, as shown in Figure 2.  
Figure 2: Inertial data curves of different body parts under various motion states.  
Step 2: Standardization and Normalization  
To ensure consistency in feature scaling, the extracted feature values were standardized and normalized:  
1. Calculation of the mean feature value across multiple motion states: \[\varepsilon=\frac{\sum_{i=1}^{n}\lambda_{i}}{n}\] (1) where \(\lambda_{i}\) represents the value of the \(i\)-th feature parameter, \(n\) is the number of states.
2. Standardization and normalization: \[\mu_{i}=\frac{\lambda_{i}}{\varepsilon},\ \eta_{i}=\frac{\mu_{i}}{\max\{\mu_{1}, \mu_{2},\ldots,\mu_{n}\}},i=1,2,3,\ldots,n\] (2) Step 3: Standard Deviation Calculation  
To evaluate feature discriminability, the standard deviation was calculated as follows:  
\[\sigma_{\text{s}}=\sqrt{\frac{\sum_{i=1}^{n}\left(\mu_{i}-\overline{\mu} \right)^{2}}{n}} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c} \hline ID & **Name** & **ID** & **Name** \\ \hline f1 & peak value of amplitude (three-axis data) & f11 & absolute mean (Y-axis) \\ \hline f2 & peak value (X-axis) & f12 & absolute mean (Z-axis) \\ \hline f3 & peak value (Y-axis) & f13 & mean of amplitude (three-axis data) \\ \hline f4 & peak value (Z-axis) & f14 & variance of amplitude \\ \hline f5 & trough Value of amplitude & f15 & standard deviation of amplitude \\ \hline f6 & trough value (X-axis) & f16 & skewness of amplitude \\ \hline f7 & trough value (Y-axis) & f17 & kurtosis of amplitude \\ \hline f8 & trough value (Z-axis) & f18 & correlation coefficient between Y-axis and Z-axis data \\ \hline f9 & duration of step segmentation & f19 & frequency band energy of amplitude \\ \hline f10 & absolute mean (X-axis) & & \\ \hline \end{tabular}
\end{table}
Table 1: Characteristic parameters.  
Figure 3: Feature discriminability heatmap of multi-source data collected from four body parts.  
Following the above procedure, the feature discriminability of each feature type from the three types of sensor data (acceleration, angular velocity, and magnetometer) was calculated across 12 motion states. Based on data collected from four body parts, a total of 228 feature discriminability values (19 features \(\times\) 4 body parts \(\times\) 3 sensor data types) were computed, as illustrated in Figure 3.