## 3 Blocked Distance Estimation
### Blocked Distance Prediction Based on Gaussian Process Regression  
To achieve optimal training and prediction outcomes, Gaussian process regression necessitates the selection of a suitable kernel function. This study constructs three Gaussian process regression obstacle distance prediction models with distinct kernel functions, which are subsequently compared through experimental analysis. The experimental setup is illustrated in Figure 2, depicting four stationary obstacles within the deck area.  
The analysis of factors influencing the distance impacted by common obstacles on a deck involves extracting characteristic data for regression analysis. Key characteristic data comprise the Euclidean distance, obstacle area, centroid deviation distance, and obstacle shape. The Euclidean distance denotes the direct distance between two positional points,  
Figure 2: Typical deck environment with obstacles.  
while the centroid deviation distance indicates the distance between the line connecting two positional points and the obstacle material's center. In the illustration in Figure 3, ABCD represents a rectangular obstacle, and EF represents two cabins. In the absence of obstacles between the two target points, the distance is the Euclidean distance. However, when obstacles are present between the two target points, the actual route follows the dotted line EF, with OH representing the centroid deviation distance.  
This study establishes the training dataset for a Gaussian process regression model using 50 sets of empirical data. The Gaussian process regression is conducted by employing the exponential kernel function, the squared exponential kernel function, and the Matern 5/2 kernel function through a 50% cross-validation approach.  
The specific prediction is illustrated in Figure 4. The figure displays the prediction response diagram when various kernel functions are applied. The blue dot represents the actual value, while the yellow dot represents the predicted value. The subsequent figure illustrates the deviation between the predicted outcome and the ideal prediction. A closer proximity to the ideal prediction line indicates a more accurate prediction.  
The commonly used regression evaluation indexes of prediction models are the coefficient of determination (R\({}^{2}\)), mean square error (MSE), root mean squared error (RMSE), and mean absolute error (MAE). This paper uses these four evaluation indexes to make a comparative analysis of the constructed regression model. The range of R\({}^{2}\) is \([0,1]\). The closer it is to 1, the better the prediction model. The range of other indicators is \([0,+\infty)\). The closer it is to 0, the better the prediction model.  
The index calculation method is shown in (26)-(29):  
\[R^{2}=1-\frac{  
These indicators are used to evaluate the training model, where the larger the R\({}^{2}\), the better the model prediction effect, and the smaller the remaining indicators, the better the model prediction effect. The above predicted results are calculated based on evaluation indicators to obtain comparative data. The data comparison is shown in Table 2.  
Through the aforementioned comparison, the square exponential kernel function has been chosen as the kernel function for Gaussian process regression. Subsequently, the obstacle influence distance regression model was developed and utilized to forecast real-world scenarios.