## 3 Data Fusion Method Based on Self-Adaptive
### Determination of Training Target Values Based on Neighborhood Search  
When confronting the challenge of selecting target values during the data fusion process using a backpropagation algorithm, the neighborhood search method is employed due to its capability to locate optimal or near-optimal solutions within the solution space. This paper adopts a method to determine the training target values based on neighborhood search. Utilizing the neighborhood search approach involves exploring the vicinity of current parameter settings to find values that minimize the objective function. The steps of the neighborhood search are illustrated in Figure 9.  
Figure 8: Diagram error histogram for the learning process. Figure 9: Neighborhood search flowchart. Let \(X_{i,j}^{t}\) be the input dataset for the backpropagation neural network, where \(i\) is the input sensor (\(i=1\) for visual sensor, \(i=2\) for inertial measurement sensor), and \(j\) represents the attitude angle corresponding to a sensor at time t (\(j=1\) for azimuth angle, \(j=2\) for elevation angle, \(j=3\) for roll angle). \(F(. )\) is the minimum value function. The training set error matrix is defined as \(Y_{i,j}^{t}\), which is shown in Equation (10):  
\[Y_{i,j}^{t}=F\Big{(}\Big{|}X_{i,j}^{t+1}-X_{i,j}^{t}\Big{|},\quad\Big{|}X_{i,j} ^{t}-X_{i,j}^{t-1}\Big{|}\Big{)}\quad i=1,2;\;j=1,2,3 \tag{10}\]  
After performing the neighborhood search, the comparative error data between the visual and inertial measurement sensors at time \(t\) are obtained as shown in Equation (11):  
\[\Delta e_{i,j}^{t}=\Big{[}\Big{|}Y_{1,j}^{t}\Big{|},\Big{|}Y_{2,j}^{t}-\Big{|} Y_{1,j}^{t}\Big{|}\Big{|}\Big{]} \tag{11}\]  
Transposing the above equation and solving for the minimum value, we obtain  
\[\Delta E_{i,j}^{t}=F\big{(}\Big{|}\Delta e_{i,j}^{t}\Big{|}^{T}\big{)} \tag{12}\]  
By solving the above equation, the minimum error value between the adjacent data of the three sensors is obtained. Due to the high precision of visual measurements, the minimum error from visual data serves as the reference value. Through inverse search calculation, the training target value at a certain time is derived as \(v_{j}^{t}\) shown in Equation (13):  
\[v_{j}^{t}=a\times X_{1,j}^{t-1}+b\times X_{1,j}^{t}+c\times X_{1,j}^{t+1} \tag{13}\]  
where \(a\), \(b\), and \(c\) are linear weighting coefficients adjusted continuously during network training. The neighborhood search method aims to analyze the temporal variation trends in sensor data to determine the target values to be used during neural network training. In summary, training sample data are input into the neural network training model for learning and training. This process yields parameters for the backpropagation algorithm structure. Subsequently, actual measurement data are fed into the network structure to achieve predictions of attitude angles. To assess the effectiveness of the neighborhood search method in the training of backpropagation algorithm models, this study conducted a simulation experiment. In this experiment, we set up the output of the neural network training set in three different ways: the first was set to the calculated output values of the IMU; the second was set to the target values obtained through the neighborhood search method; and the third was set to the true rotation angle values in the simulation analysis. Subsequently, we used another set of simulation data generated under the same conditions for the verification experiment, aiming to explore whether the neighborhood search method can serve as an effective output target value for neural network training data. The training results are shown in Table 1: the network with the output of the neural network training using true value is Net 1, the network using the value of the IMU is Net 2, and the network using neighborhood search is Net 3. From Table 1, we can see that the MSE of Net 3 decreased to 0.196, which is a 34% reduction compared to the MSE of Net 2. The R of Net 3 has increased from 0.901 to 0.929.