## 3 Results and Discussion
### BP Data Network Input Factor Selection and Training  
The front wheel steering angle detection value was found to be directly related to the equivalent steering angle. Therefore, the left and right front wheel steering angle data were selected as basic input factors, and the corresponding spectral peak frequency was used as the basis for time dimension selection for the benchmark training subset. Therefore, a 5 s time period was used for the training subset. The filtered data were processed using various time periods, in order to obtain 148 training subsets. We randomly selected 80% of the subset as the training set, while the remaining 20% were used as the test set for evaluating the training effect.  
The presence or absence of a power spectrum peak frequency point in the attitude data was taken as an input factor. We evaluated the effectiveness by performing training  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Index** & **Mode** & **One** & **Two** & **Three** & **Four** & **Five** & **Six** \\ \hline Left front wheel steering angle & 0.2 & 0.21 & 0.24 & 0.22 & 0.22 & 0.21 \\ Right front wheel steering angle & 0.21 & 0.22 & 0.19 & 0.19 & 0.21 & 0.18 \\ \(x\)-axis acceleration & 0 & 0 & 0 & 0 & 0 & 0 \\ \(y\)-axis acceleration & 0 & 0 &  
followed by evaluation with three combinations, in order to confirm the effectiveness of feature extraction. The combinations used are described in Table 3.  
The network structure of the corresponding BP neural network is shown in Figure 10.  
The training process (in terms of the training loss) is depicted in Figure 11.  
A total of 500 epochs were used for training the neural network. The loss decreased throughout the training process, indicating that the network converged well.  
Once the test sets with the three training input combinations had been implemented, a comparison table between the test and real values could be compiled, as shown in Table 4.  
The corresponding mean squared errors (MSEs) are given in Table 5.  
By training with the three combinations of input factors and conducting verification on the corresponding test sets, we found that when the left and right front wheel steering angle parameters with the peak frequency points of the power spectrum and the \(z\)-axis rotation angular velocity parameter were used as the BP neural network training input factors to obtain the best prediction effect, the corresponding mean square error was 0.44 and the mean square error of the equivalent steering angle was less than 0.66\({}^{\circ}\), indicating a good prediction effect. For the other combinations, although the number of training input factors was increased, the prediction effect decreased. Therefore, by using a BP neural network equivalent steering angle prediction algorithm with the characteristics of the peak frequency point of the power spectrum, we could effectively predict the equivalent steering angle of the front wheels of an independent-steering paddy field management machine.  
Figure 10: BP neural network training structure.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Combination No.** & **Mix of Factors** \\ \hline
1 & Left and right rotation angles, \(z\)-axis angular velocity \\ \hline
2 & Left and right rotation angles, \(x\)- and \(y\)-axis acceleration, \(z\)-axis angular velocity \\ \hline
3 & Left and right rotation angles, \(x\)- and \(y\)-axis acceleration \\ \hline \hline \end{tabular}
\end{table}
Table 3: Training input factor combinations.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Combination 1**} & \multicolumn{2}{c}{**Combination 2**} & \multicolumn{2}{c}{**Combination 3**} \\ \hline
**True Value** & **Expected Value** & **True Value** & **Expected Value** & **True Value** & **Expected Value** \\ \hline \(-0.33\) & \(-0.64\) & \(-0.33\) & \(-0.28\) & \(-0.54\) & \(-0.63\) \\ \(