## 4 Conclusions  
In this work, an effective steering angle prediction method was proposed for front-wheel independent-steering paddy field machinery. By collecting data on the steering angle and body attitude sensors, then adopting FFT and power spectrum conversion to extract the spectrum characteristics of the sensors, we determined that the peak frequency of the steering angle sensor power spectrum was 0.2 Hz, and that the \(z\)-axis angle speed power spectrum presented a peak frequency, while systemic characteristic information of the power spectrum frequency could not be found with the other sensors. On this basis, different combinations were selected as input factors for equivalent steering angle prediction using the proposed BP neural network, in order to verify the validity of the input factors consisting of characteristic information on the peak frequency points of the power spectra. Finally, the left and right front wheel steering angle values and \(z\)-axis steering angle speed were selected as the optimal input factors for equivalent steering angle prediction, and the training set was divided using basic rules for data processing with a data analysis frequency of 0.2 Hz. By analyzing and processing 148 sample data points obtained under two different ground states, two different driving speeds, and three preset steering angles, the predicted mean squared error on the test set was found to be 0.44, the equivalent steering angle mean squared error was less than 0.66\({}^{\circ}\), and the equivalent steering angle prediction was good, which essentially meets the accuracy requirements for the navigation control steering angle. Compared with the steering angle value obtained by directly calculating the steering angle of the left and right steering wheels, the steering angle was calculated by Formula (20):  
\[\gamma=(\alpha_{\text{Left}}+\alpha_{\text{Right}})/2 \tag{20}\]  
By comparing the steering angle value of the body obtained by using the above calculation formula with the real steering angle value, it was found that the mean square error of steering angle detection was 1.97, and the maximum steering angle deviation was 4.81\({}^{\circ}\). Compared with the traditional method, the neural network was used to calculate the equivalent steering angle. The mean square value of prediction error was increased by 1.53, and the maximum error angle was 1.66\({}^{\circ}\), which could obtain better detection effect and meet the accuracy requirements of navigation control steering angle. Compared with the conventional BP neural network training, which uses massive data input to improve the training effect, this study extracted the signal features of the left and right front wheel steering angles, \(x\), \(y\), \(z\)-axis acceleration values, and \(z\)-axis angular velocity values to obtain effective training input factors. In the comparison test, compared with using more input factors, only using three input factors of left and right front wheel steering angle value and \(z\)-axis rotation angular velocity, the equivalent steering angle prediction effect was better, which provides a new method for the selection of BP neural network training factors. The study also provides the possibility for the fast and effective implementation of the BP neural network algorithm. Since the sample time for neural network training is 5 s, for applications that require continuous steering adjustment, such as non-linear assisted navigation and driving, auxiliary means such as multi-sensor fusion are needed to improve the real-time detection. These are points to be aware of when steering the system for unmanned navigation. Conceptualization, S.J. and W.H. ; methodology, P.J. and W.H. ; software, S.J. and J.Y. ; validation, J.Z. and W.H. ; formal analysis, S.J. ; investigation, Y.L. and Y.S. ; data curation, J.Y. ; resources, C.S. ; writing--original draft preparation, W.H. ; writing--review and editing, J.Z., S.J. and W.H. ; visualization, J.Z. ; supervision, P.J. and W.H. ; project administration, P.J. and W.H.