## 1 Introduction  
With the development of digital agriculture, the working environment for agricultural practitioners has been improved and their labor intensity has been reduced [1]. As a key technology in precision agriculture, automatic driving has been greatly emphasized by an increasing number of researchers [2, 3, 4, 5, 6]. Unmanned agricultural machinery can play a role in reducing labor intensity, decreasing input costs, and increasing profitability [7]. High-precision navigation and driving systems can reduce damage to crops by repeated-trajectory driving [8], while high-precision steering angle detection benefits the navigation performance of autonomous driving systems [9, 10]. Precise detection of the steering angle of autonomous agricultural machinery can be achieved by direct or indirect means [11]. [PERSON] et al. [12] established a steering wheel motion model and realized the steering wheel angle measurement by detectingand tracking the main features on the steering wheel. [PERSON] et al. [13] proposed a wireless steering wheel angle sensor using optical media for angle detection and gave a wireless steering wheel angle sensor. The modeling and simulation results of steering sensor and wired steering system were presented, and the feasibility of the system was discussed based on the simulation results. [PERSON] et al. [14] mounted a CCD sensor on the vehicle to form a visual detection system, extracted the contour edge points of the steering wheel image collected by the CCD, and performed ellipse fitting on the edge points to detect the steering angle. [PERSON] et al. [15] directly obtained the steering angle data of rice harvesters using an absolute value rotary encoder, while [PERSON] et al. [16] utilized a displacement sensor and four-link angle sensor to calculate a tractor's front wheel angle, which was achieved by adopting the least squares fitting method to calibrate the sensor, in order to establish a sensor model for identification of the tractor's steering angle. [PERSON] et al. [17] carried out gyroscope-based steering angle detection research, in which they established an autoregressive-moving-average (ARMA) model of the microelectromechanical system (MEMS) drift signal and integrated a Kalman filter. [PERSON] et al. [18] proposed a wheel steering angle measurement system based on dual global navigation satellite system (GNSS) antennas and dual MEMSs, combined with an adaptive Kalman filter designed with respect to the drift and accumulated error of the gyroscope. In an agricultural machinery navigation test, the average error of the straight-line driving angle was 0.06\({}^{\circ}\) and the variance of the error was 0.215\({}^{\circ}\). [PERSON] et al. [19] studied the calibration and detection of the steering wheel angle of wheeled tractors, taking a Levo M904-D wheeled tractor as the research platform and adopting a WYH-3-type contactless angle sensor. In this study, four-wheel independent-steering paddy field machinery (shown in Figure 1) was taken as the object of steering angle detection research. The four-wheel independent-steering paddy field management machine was multi-functional and was developed for deep mud paddy field management. Each of the four wheels can be turned independently and the chassis ground clearance and wheelbase heights can be adjusted. The management machine adopts the combination of four hydraulic motors and a reducer to drive four-wheel independently and adopts a combination of four hydraulic motors and a reducer to perform four-wheel independent steering, through the use of computer control, special driving modes (e.g., horizontal driving, in situ steering, and small turning radii) may be realized to meet the needs of small-area field operations in hilly and mountainous areas. Given that the rear wheels only perform steering control in specific scenarios such as small-radius transitions or lateral shifts, this study only focused on the detection of the steering angle of the front wheels during travel.