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To address the complicated installation and maintenance of the steering angle sensor and inaccurate angle estimation in traditional agricultural machinery navigation systems, the ARMAX-KF method and vehicle speed compensation were proposed to estimate the steering angle of tractors without steering angle sensors. Initially, the Hammerstein nonlinear system was used to model the tractor’s steering system, followed by identification using the RLS method as an ARMAX model. Subsequently, a method was proposed to obtain the velocity of the rear axle center point through speed lever arm compensation. Finally, ARMAX-KF was designed to estimate the steering angle, utilizing the correcting characteristics of the Kalman filter, using the tractor’s kinematic steering angle as the observation value to correct the integrated angle velocity predicted by the ARMAX model, thus estimating the steering angle of the tractor. The method of measuring speed for speed lever arm compensation achieved the average absolute error of the compensated kinematics steering angle of 1.110°, with a standard deviation of 1.727°, reducing the error by 61.13% and 31.55% compared with the values obtained before compensation. In the dynamic angle test, the standard deviation of the angle velocity predicted by the ARMAX model was 2.439(°)/s, reducing the error by 56.58% compared with the method using a fixed transmission ratio. The absolute average error of the steering angle estimation based on ARMAX-KF was 0.649°, with a standard deviation of 0.371°, reducing the error by 56.9% and 78.82%, respectively, compared with the methods using a fixed transmission ratio and the Kalman filter. In the straight-line navigation tracking test, the steering angle estimation standard deviation based on ARMAX-KF was 0.649°. The proposed method improved the accuracy of angle estimation and enhanced the quality of agricultural machinery navigation.