Automatic navigation based on dual-antenna real-time kinematic (RTK) positioning has been widely employed for unmanned agricultural machinery, whereas GNSS inevitably suffers from signal blocking and electromagnetic interference. In order to improve the reliability of an RTK-based navigation system in a GNSS-challenged environment, an integrated navigation system is preferred for autonomous navigation, which increases the complexity and cost of the navigation system. The information fusion of integrated navigation has been dominated by Kalman filter (KF) for several decades, but the KF cannot assimilate the known knowledge of the navigation context efficiently. In this paper, the geometric characteristics of the straight path and path-tracking error were employed to formulate the constraint measurement model, which suppresses the position error in the case of RTK-degraded scenarios. The pseudo-measurements were then imported into the KF framework, and the smoothed navigation state was generated as a byproduct, which improves the reliability of the RTK positioning without external sensors. The experiment result of the mobile vehicle automatic navigation indicates that the tracking error-constrained KF (EC-KF) outperforms the trajectory-constrained KF (TC-KF) and KF when the RTK system outputs a float or single-point position (SPP) solution. In the case where the duration of the SPP solution was 20 s, the positioning errors of the EC-KF and TC-KF were reduced by 38.50% and 24.04%, respectively, compared with those of the KF.