To improve the attitude determination accuracy of vehicle-mounted strapdown attitude and heading reference system (AHRS), the non-holonomic constraint (NHC) is adopted to compensate the errors of attitude and heading system online. However, traditional integrated navigation schemes suffer from problems such as the failure of non-holonomic constraint (NHC) and inaccurate modeling of lateral velocity noise, which lead to the accumulation of heading angle errors and seriously affect the reliability and stability of on-board positioning and orientation. Considering the lateral velocity component caused by the tire camber effect during vehicle turning, this study proposes a vehicle orientation algorithm based on the adaptive non-holonomic constraint (NHC) measurement noise. Firstly, based on the vehicle dynamics model with the two-degree-of-freedom, a nonlinear coupling function of forward velocity and lateral acceleration is constructed to accurately characterize the characteristics of lateral velocity noise during vehicle motion and complete the dynamic correction of non-holonomic constraint (NHC) measurement noise; Meanwhile a variance-limited adjustment mechanism is introduced to adjust the constraint intensity in real time according to the vehicle motion state. The real vehicle experiments of integrated navigation based on the global navigation satellite system/strapdown inertial navigation system (GNSS/SINS) demonstrate that, the proposed algorithm in both typical turning scenarios (continuous curves and circular driving) significantly improves the heading angle estimation accuracy while maintaining almost unchanged measurement accuracy of pitch and roll angles. The heading angle measurement accuracy is improved by more than 15% compared to the traditional method, which shows the good robustness and convergence in abnormal conditions such as short-term interruption and occlusion of global navigation satellite system (GNSS) signal. The algorithm simultaneously optimizes the noise modeling and constraint adaptation, which effectively solves the problems of heading angle accuracy degradation and filter divergence in the integrated navigation system during the vehicle turning motion. It can provide the higher-precision and higher-reliability heading and attitude references for the ground unmanned vehicles, intelligent vehicle navigation and other systems.