The automobile industry usually ignores the height of the path and uses planar vehicle models to implement automatic vehicle control. In addition, existing literature mostly concerns level terrain or homogeneous road surfaces for estimating vehicle dynamics. However, ground vehicles utilized in forestry, such as forwarders, operate on uneven terrain. The vehicle models built on level terrain assumptions are inadequate to capture the rolling or pitching dynamics of such machines as rollover of such vehicles is a potential risk. Therefore, knowledge about the height profile of the path is crucial for automating such off-road operations and avoiding rollover. We propose the use of a six-degrees-of-freedom (6-DOF) dynamic vehicle model to solve the autonomous forwarder problem. An adaptive linear tire model is used in the 6-DOF model assuming the vehicle operates in a primary handling regime. The force models are modified to include the three-dimensional (3D) map information. The calibration procedures, identifying actuator dynamics, and quantifying sensor delays are also represented. The proposed vehicle modeling contributed to realizing the continuous-discrete extended Kalman filter (CDEKF), which takes into account the 3D path during filtering and fixed-lag smoothing. Polaris (an all-terrain electric car) is used as a case study to experimentally validate the vehicle modeling and performance of the state estimator. Three types of grounds are selected – an asphalt track, a concrete track with a high elevation gradient, and a gravel track inside a forest. Stable state estimates are obtained using CDEKF and sparse 3D maps of terrains despite discontinuities in satellite navigation data inside the forest. The height estimation results are obtained with sufficient accuracy when compared to ground truth obtained by aerial 3D mapping. Finally, the proposed model’s applicability for predictive control is demonstrated by utilizing the state estimates to predict future states considering (3D) terrain. •Prior knowledge about the height profile of the path is crucial for automating forest machine chain operations and avoiding rollover.•A six-degrees-of-freedom (6-DOF) dynamic vehicle model is used to solve the autonomous forwarder problem.•The calibration procedures, identifying actuator dynamics, and quantifying sensor delays are also represented.•Stable state estimates are obtained using continuous-discrete extended Kalman filter (CDEKF) and sparse 3D terrain maps despite satellite navigation data discontinuities.•The applicability of the proposed vehicle dynamic modeling for predictive control is demonstrated.