The Generalised N-Trailer (GNT) vehicle is a tool for field operations that optimises harvesting and transportation tasks, offering a highly scalable payload using only one tractor. Precise knowledge of the position and attitude of each segment in the chained vehicle is crucial for the controller's success during operation. In this study, we propose the use of a Nonlinear Moving Horizon Estimator (NMHE) to estimate the system's state when the GNT vehicle is equipped with incremental encoders on its joints. A first NMHE serves as a virtual calibration procedure, estimating initial joint angle values and the system's state using noisy and biased measurements of the joints and the tractor pose. This calibration is performed while the chained vehicle travels along a straight path, whose length is determined by the number of trailers and their geometrical properties. Subsequently, a second NMHE, with fewer optimisation variables and constraints replace the first to effectively reduce the computational burden. Moreover, it treats the incremental encoder measurements as if they were absolute encoders after the initial joint angles have been estimated by the first NMHE. The proposed method is compared against the Extended Kalman Filter (EKF) and validated through simulated and practical real-time experiments, showcasing its effectiveness in achieving precise control and enhancing operational efficiency.