This paper investigates the improvements from an intelligent self-adaptive modification to a Global Navigation Satellite System (GNSS)-Based Rear Axle Kinematic Parameter Estimator (SA-RAKPE) for an automatic-driving-system in a passenger vehicle. The required highly accurate dead-reckoning localization can be achieved by a well-calibrated kinematic odometry model. For this purpose, the presented Extended Kalman filter approach combines a Differential-Velocity system model and a GNSS measurement model. Subsequently, the intelligent self-adaptive modifications are introduced to allow the SA-RAKPE to work even under difficult conditions. The self-adaptive modifications include a GNSS-Delay-Finder- Module that calculates variable delays of the signals used in complex vehicle architectures. The newly developed SA-RAPKE deals with changes in the system and measurement model accuracies and even works during interruptions caused by GNSS-shortages. To do this, it changes the update equations and fills the interruptions with virtual parameter measurements to avoid estimation inaccuracies from observability loss and even to store the level of learned parameters. After passing the GNSS-shortages, the filter compensates the error in the system model depending on the length of the GNSS-shortage. This makes it possible to continue the parameter learning while passing a great number of bad condition passages. This newly developed self-adaptive filter learns the true axle parameters faster than a restartable filter. The results show that despite numerous high-rise zones, tunnels and bridges, outstanding performance and a short learning phase ensue, especially in urban areas.