Currently, the use of Global Navigation Satellite Systems-GNSS has been widely disseminated for the most different applications, from the aeronautical navigation to the car traffic system, being the Global Positioning System-GPS the most used system for such objectives. New applications of such systems have presented more demanding requirements in terms of precision for the position and velocity provided by these systems. Some solutions, as the precision augmentation systems based on satellite or ground improve the precision of the position and velocity estimates. However, the sampling rate of these systems is not substantially improved. Therefore, it constitutes a major limitation of such systems for the position and velocity estimates during high acceleration transients. On other hand, Inertial Navigation Systems- INSs present superior performance under these circumstances. In this work we study refinements of the GPS Kalman estimates for the position and velocity of a vehicle during high acceleration transients using measurements from the Inertial Measurement Unit-IMU of an INS. For that, we: 1- identify a case in the literature with discrete-discrete type Kalman Filter applied to the linearized version of a two dimension vehicle movement, with uncertainties from the GPS sensors modeled as stochastic gaussian processes characterized for small or null acceleration transients; 2- apply the case for high acceleration transients; and 3- repeat this with GPS and INS for high acceleration transients. We expect to show: 1- the difficulties to tuning the Kalman Filter to obtain a behavior of convergence; 2- after the Kalman Filter is tuned, the estimates of the state variables can be obtained with sufficient precision; and 3- the use of IMU measurements refines the GPS Kalman estimates for the position and velocity of a vehicle during high acceleration transients.