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, being the Global Positioning System-GPS the most used system for such objectives. New applications have presented challenges in terms of the main requirements associated to such systems, namely: precision, reliability, availability, continuity and integrity. It is because proposed solutions, such as satellite or ground-based augmentation systems, depend on signals provided by the GNSS satellite constellation. It constitutes a limitation for using such systems for position and velocity estimations. On other hand, Inertial Navigation Systems-INS, being independent of external signals, have a big potential to be applied on these circumstances; furthermore, they present characteristics that may be considered complementary to the GNSS. In this work we study refinements of the Kalman estimates for the position and velocity of a vehicle obtained with GPS using Inertial Navigation System's measurements. For that, we: 1- perform simulation of a vehicle movement using position and velocity estimates obtained from a GNSS constellation; 2- perform the simulation of a vehicle movement using accelerometer data being updated with measurements obtained from a GNSS constellation by a Kalman Filter, with uncertainties from the accelerometers and GNSS data modeled as stochastic Gaussian processes; and 3- compare the results of the simulation, discussing the possible advantages and disadvantages of the application of GNSS-INS integration techniques. We expect to show: 1- the difficulties to tuning the Kalman Filter to obtain a behavior of convergence; 2- the limitations of using GPS data without integration or Navigation; and 3- the use of accelerometer data integrated to GPS contributes for the improvement of onboard navigation systems.