A positioning apparatus of a vehicle includes a measuring module and a triaxial orientation sensor to provide measured axial accelerations in a Cartesian reference system during a certain time interval. The apparatus also includes a triaxial movement sensor to supply at least one angular variation signal proportional to the axial angular speed of the vehicle during the time interval. A processing unit receives a distance signal proportional to the distance traveled by the vehicle in the time interval, receives the at least one angular variation signal, and supplies at least one reference acceleration of the vehicle. An estimator-calibrator block recursively estimates at least one calibrated acceleration as a function of the measured axial accelerations and of the at least one reference acceleration. The estimator-calibrator block includes a calculation unit to calculate an altitude variation as function of the distance signal and recursively calculates an estimated pitch angle as a function of at least one calibrated acceleration.