A system and a method for the navigation of a mobile vehicle, suitable for determining and displaying a safe navigation zone for the mobile vehicle. The navigation system includes a dead reckoning navigation system (10), a calculator (50), a storage memory (60), an embedded sensor (20), and an electronic mapping system (70). The calculator (50) is suitable for calculating an estimated position of the mobile vehicle from speed and/or acceleration measurements and a comparison of the measurement of an environmental parameter with a geographical database. The calculator (50) is suitable for calculating the probability density of the presence of the mobile vehicle around each point on the map in order to deduce a safety zone (12) corresponding to a presence probability higher than, or equal to, a pre-determined threshold p.