Most of present work for autonomous navigation in dynamic environment doesn't take into account the dynamics of the obstacles or the limits of the perception system. To face these problems we applied the Probabilistic Velocity Obstacle (PVO) approach to a dynamic occupancy grid. The paper presents a method to estimate the probability of collision where uncertainty in position, shape and velocity of the obstacles, occlusions and limited sensor range contribute directly to the computation. A simple navigation algorithm is then presented in order to apply the method to collision avoidance and goal driven control. Simulation results show that the robot is able to adapt its behaviour to the level of available knowledge and navigate safely among obstacles with a constant linear velocity. Extensions to non-linear, non-constant velocities are proposed.