A navigation system comprising: an inertial navigation system arranged to output a first position estimate; a terrain based navigation unit arranged to output a second position estimate; a gravity based navigation unit arranged to output a third position estimate; a stored gravity map arranged to receive a position and to output gravity information for that position; and an iterative algorithm unit arranged to determine an INS error state in each iteration; wherein in each iteration the iterative algorithm unit is arranged to: receive the first position estimate, the second position estimate, and the third position estimate; determine a gravity corrected position estimate based on the first position estimate, the INS error state and the gravity information; and update the INS error state for the next iteration based on the INS error state, the gravity corrected position estimate, the second position estimate and the third position estimate.