Abstract: A navigation apparatus provided with: a vertical movement detecting device for detecting a presence or absence of a movement in a vertical direction of a moveable body associated with the movement of the movable body; a judging device for judging a position in the vertical direction of the movable body on the basis of the presence or absence of the movement in the vertical direction detected by the detecting device; and a notifying device for notifying a present position of the movable body on the basis of the position in the vertical direction judged by the judging device.

Abstract: A method of calculating a present position of a movable body for use in a navigation system, is provided with the processes of: measuring an electric-wave-based measurement position which is a position of the movable body measured on the basis of electric waves for positional measurement, which are transmitted from satellites accompanied by time data indicating an electric-wave-based measurement time which is a time when measuring the electric-wave-based measurement position, at the electric-wave-based measurement time; measuring a self-sustained measurement position which is a position of the movable body measured on the basis of data from self-sustained type sensors built in the movable body; calculating a time difference between the electric-wave-based measurement time and a time when measuring the self-sustained measurement position; correcting the electric-wave-based measurement position on the basis of the calculated time difference; and calculating the present position of the movable body on the basis

Abstract: A method and system for deriving a travel distance of an object which travels. As one aspect, a travel velocity of the object producing a pulse signal in response to travel of the object on the basis of a number of pulses of the pulse signal per unit time is calculated, and a plurality of unit travel distances corresponding to a plurality of travel states of the object every travel state are calculated. The plurality of travel states are different from each other and the unit travel distance is a travel distance per pulse calculated by dividing the calculated travel velocity by the number of the pulses of the pulse signal per unit time. And the plurality of calculated unit travel distances are memorized individually, from the plurality of memorized unit travel distances, the unit travel distance corresponding to the travel state of the object which is under travel is selected, and the travel distance of the object on the basis of the selected unit travel distance and the pulse signal is derived.