As an embodiment of the present invention, in a navigation system using an acceleration sensor, when position information cannot be obtained from a GPS processing section, a velocity detecting unit performs an operation using detected acceleration .alpha.G, a measurement time mt, a velocity V0 at a time t0, gravity acceleration g and an amount of height change Dh, according to Expression (11). By using the relationship among a gravity acceleration component gf, the gravity acceleration g, the amount of height change Dh and distance Dm shown in Expression (4), the gravity acceleration component gf can be offset by the amount of height change Dh. Therefore, velocity V can be calculated with high accuracy without receiving the effect of the gravity acceleration component gf.