An on-board navigation apparatus having a GPS receiver detects a difference between the current and the previous values of the estimated current position in terms of the longitude and latitude information gained from GPS data. The difference is added to the coordinates of the previously established position, the result being taken for the coordinates of the estimated current position. This makes it possible to estimate the current position coordinates accurately even if the accuracy of GPS data is not high enough. When the GPS receiver is in a two-dimensional measuring state, the coordinates of the estimated current position are obtained from a manually or automatically designated elevation value and from the GPS data. This allows the current position coordinates to be estimated with accuracy even if the accuracy of GPS data has dropped due to the two-dimensional measuring instead of a three-dimensional measuring.