A positioning system, comprising: a first positioning unit configured to calculate a satellite-based position of a mobile body based on radio signal travel time of radio signals emitted from artificial satellites and received by a receiver; a second positioning unit configured to calculate an inertial-navigation-based position of the mobile body by autonomous navigation; and an estimation unit configured to estimate an error in the inertial-navigation-based position based on the inertial-navigation-based position and the satellite-based position and to estimate a correction value for the inertial-navigation-based position only from previous inertial-navigation-based positions by using an estimation filter; characterised in that the positioning system is configured so that when the number of the artificial satellites from which the receiver receives the radio signals is one, the first positioning unit estimates a position of the mobile body by determining a point that is on a sphere obtained based on the radio signal travel time and composed of points equidistant from the one of the artificial satellites and that is closest to the inertial-navigation-based position corrected based on the correction value; and so that when the number of the artificial satellites from which the receiver receives the radio signals is two, the first positioning unit estimates the position of the mobile body by determining a point that is on a curved line where two spheres intersect, each of the two spheres being obtained based on the radio signal travel time and composed of points equidistant from the corresponding one of the two of the artificial satellites, and that is closest to the inertial-navigation-based position corrected based on the correction value. a first positioning unit configured to calculate a satellite-based position of a mobile body based on radio signal travel time of radio signals emitted from artificial satellites and received by a receiver; a second positioning unit configured to calculate an inertial-navigation-based position of the mobile body by autonomous navigation; and an estimation unit configured to estimate an error in the inertial-navigation-based position based on the inertial-navigation-based position and the satellite-based position and to estimate a correction value for the inertial-navigation-based position only from previous inertial-navigation-based positions by using an estimation filter; characterised in that the positioning system is configured so that when the number of the artificial satellites from which the receiver receives the radio signals is one, the first positioning unit estimates a position of the mobile body by determining a point that is on a sphere obtained based on the radio signal travel time and composed of points equidistant from the one of the artificial satellites and that is closest to the inertial-navigation-based position corrected based on the correction value; and so that when the number of the artificial satellites from which the receiver receives the radio signals is two, the first positioning unit estimates the position of the mobile body by determining a point that is on a curved line where two spheres intersect, each of the two spheres being obtained based on the radio signal travel time and composed of points equidistant from the corresponding one of the two of the artificial satellites, and that is closest to the inertial-navigation-based position corrected based on the correction value.