Positioning apparatus and positioning system

A positioning apparatus comprising:

• a satellite signal receiver which receives satellites' signals transmitted from the satellites,
• a base-station data receiver whose position is known, the base-station data receiver receiving a base-station positioning data from a base-station, and
• a position estimating device which:
• observes code pseudoranges and carrier phase integration values at the satellite signal receiver and the satellites by utilizing satellite data got by the satellite signal receiver;
• sets up unknown values which includes integer ambiguity at the satellite signal receiver and the base-station, clock errors at the satellite signal receiver and the base-station, delays of an ionosphere at the satellite signal receiver and the base-station, delays of an troposphere at the satellite signal receiver and the base-station, a position of the satellite signal receiver, and except a position of the base-station data receiver;
• linear-approximates a position of the satellite signal receiver with a Linear Taylor series expansion about estimated positions of the satellite signal receiver;
• sets up explanatory variables that include the integer ambiguities, the clock errors, the delays of the ionosphere, the delays of the troposphere, and the position of the satellite signal receiver;
• sets up objective variables that include the carrier phase integration values, and the code pseudoranges observed by the satellite signal receiver and the base-station;
• derives only one linear regression equation which includes the objective variables and the explanatory variables;
• and
• estimates the position of the satellite signal receiver.