Patent ID: 7629925

Claim:
A positioning apparatus comprising: antennas which receive satellites signals transmitted from satellites and whose distances from one to another are configured, receivers which are set with every antennas respectively and demodulate the satellite signals inputted from the antennas, and a position estimating device which: linear-approximates positions of receivers with a Linear Taylor series expansion about estimated positions of the receivers by using estimation results of previous positions of the receivers and positions of satellites with a Linear Taylor series expansion about orbital positions of the satellites by using estimated orbital positions of the satellites from a broadcast orbit data; sets up objective variables, as observable values, that include carrier phase integrated values and code pseudoranges related to distances between the antennas and the satellites; sets up explanatory variables, as unknown values, that include integer ambiguities, clock errors of the receivers, the positions of receivers, clock errors of the satellites, and the orbital positions of the satellites; sets up a regression equation whose operational elements set by an approximate matrix derived from the linear-approximation; and estimates at least the positions of receivers and the integer ambiguities by using the regression equation, and detects a point position of the positioning apparatus with the positions of the receivers and the distances of the receivers from each other.