In the positioning system, a computing device obtains a first position measured by a first positioning antenna, a second position measured by a second positioning antenna, and a third position measured by a third positioning antenna. The computing device calculates the current attitude of the oscillating body at the first position from a first vector from the first position to the second position and the acquired second vector from the first position to the third position. The computing device modifies a reference vector from the first positioning antenna to the predetermined point in the attitude of the oscillating body at the predetermined time, according to the calculated current attitude of the oscillating body at the first position. The computing device then calculates the position of the predetermined point in the current attitude of the oscillating body by adding the modified reference vector to the first position.

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