Abstract
This paper is to develop the position error equations including the attitude errors, the errors of nadir and ship's heading, and the errors of ship's position in the free-gyro positioning and directional system. In doing so, the determination of ship's position by two free gyro vectors was discussed and the algorithmic design of the free-gyro positioning and directional system was introduced briefly. Next, the errors of transformation matrices of the gyro and body frames, i.e. attitude errors, were examined and the attitude equations were also derived. The perturbations of the errors of the nadir angle including ship's heading were investigated in each stage from the sensor of rate of motion of the spin axis to the nadir angle obtained. Finally, the perturbation error equations of ship's position used the nadir angles were derived in the form of a linear error model and the concept of FDOP was also suggested by using covariance of position error.