This paper describes an analytic method for calculating the position by the observation of celestial bodies as effective alternative to traditional graphic methods used in celestial navigation.

The algorithm is totally general, allowing the use of simultaneous sights, or observations taken at different times, including navigating a course and a certain speed. It uses the method of least squares to obtain the most probable position, and through successive iterations makes it possible to reduce the error to approximate the circle of equal altitude by the straight line of position. It also provides the error in the calculation of the position and the Confidence ellipse.

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