Applying the least square method to calculate the non-simultaneous errors of ship’s position determined by global positioning system (GPS)

Abstract

Global Positioning System – GPS can determine accurately a specified position on the earth surface, in the sky and in the space. Ship’s position is determined on the true horizontal plane which is considered approximately as sea surface. Satellite equation is created basing on the pseudo distances to satellite in the system. Set of satellite equations which is corresponding to a specified set of satellites is able to determine ship’s position. Similar as taking measurements to celestial and terrestial objects, measuring distance to satellites is unable to carried out at the same time. Therefore, non-simultaneous errors that depends on ship’s speed and duration of observation are created by ship’s motion in the mentioned methods. In the traditional methods of determining ship’s position, navigation officers often use some methods to minimize the non-simulataneous errors in determining ship’s position and to evaluate effects of other errors. However, in the method of determining ship’s position by GPS, the error minimizing methods which are applied in the traditional methods are not suitable to be used because the direct distance to satellite is not measured and the line of position is not drawn on nautical chart. In this article, the author introduces the method to determine and to elimate non-simultaneous errors by applying the least square method.