A Navigation Solution Involving Changes to Course and Speed

In a previous paper, an approach to celestial navigation is presented that allows a vessel's latitude, longitude, course, and speed to be estimated simultaneously. The development in that paper assumes that the vessel is sailing a rhumb-line track at a constant speed. In this paper, the approach is extended to cover the case where observations are taken over several legs of a voyage. A single least-squares solution for all sailing parameters is developed. The algorithm presented in this paper is not limited to celestial navigation, but is applicable to any situation in which observations over several legs of a voyage are to be combined in a single solution.