The bearings and distances isolines combinations of the navigational landmarks pair for the vessel fixed position determination

The issues of applying basic navigation parameters (bearing and distance), and their isolines traditionally used in navigation practice in coastal waters are studied in the paper. A new distinctive feature is the use of isolines combinations (three distance arcs, two isoazimuths, a hyperbola and an ellipse) based on measured bearings and distances to the pair of landmarks to obtain the vessel fixed positions with high precision. The traditional navigation methods (the theory of isolines, the generalized method of lines position, the method of least squares) are involved as a mathematical framework. The mathematical argumentation and the isolines characteristics of bearings and distances, their combinations (difference and sum of distances, difference of bearings) are given. The solutions of the surplus equations of the lines position under random error influence by the least squares method and the accuracy assessment of the vessel fix position by the radial error including the reduced variant to compensate the systematic errors are suggested. The principal points of the research are supported by the graphic interpretation, and the given expressions are adjusted to the practical application and navigation systems software development. The computer simulation that shows the radial error of the fixed position by seven position lines is at least two times less than by any pair of position lines has been carried out. The formalization of the proposed methods in the automatic navigation systems or in autonomous ship control systems will enable the navigator on board or at operating the vessel remotely to solve the problems of the navigation information processing in coastal and congested waters on a new level.

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