Method for solving the isostage equations

The method for obtaining the vessel fixed position from redundant measurements of one of the main navigation parameters that is distance which is traditionally used in navigation practice in coastal navigation is being under the present research. A new approach to solving the isostages equations based on measured distances to the corresponding pairs of landmarks is reduced to solving equations of straight lines obtained from the intersection points of the corresponding pairs of isolines. These lines are similar to the position lines built along the chords. In contrast to the classical method for the position lines the proposed chord lines directly converge at the fixed position which is obtained from the isolines. The proposed method eliminates the methodological error from replacing the isolines with the position lines and the need for additional iterations. The traditional navigation methods (the theory of isolines, the generalized method for position lines, the least square method) are facilitated as a mathematical framework. The solutions of the original redundant equations for position lines along chords using the least squares method are proposed. Hence, the hypothesis of random errors in measurements and reduced versions of the chords position lines for compensating the systematic errors and assessment of the vessel fixed position by the radial error is advanced. The expressions for estimating systematic errors in measurements for the purpose of their further compensation are given. 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 formalization of the proposed methods in the automatic navigation 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 by the pair of landmarks in coastal and congested waters on a new level.

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