Non-iterative algorithm for calculating geodetic latitude at a spatial rectangular coordinates
When construction of global geodetic networks associated with processing of satellite observations, and the solution of geodetic problems to determine the position of point on the earth surface are applied the spatial rectangular coordinates and geodetic coordinates. In this context arise the problem of transforming these systems of coordinates. This article illustrates the shortcomings of mathematical solutions of the problem of calculating the geodetic latitude B using the method of iterations, having applied the known spatial rectangular coordinates X, Y, Z. Iteration process convergence to an sought quantity does not prove, area and speed of iteration process convergence is not determined, analysis of approaching due to iterations is not carried, comparative study is not carried, advantages and disadvantages of suggested formulas in comparison with existing formulas are not shown. With these drawbacks, the Russian Federation Standard proposes an algorithm for calculating the latitude using the auxiliary angle. On the basis of the previously developed theory of transcendental analysis of solutions a non-iterative algorithm for determination the precise geodetic latitude is derived. To this end, root gap insulation is pre-reduced and a formula for calculating the latitude with high precision by the method of the tangents at one iteration is made. The formula for calculating the error of the proposed algorithm is derived, on the basis of which limits on the accuracy of the results determined by the latitude are set. For the prediction of accuracy and computational calculation of the length of the bit error grid algorithm expressed by the original data. The reliability of the research confirmed in a numerical example.