GEOID APPROXIMATION BY SPLINE FUNCTIONS METHODS

The conception of navigational space has been actualized by ship’s positioning with three fixed coordinates on the «marine geoid» geodetic base. With the advent of innovative computer technologies becomes possible to refuse from the widely used in navigation the approach of geometric primitivities and to utilize practically such factual attributes as approximated isosurface and interpolated isoline. The mistake of the marine mobile object space-time position arising from the mathematical manipulation of substitution the real complex geoid figure by simple two-axis ellipsoids for avoiding the complexity of the calculation scheme may cause a navigation accident. It is assumed that any illusory representation about the concept of Euclidean space for water transport logistics forms the hidden threat of a mathematically programmed emergency situation. The foreshortened screenshot of synthesized geoid isosurface is shown as the fragment of model of the liquid planet state within the concept of navigation continuum. The issue of the approximation accuracy is investigated in 3D format with a specially organized experiment. It is proposed optimally to take into account dynamically changed the «pear-shaped» Earth with the effects of gravitational pulsating undulations based on the developed hybrid method. With the spline approach, there is no need to change the mathematical apparatus of the «functions-roofs» as such with a real algorithmic possibility of reconstructing the refined Earth gravitational appearance. In modern conditions, a practicing navigator is faced with the need to identify an ellipsoid activated in a satellite equipment with a datum of marine navigation or vector electronic chart. While determining the ship location using traditional methods, the seafarer is obliged to make corrections to the coordinates from the legend of the paper chart if the geodetic systems don’t match. It is noted that it becomes possible to solve the problem radically when marine logistics is reoriented to the spline geoid model with the condition that cartography is repurposed on the new mathematical basis. When using the spline model of the geoid, there is a real opportunity to free the watch officer from the routine procedures of transforming coordinates for different ellipsoids. This automatically increases the safety standards of modern navigation. A trivial conversion of coordinates to another geodesic basis creates the probability of a navigation error precedent. When manually correcting electronic charts based on notices to mariners, the transition from the ellipsoid of paper chart to the world ellipsoid is implemented by entering modifications with the reverse sign to the geographical latitude and longitude, which can provoke a navigator’s omission with possible serious consequences. With the software implementation of algorithms of the advanced technology of the function approximation theory in the onboard computer, a paradigm of absolute navigational accuracy with the possibility of abstracting from dubious mathematical stylizations is formed.

«морской геоид», «функции-крыши», navigational space, «pear-shaped» Earth, gravitational geoid undulations, «functions-roofs», paradigm of absolute accuracy

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