The optimized algorithm for navigational isosurface of any constructional complexity is proposed in the paper. Spline interpolation of navigational isoline is considered only as a particular case of decision for three-dimensional problem. The formalization of the modified mathematical apparatus for the practical synthesis of navigational isosurface based on the methods of basic finite splines is given. The advantage of the offered approach is demonstrated by the decision of the task for the generation of geoidal spline model as an argument, of the practical applicability of the developed method. The hybrid algorithm of approximation by B-splines in the combination with smooth analogues of Lagrangian splines is absolutely universal in independence from the specific factual presentation of the real navigational isosurface that allows us to solve the wide spectrum of applied navigation problems. The effective search for measurement errors of navigation parameters by the methods of computer visualization of the geometrically restored base of the digital data becomes possible when using the optimized model of spline approximation. The fictitiousness of any measurement will be unambiguously detected by the noise peak of blunder which occurs due to the breach of the smoothness of the approximated navigational isosurface. Based on the analysis of the imitation spline surface, the identified measurement error can be promptly eliminated from the data set with minimal time consuption without using special computer animation tools. The issue of calculative accuracy of the algorithm and compactness of navigational information storage has been investigated by the author's organized computing experiments.
It is proposed to consider any movement of a vessel as passage in a three-dimensional navigation space and to identify bathymetric navigation with three-coordinate positioning of the vessel with a visual triaxial representation of the route with a constant indication of the depths field under the ship's keel. The third coordinate is taken into account in the form of a depth mark, which is ignored when sailing on the high seas, but is mandatory in the coastal navigation for the accident-free transit of the vessel in the restricted navigation conditions. A scientific hypothesis about the prospects of mathematical operation of the bathymetric database from the standpoint of the theory of functions approximation is put forward. It is assumed that mathematical modeling of the seabed relief genesis can be effectively implemented on the basis of an adapted hybrid B-spline model with simultaneous display of underwater topography in the electronic mapping system. The expediency of using spline structures in the mathematical support of the on-board computer for creating a realistic synthesized image of the digital model of the bottom is substantiated. A virtual reconstruction of underwater topography is being tested on the basis of our own software developments with the actual refusal to appeal to the foreign applied projects. A three-dimensional computer visualization of a bathymetric chart fragment of the Chatham Strait is performed using the spline approximation method in order to demonstrate the principle operability of the proposed algorithm. It is concluded that when navigating with synchronous representation of bathymetry data, visual safe navigation is provided in conditions of a minimum under keel clearance based on the computer visual effect of the constant positioning of depth. A comparative assessment of methods for creating bathymetric charts is given, and the advantages and disadvantages of each mathematical approach are considered. The aspects of applying the mathematical apparatus of spline functions in the research of the problem of studying natural disasters of the Earth are expanded. The issue of applicability of digital bathymetry for numerical modeling of operational forecast of tsunami propagation is considered. It is assumed that the use of spline functions method in bathymetry will optimally update the planning horizon for creating a new generation of three-dimensional electronic navigational charts.
It has been assumed about the hypothetical possibility of independent control of the ship isolinear movement in the presence of special equipment on board that can constantly determine the values of the parameters of the navigation isoline, taking into account the changing of geometric characteristics. It is possible that the sequence of approximated navigation data can be an argument for calculating continuous values of the true course with synchronous transmission of commands to the steering wheel to ensure adaptive self-regulating movement of the vessel. The need to use the approximation of navigation functions is justified by the expert ability for the fast calculation the functionals of analytical inflections of spline isolines, interpreted in mathematics as characteristic points of changing the signs of derivatives, but corresponding in practical application to the signals of automatic command submission to ship controls in the form of a rudder and a telegraph. The technology of using spline functions for navigation through geophysical fields is considered on the specific example of reconstructing the chart of the anomalous gravity field in Peter the Great Bay from the data of trajectory measurements of an autonomous uninhabited underwater vehicle. Computer simulation of gravimetric procedures based on a hybrid algorithm of two-dimensional B-spline approximation as a reference geophysical field for matching with the data of measurement studies is performed. As a proof of the efficiency of the proposed approach, a three-dimensional synthesis of a fragment of the field of gravity anomalies in the Japanese Sea region is implemented. It is noted that computer visualization of the 3D format of the programmed ship movement provides the possibility of intellectual assistance to the navigator in the strategy of instantaneous determination of the ship position under any circumstances of navigation. The approved spline algorithms can serve as harmonized support for the sefarer's staff when making a competent decision on the management of the vessel in any emergency situation. The theoretical possibility of practical application of the theory of spline functions to the approximation of the newest isolines, the introduction of which in the navigation of the future is associated with the innovations of technical means of navigation, is predicted. It is assumed that isolinear passages through geophysical fields can be effectively used in the unpredictable conditions of modern shipping, under various force majeure circumstances and natural disasters, and become a real autonomous alternative to the satellite navigation.
The paper focuses on the understanding of informativity as a measure that determines the effectiveness of using the geophysical field to obtain a position fixing. The factology of map-aided navigation is revealed as a sequence of instantaneous comparison of navigation measurements with the standard of informativity of field stored in the memory of the on-board computer. Correlation-extreme navigation is synchronized with the parallel task of organizing an informative path as the best optimal trajectory of movement in three-dimensional space when following a marine mobile object in a given direction, taking into account restrictive obstacles. An explanation of the understanding of innovative navigation as a "binding" of measurements to a standard based on the search for the global extremum of the functional of correlational comparison of the measured fragment with the informativity of the geophysical field chart is given. The navigation process is interpreted into an extreme task of route planning as a tactical spline method of the roadmap in a conflict environment, taking into account the factor of avoiding navigational hazards.The assumption on developing the technology of correlation-extreme navigation using the methods of spline functions as a realization of the practical navigability of a perspective concept in the full scope of the progressive capabilities of an autonomous project is made. In the development of the idea of correlation-extreme navigation, a threedimensional synthesis of a geophysical field fragment based on reproduced digital values from an isolines contour chart is implemented to create a hybrid B-spline approximation of a possible reference standard of informativity. The disadvantages of traditional methods of processing navigation information in the project of correlation-extreme navigation are analyzed. It is noted that the spline algorithm is mathematically devoid of the «curse of dimensionality» phenomenon as the main difficulty in achieving the speed of computational implementations of alternative methods of nonlinear filtering. The hypothesis of the possibility of using the proposed approach as a mathematical support for the future automated navigation system with artificial intelligence within the framework of the unmanned navigation concept in accordance with the e-Navigation project is put forward.
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