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• Author: Wacław Morgaś
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Open access

## Abstract

In its mathematical essence, the task of determining ship’s position coordinates, is to minimize appropriately defined goal function. This paper proposes to use the method of conjugate gradient for this purpose. The reason is that calculations may be performed in some seconds time because Microsoft and Apache implemented the conjugate gradient method as a tool called the Solver and embedded this tool in their widely offered and popular spreadsheets, namely Excel and the Open Office Calc, respectively. Further in this paper it is shown how to precisely assess errors of ship’s position coordinates with the Monte Carlo method that employs the Solver.

Open access

## Abstract

This paper presents mathematical interdependences in converting geodetic coordinates into flat rectangular coordinates and inverse transformation recommended in the Ordinance by Prime Minister on the State System of Spatial References. It especially presents formulas contained in works by M. Hooijberg (1997) Practical Geodesy and R. Kadaj (2001) Projection Formulas and Parameters of Coordinate Systems. G-1.10. In order to illustrate uses of the presented formulas relevant calculation examples based on the reference ellipsoids WGS 84 and GRS 80 are included.

Open access

## Abstract

Proposals of algorithms for solving Navigation faculty’s problems regarding navigation along rhumb line (loxodrome), for officer trainees and civil students of Faculty of Navigation and Naval Weapons and for deck seamen on operational level, are presented in this paper. Proposals of calculation algorithms given in the article cover simple mathematical totting based on plane sailing (navigational) triangle and Mercator triangle (Mercator sailing). The algorithms refer to traditional methods of solving problems and they do not cover solutions applicable in automated (integrated) navigational systems.

The formulas enable to solve the tasks with a use of electronic calculator and application of traditional methods on plane and sphere, and they also take the Earth’s ellipsoidal shape into consideration.

Open access

## Abstract

This article presents mathematical dependence relations used for direct conversion of geodetic coordinates into UTM (Universal Transverse Mercator) and inverse conversion recommended by military standards. It mainly focuses on some formulas taken from the National Geospatial- -Intelligence Agency publication NGA.SIG.0012_2.0.0_UTMUPS - March25, 2014 and additionally from IHO Manual of Hydrography published by the International Hydrographic Office. In order to illustrate application of the presented formulas the article includes some relevant calculation examples on the reference ellipsoid WGS 84 (World Geodetic System of 1984).