Computational and Statistical Aspects of Determining Ship’s Position

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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.

[1] Fletcher R., Reeves C. M., Function minimization by conjugate gradients, ‘The Computer Journal’, 1964, Vol. 7, Issue 2, pp. 149–154.

[2] IALA Guideline 1111, Edition 1, May 2015.

[3] Kopacz Z., Morgaś W., Urbański J., Evaluation of the accuracy of the ship’s position [in Polish], AMW, Gdynia 2007.

Annual of Navigation

The Journal of Polish Navigational Forum

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