Computational and Statistical Aspects of Determining Ship’s Position

Antoni Drapella and Wacław Morgaś 1

1Polish Naval Academy, Gdynia, Poland

2Polish Naval Academy, Gdynia, Poland

DOI: 10.1515/aon-2017-0001


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.


determining ship’s position, the Least Square method, conjugate gradient, the Monte Carlo method.


[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.