The Impact of Developed Polynominal on Accuracy of Setting Down a Position’s Coordinates Based on Measurements of Two Bearings

Arkadiusz Narloch 1, Stanisław Kołaczyński 2

1Polish Naval Academy, Gdynia, Poland

2Polish Naval Academy, Gdynia, Poland

DOI: 10.1515/aon-2017-0008


An attempt to determine the impact of developing polynomial on the accuracy of setting
down a ship’s position coordinates based on measurements of two bearings has been
ventured in this paper. A navigation structure consisting of two aids has been analysed.
A ship maneuvering within a given area was setting down her position in respect to them.
As a result of this, numeral accuracy indexes were calculated. They gave principles for
conclusions regarding the impact of the distance between the aids of navigation on the
accuracy of setting down the position’s coordinates.


accuracy, navigation, positioning, terrestrial.


[1] Czaplewski K., The optimization of the set-up of the quotient navigational system
in relation to the mean error of the position with the simplex method [in Polish],
‘Zeszyty Naukowe AMW’, 1998, No. 2, pp. 5–14.
[2] Czaplewski K., The optimization of the navigational system based on the quotient
of the distances [in Polish], Doctoral thesis, Polish Naval Academy, Gdynia 1999.
[3] Czaplewski K., Positioning with Interactive Navigational Structures Implementation,
‘Annual of Navigation’, 2004, No. 7.
[4] Felski A., Specht C., Some aspects of the optimization in the utilization of DGPS
on South Baltic, ‘Zeszyty Naukowe AMW’, 1995, No. 3, pp. 21–29.

[5] Fortuna Z., Macukow B., Wąsowski J., Numerical methods [in Polish], WNT, Warszawa 1993.
[6] Gołąb S., The outline of higher mathematics [in Polish], Czytelnik, Warszawa 1948.
[7] Górski S., Jackowski K., Urbański J., Estimation of the accuracy of the navigation
[in Polish], WSM, Gdynia 1990.
[8] Kołaczyński S., Methodical and accuracy aspects of using the quotient of the distance as the navigational parameter to positioning [in Polish], ART Publishers,
Olsztyn 1978.
[9] Kołaczyński S., The expository content of results of inspected measurements of the depth
[in Polish], ‘Zeszyty Naukowe AMW’, 2013, No. 2, pp. 49–56.
[10] Kopacz Z., Morgaś W., Urbański J., Evaluation of the accuracy of the position of
the ship [in Polish], Polish Naval Academy, Gdynia 2007.
[11] Narloch A., The settlement of the position of the navigational sign erection in the digraph structure [in Polish], ‘Logistyka’, 2014, No. 6, pp. 974–979.
[12] Naus K., The influence of fatal errors on the accuracy of the ship’s position by means
of the method of the extended Kalman filter and the geodesic resistant settlement
[in Polish], ‘Logistyka’, 2014, No. 3, CD 1.
[13] Naus K., Narloch A., The distribution of the accuracy of coordinate appointive
with terrestrial methods in relation to two and three navigational signs [in Polish],
‘Logistyka’, 2014, No. 3, CD 1.
[14] Naus K., Wąż M., Accuracy in fixing ship’s positions by camera survey of bearings,
‘Geodesy and Cartography’, 2016, Vol. 60, No 1, pp. 61–73.
[15] Wiśniewski Z., Methods of the elaborations of measurements results in the navigation
and the hydrography [in Polish], Polish Naval Academy, Gdynia 2004.
[16] Wiśniewski Z., The algebra of the matrix. Probabilistic and statistical bases of the
adjustment theory [in Polish], ART Publishers, Olsztyn 1999.