Assessing the accuracy of ship position through real-time measurements
Authors: Loginovsky V. A. 
Published: August 2024

One of the most important tasks of shipping for ensuring the efficiency and safety of navigation is accurately determining the ship position during the voyage. Research on the accuracy of finding a ship coordinates is always at the top of the list of urgent navigational issues, even nowadays with the widespread implementation of state-ofthe-art information technologies and the progress of navigation systems and techniques. If to follow measurement standards, there are two close terms applied in marine navigation in this context. They are “accuracy” and “precision” of measurements, which in principle might confuse the understanding of the task onboard the ship. In marine navigation, the traditional understanding of ship current position accuracy is to assess the impact of a combination of random errors in measured navigation parameters on random errors in computed coordinates. Two-dimensional confidence intervals centered on the fixed ship position serve as a graphical representation of the assessed accuracy, which is algebraically, might be described by the covariance matrix of coordinate errors. As a result of the high level of uncertainty caused by the effect of random errors in real-time measurements, it is impossible to assess the accuracy of ship position during the voyage. The magnitude and mathematical sign of these errors are unknown, and the navigation parameter indications themselves do not provide any information on their accuracy. For this reason, a priori prediction of the precision of navigation parameters associated with certain sets of measurements made in the past under specific standard conditions are used to assess the accuracy of the real-time ship position. This priori data inspires to substitute the concept of accuracy of the real-time ship position with the concept of precision of the navigation system, technique, or device operation, which is essentially the theoretical inconsistency. The purpose of this study is to partially solve this inconsistency. The study outcome is a proposed indicator that, by using information gathered from redundant measurements of navigation parameters obtained in real time without the use of priori data, can indirectly assess the accuracy of the real-time fixed coordinates of the ship position. The indicator concept is based on assessing the area of the real-time figure of errors. This area is limited by its outer contour of position lines and has a high degree of measurement redundancy to guarantee that, the probability of locating the true point within this figure is 100 %. In addition to having high precision features, modern navigation technology also makes it possible to handle a larger volume of measurement data utilizing contemporary technologies, such as Big Data platforms, which do not restrict the number of measurements. Consequently, higher number of navigation measurements can significantly raise the probability of finding the true position in the ensuing complicated figure of errors. The shape of the figure allows for a spatial analysis of the proximity of potential navigational hazards and the ship location, by using, for example, the least squares method. The area of such a figure is a characteristic of the uncertainty (an analog of precision) of coordinate errors, and its minimum area provides the best accuracy. The ability to determine the real-time figure area with sheer certainty of existing the true point in it stimulates the development of the next more technologically advanced and encouraging level of alternative and autonomous methods for determining the vessel position. These methods are based primarily on the possibility of increasing the volume of processed measurement information. It directly relates, for example, to the development of azimuthal methods of nautical astronomy, which make it possible to perform an unlimited number of autonomous navigation measurements in the absence of a visible horizon, which undoubtedly becomes valuable when ships are sailing in high latitude regions, especially during a long period of polar night.