Two algorithms of geodesic line length calculation considering elevation in eLoran systems

Abstract

Abstract The existing LOng RAnge Naviating System stations are mostly used by marine users and are situated at offshore, low‐altitude locations. As a result, the impact of height on the system's positioning accuracy is usually ignored. However, the direct transplantation of low‐altitude calculation methods to high‐altitude areas will bring errors in the positioning results due to the lack of elevation consideration. In order to improve the accuracy of the new enhanced Loran system and reduce the error caused by the calculation of the geodetic line length without considering elevation in high altitude areas, this paper proposes two different algorithms to establish new reference ellipsoids to reduce the height‐caused error, namely the direct algorithm and the expansion ellipsoid algorithm. Experiments show that the error of the calculation results by direct algorithm is smaller, except that it is not applicable when the azimuth is 90° or 270°. The new ellipsoid created by expansion ellipsoid algorithm has smaller changes, and the elevation and geographical coordinates can be considered independent, which is more in line with the Loran system's application requirements.

Keywords

• geodesy
• Loran
• position, navigation and timing (PNT)