Study and Comparison of Hyperbolic and Pseudorange Positioning Algorithms in the eLoran System

Abstract

The positioning algorithms of the Enhanced Long-Range Navigation (eLoran) system primarily include the hyperbolic positioning algorithm and the pseudorange positioning algorithm. However, the calculations present in the existing literature are inaccurate and lack empirical data, and a thorough and precise comparison of the two algorithms has yet to be conducted. Therefore, this paper employs a combination of simulation analysis and empirical analysis to explore these two positioning algorithms in depth, with an optimization of the initial position calculation in the pseudorange algorithm. Under ideal conditions without observational errors, through precise calculations and analysis, the positioning errors of both algorithms are approximately zero, and full-area solutions can be achieved. Under conditions with observational errors, this study shows that both algorithms exhibit positioning errors, with the pseudorange algorithm achieving a level of accuracy comparable to that of the hyperbolic algorithm. At the same time, the empirical analysis further verified this conclusion. Additionally, this study found that the pseudorange positioning algorithm demonstrated better applicability in practical applications, as it successfully resolved the multivalued and singularity issues present in the hyperbolic positioning algorithm.