The Loran-C Pseudorange Positioning and Timing Algorithm Based on the Vincenty Formula

Abstract

To improve the positioning accuracy of the Loran system and meet the requirements of Loran/BDS integrated positioning and timing, it is necessary to enhance the traditional Loran hyperbolic positioning method, making its pseudorange calculation consistent with the BDS positioning and timing solution. The existing pseudorange algorithm based on the Andoyer-Lambert formula has issues such as strict initial value selection range and susceptibility to singularities during calculations. This study proposes a new Loran pseudorange calculation method based on the Vincenty distance formula and conducts a simulation analysis of it. The results show that, in the absence of noise interference, the positioning and timing errors of this pseudorange algorithm are close to zero, demonstrating high accuracy. When subjected to random noise with a standard deviation of less than 100 ns, the latitude and longitude errors are both less than 10 m, and the timing error is less than 10−4 ns, meeting the requirements of Loran positioning and timing. Compared to the pseudorange algorithm based on the Andoyer-Lambert formula, the one based on the Vincenty formula has comparable positioning longitude accuracy but superior timing accuracy. Moreover, the latter offers a wider range of initial value selection and can avoid more singularity issues during calculations.

Keywords

• Loran-C
• positioning
• timing
• pseudorange
• Vincenty formula