A New Method for Loran-C ASF Calculation over Irregular Terrain

The finite-difference time-domain (FDTD) method is employed to improve the prediction accuracy of the Loran-C additional secondary factors (ASFs) over irregular terrains. The FDTD method is validated by comparing the results with the theoretical method with flat Earth formula, and then the ASFs are studied as functions of the mountain's slope gradient, height, and width, respectively. The cases with multiple mountains in the propagation paths are also studied. Numerical results show that when the gradient of the mountain is low, the FDTD and integral equation methods both perform well. However, when the gradient of the mountain is rather high, before the mountain area, the FDTD method predicts the ASFs oscillation caused by the reflected and scattered wave from the terrains, whereas the integral equation method is not applicable. Therefore, the FDTD method is better than the integral equation method in predicting Loran-C signals propagating over the region with serious irregularities. The measured ASFs of Loran signals are taken along two real paths between Pucheng and Qinling Mountains in Shaanxi Province, China. It is found that most of the measured and FDTD results have good agreement while some still have certain errors due to the model approximation measured. The ASFs change rapidly in the region with serious irregularities.