Accurate, rapid estimation of epicentral distance, Δ, is essential for earthquake early warning systems. To improve Δ estimation, new methods to calculate the empirical relationship between the amplitude growth rate parameter, C, and Δ are investigated. Using orthogonal regression is most appropriate for application to EEW systems for Japanese high-speed trains. Evaluation using a K-NET dataset, of earthquake epicenters up to 200 km from the recording station, showed that the proposed method reduces maximum error from 546.2 km to 209.8 km. The percentage of correct estimations, defined as estimates within ±30% of the measured epicentral distance, is increased from 38.0% to 55.3%.