Part I: Local representation of the clothoid

High-speed-railways also called bullet trains or Transrapid need extreme reliable control systems (extasy) to avoid catastrophic events. Here we consequently focus on two sensitive problems related to extasy: a local high resolution representation of the track design (clothoid, circle, straight line) in UTM map matching coordinates is given. The Mixed Model (universal Kriging) is used to discriminate measurement errors from track displacements. In this first part we develop the local high resolution representation of the clothoid (special case: circle, straight line) which is needed for creating an expert base of extasy.