# A Method for Determining the Directional Angle of a Railway Route Based on Field Measurements

## TL;DR

This paper introduces a method to determine the directional angle of a railway route using field measurements when satellite signals are unavailable.

## Contribution

A novel method for calculating the directional angle of railway routes using inertial systems and Cartesian coordinates is proposed.

## Key findings

- The method uses Cartesian coordinates of the track axis to determine the directional angle.
- The accuracy of the method is evaluated using a model geometric layout.
- An example demonstrates how the directional angle is calculated from measurement data.

## Abstract

The most effective method for determining the coordinates of the railway track axis is based on using mobile satellite measurements. However, there are situations in which the satellite signal may be disturbed (due to field obstructions) or completely disappear (e.g., in tunnels). In these situations, the ability to measure the value of the directional angle of a moving rail vehicle using an inertial system is useful. The directional angle is determined on a topographic map as the angle between the direction of the vehicle’s longitudinal axis (or the direction of a tangent to the track axis) and the reference direction, which is the north. This article presents a method for determining the directional angle of a railway line based on appropriate measurement data. The latter should be Cartesian coordinates of the track axis, allowing for the visualization of a given railway route and permitting a general orientation of its course to be obtained. The presented proposal for solving the problem refers to the assumptions made in the method for determining the curvature of the railway track axis using the moving chord. The assumptions of the proposed method for determining the directional angle of the railway route are discussed, along with the appropriate computational algorithms. The accuracy of this method is assessed using the adopted model geometric layout. Reference is also made to the appropriate method for determining the curvature of the railway track axis. In conclusion, we provide an example of determining the directional angle based on measurement data.