Determining the spatial coordinates of traction rolling stock using signals from unlimited track circuits with a locomotive receiver

Determining the spatial coordinates of locomotives, special self-propelled rolling stock, and the head cars of multiple-unit rolling stock is a fundamental task for train control systems. To solve this problem, floor-mounted sensors, odometry devices, and global navigation satellite system receivers have become widely used. Based on the mathematical apparatus of four-terminal network theory, this paper proposes calculation expressions for determining the current under the receiver coils of moving rolling stock at any position along the track. These same expressions can be considered as transcendental equations for determining the spatial coordinates of a traction rolling stock unit based on the known signal current under the receiving coils with a given adjustment at the feeder end. The obtained results can be used as mathematical support for solving the problem of positioning traction rolling stock under conditions of unstable operation of global navigation satellite systems.