Determining coordinates in a projected coordinate system of nodes on a towed wire

A system for determining coordinates for nodes on a wire 16 secured to tow lines 18a, 18b of a floating vessel 22 for analyzing geological formations is provided. The system includes sensors 24,28 in communication with a processor 32 to determine the coordinates of nodes and provide azimuths tangential to the wire. A library of nominal values for third, fourth, or fifth order polynomial coefficients, a library of known distances along the wire, and a library of preset limits can be stored in a data storage 34. The system includes computer instructions to receive sensor information, compute bearing, reorient the coordinates, rotate the azimuth, construct a third, fourth, or fifth order polynomial algorithm, compute the azimuth, form a residual, compute updated differences until the residual is within preset limits, calculate local coordinates for nodes, and rotate the local coordinates from the local coordinate system to the projected coordinate system.