Abstract
For the shape sensing of long-range cables, we study a shape sensing method that utilizes the strain data from optical fibers installed around the cable. We estimate the shape by solving the equation of a moving frame whose coefficient contains the curvature and twist rates obtained by the strain data. The estimation error process is formulated by a stochastic differential equation, and the error variance is obtained by solving the variance equation. The obtained theoretical error variance indicates that the shape estimation error becomes maximum when the curve is straight, and the general curve's error is smaller than that for the straight line. We validated these results by numerical simulation.
