Observer design for a towed seismic cable

We consider observer design for a towed seismic cable, attached to a depth controller at one end and with a prescribed motion at the other. Based on a finite number of measurements, a globally asymptotically stable observer is proposed. Locally, the proposed observer is exponentially stable. The stability analysis of the observer is based on Lyapunov theory. The existence and uniqueness of the solutions of the observer are based on semigroup theory. The implementation of the observer requires at least two measurements: the position of the cable, and the slope of the cable at the location of the depth controller.