Dynamics of a towed cable with sensor-array for underwater target motion analysis

The underwater target motion analysis is performed using bearing-only measurements, obtained from a sensor-array, which is towed by an own-ship through a connected cable. It is well known that the own-ship is required to perform a manoeuvre in order to make the system observable and localize the target successfully. During the manoeuvre, it is important to know the location of the sensor-array with respect to the own-ship. This paper develops a dynamic model of a cable sensor-array system to localize the sensor-array, which is towed behind a sea-surface vessel. A lumped-mass approach is adopted to represent the towed cable. The discretized cable elements are modelled as an interconnected rigid body, kinematically related to one another. The governing equations are derived by performing the moment balance condition and quasi-static equilibrium condition at each node, thereby incorporating the rotational inertia effects of own-ship motion on the towed body, which is a novel aspect of the proposed approach. The derived dynamics are solved simultaneously for all the nodes to determine the orientation of the cable and sensor-array. The position of the sensor-array obtained from this proposed model will further be used by target motion analysis algorithms to enhance the accuracy of the tracking system. The proposed model is implemented for various own-ship manoeuvres, and the resulting response of the towed system is presented graphically. The depth attained by sensor-array’s centre of gravity is compared to existing modelling approaches to validate its effectiveness.