Dynamics of a Towed Cable with Sensor-Array for Underwater Target Motion Analysis
Rohit Kumar Singh, Subrata Kumar, Shovan Bhaumik
TL;DR
This work tackles bearing-only target motion analysis by modeling a towed sensor array behind a ship using a lumped-mass cable representation. It derives Newtonian-dynamics-based governing equations, including moment balance and drag/heave interactions, to compute the orientation of each cable segment and the end sensor array in response to ship maneuvers. The resulting sensor-array position, particularly the CG of the array, feeds TMA algorithms to enhance tracking accuracy under dynamic conditions. A simulated engagement demonstrates that the model captures straight-line alignment and transient deviations during maneuvers, with eventual stabilization, highlighting its potential to improve observability and localization in BOT scenarios. Future work includes a generalized multi-segment framework and integration with state-estimation or control schemes for safe, optimal tracking of quiet submerged targets.
Abstract
During a war situation, many times an underwater target motion analysis (TMA) is performed using bearing-only measurements, obtained from a sensor array, which is towed by an own-ship with the help of 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 localise the target successfully. During the maneuver, 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 localise the sensor array, which is towed behind a sea-surface vessel. We adopt a lumped-mass approach 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 balancing the moments acting on each node. 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 TMA algorithms to enhance the accuracy of the tracking system.