A new towed array shape estimation technique using directional sensor outputs

Abstract

Based on Kennedy's (NUSC 93231-TMU-8-79, July 1979) analysis of Paidoussis's [J. Fluid Mech. 26, 717–751 (1966)] equation for the dynamics of a towed cylinder, a computer model has been developed, which estimates array shape using a Kalman filter, with directional sensor information as inputs. Kennedy and Rispin [J. Underwater Acoust. 30, 111–123 (1980)] have validated the concept that the propagation down the array of disturbances at the forward end of an array is governed by a dissipative and dispersive wave equation whose coefficients are functions of the ratio of the longitudinal to the transverse drag coefficient, array length, and tow speed. We formulate the partial differential equation describing array motion as a linear, discrete, state-variable, matrix difference equation with the state vector elements being the transverse displacements of specified array grid points. Using directional sensor outputs as the observations, the system has been shown to be observable. The model has been used to predict array motions using real sea data. Comparison of predictions to measurements are encouraging.