Towed array shape estimation using Kalman filters-theoretical models - Oceanic Engineering, IEEE Journal of

The dynamical behavior of a thin flexible array array motion, becomes more critical. Typical of the more towed through the water is described by the Paidoussis equation. sophisticated towed array processing techniques are adaptive By discretizing this equation in space and time a finite dimenbeamforming [31, adaptive cancellation of tow vessel noise sional state space representation is obtained where the states are the transverse displacements of the array from linearity in either 141, bearing estimation using eigenvectors [ 5 ] , and ranging the horizontal or vertical plane. The form of the transition matrix techniques such as triangulation [6] or wave-front curvature in the state space representation describes the propagation of 171. transverse displacements down the array. The outputs of depth o n e way to overcome this problem is to instrument the array sensors and compasses located along the array are shown to be related in a simple, linear manner to the states. From this state with depth sensors and compasses; these give localized vertical space a ~~l~~~ filter is derived recursivelv and horizontal information of the transverse displacements of estimates the transverse displacements and hence the array shape. the array respectively. As an example, one approach would be It is shown how the properties of the Kalman filter reflect the to use the outputs of a depth sensor and compass located at physics of the propagation of motion down the array. Solutions each receiver to estimate its position. In practice, however, of the Riccati equation are used to predict the mean square error of the Kalman filter estimates of the transverse displacements. such a solution is neither econOmicall~ feasible and often, the number of sensors is too small to be able