TOWED ARRAY SHAPE ESTIMATION USING KALMAN FILTERS - THEORETICAL-MODELS

The dynamical behavior of a thin flexible array towed through the wate r is described by the Paidoussis equation. By discretizing this equati on in space and time a finite dimensional state space representation i s obtained where the states are the transverse displacements of the ar ray from linearity in either the horizontal or vertical plane. The for m of the transition matrix in the state space representation describes the propagation of transverse displacements down the array. 'rhe outp uts of depth sensors and compasses located along the array are shown t o be related in a simple, linear manner to the states. From this state space representation a Kalman filter is derived which recursively est imates the transverse displacements and hence the array shape. It is s hown how the properties of the Kalman filter reflect the physics of th e propagation of motion down the array. Solutions of the Riccati equat ion are used to predict the mean square error of the Kalman filter est imates of the transverse displacements.