Gray, Douglas A.Anderson, Brian D.O.Bitmead, Robert R.2026-04-062026-04-060364-9059ORCID:/0000-0002-1493-4774/work/174739591https://hdl.handle.net/1885/733808152The dynamical behavior of a thin flexible array towed through the water is described by the Paidoussis equation. By discretizing this equation in space and time a finite dimensional state space representation is obtained where the states are the transverse displacements of the array from linearity in either the horizontal or vertical plane. The form of the transition matrix in the state space representation describes the propagation of transverse displacements down the array. The outputs of depth sensors and compasses located along the array are shown to be related in a simple, linear manner to the states. From this state space representation a Kalman filter is derived which recursively estimates the transverse displacements and hence the array shape. It is shown how the properties of the Kalman filter reflect the physics of the propagation of motion down the array. Solutions of the Riccati equation are used to predict the mean square error of the Kalman filter estimates of the transverse displacements.Manuscript received January 20, 1993; revised April 25, 1993. This work was performed while one of the authors (D. A. Gray) visited the Department of Systems Engineering at the Australian National University. This work was supported by the Australian Department of Defence. D. A. Gray is with the Department of Electrical Engineering, University of Adelaide, Adelaide, South Australia. He is also with the Cooperative Research Centre for Sensor Signal and Information Processing. B. D. 0. Anderson and R. R. Bitmead are with the Department of Systems Engineering, Australian National University, Canberra, ACT, Australia. They are also with the Cooperative Research Centre for Robust and Adaptive Systems. IEEE Log Number 921 1450.14en199310.1109/48.2623040027677565