Position estimation of a towed underwater body

The following ocean engineering problem is considered. An underwater body, to be called hereafter the fish, is towed by a surface ship, at a depth of 100 m approximately. The purpose of the experiment is to make observations of the, bottom of the sea, a few kilometers below. In order to be able to use this moving array as a synthetic array, one needs to know with an accuracy of 10 cm, the trajectory of the fish relative to its otherwise unknown initial position, during a short experiment of approximately 30s. For this purpose, acceleration measurements provided by an INS (inertial navigation system) located on board the fish, can be integrated. In the problem of interest here, an additional difficulty is that the satellite involved in GPS cannot provide any position estimate of an underwater body such as a towed fish, but only position estimates of the surface ship. The idea described in this paper, is to introduce a numerical model for the towing cable, in order to transform GPS measurements of the surface ship position into measurements of the towed fish position, so as to be able to combine these measurements with INS measurements