This report treats the problem of tracking and predicting the motion of a hostile submarine using adaptive planning for the positioning of passive sonobuoys. When four or more buoys are deployed in a favourable way, a position estimate and a confidence ellipse for the estimate are obtained at each time step. Using a Kalman filter the future position of the target is predicted. The uncertainty in the future position estimate is determined and by keeping the maximum uncertainty for a position estimate in the predicted area under control the time point can be determined when a new buoy must be developed. The position for this buoy is then chosen in balance between the two requirements of minimal measurement uncertainty and maximal use of the buoy. Simulations show that the strategy works in the simple two dimensional model of the real world that the simulator knows.