Terrain navigation for underwater vehicles

Abstract: In this thesis a terrain positioning method for underwater vehicles called the correlation method is presented. Using the method the vehicle can determine its absolute position with the help of a sonar and a map of the bottom topography. The thesis is focused towards underwater positioning but most of the material is directly applicable to flying vehicles as well. The positioning of surface vehicles has been revolutionized by the global positioning system (GPS). However, since the GPS signal does not penetrate into the sea water volume, underwater vehicles still have to use the inertial navigation system (INS) for navigation. Terrain positioning is therefore a serious alternative to GPS for underwater vehicles for zeroing out the INS error in military applications. The thesis begins with a review of different estimation methods as Bayesian and extended Kalman filter methods that have been used for terrain navigation. Some other methods that may be used as the unscented Kalman filter or solving the Fokker-Planck equation using finite element methods are also discussed. The correlation method is then described and the well known problem with multiple terrain positions is discussed. It is shown that the risk of false positions decreases exponentially with the number of measurement beams. A simple hypothesis test of false peaks is presented. It is also shown that the likelihood function for the position under weak assumptions converges to a Gaussian probability density function when the number of measuring beams tends to infinity. The Cramér-Rao lower bound on the position error covariance is determined and it is shown that the proposed method achieves this bound asymptotically. The problem with measurement bias causing position bias is discussed and a simple method for removing the measurement bias is presented. By adjusting the footprint of the measuring sonar beams to the bottom topography a large increase in accuracy and robustness can be achieved in many bottom areas. This matter is discussed and a systematic theory about how to choose way-points is developed. Three sea-trials have been conducted to verify the characteristics of the method and some results from the last one in October 2002 are presented. The sea-trials verify to a very high degree the theory presented. Finally the method is briefly discussed under the assumption that the bottom topography can be described by an autoregressive stochastic process.