Models, algorithms, and measurements for underwater acoustic positioning

Several problems in underwater acoustic position estimation are investigated within the context of their associated models, algorithms, and measurements. The first appendix provides a detailed discussion of these concepts and demonstrates the fact that simultaneous consideration of all three is necessary in order to properly address a particular position estimation problem. The particular problems addressed herein stem from the so-called long baseline underwater acoustic positioning method whose principle of operation is hyperbolic multilateration; a technique employed in the now common Global Positioning System and its predecessor systems such as Long Range Navigation (LORAN), Decca and Omega. Although motivated by this application, many of the results are quite general and can be applied to other types of positioning systems and other types of problems. The first manuscript investigates the problem of position estimation in an inhomogeneous medium. The second manuscript treats the problem of geodetic position estimation of underwater acoustic sensors placed at fixed but unknown locations on the seafloor where the goal is to obtain the most accurate positions possible from the available measurements. The third manuscript addresses the problem of optimal recursive non-linear estimation for non-linear measurement models by application of a newly proposed algorithm to underwater acoustic positioning. It is referred to as the two-step estimator and is shown to work well with certain models but has difficulty with the newer models developed in the previous manuscript. The last manuscript develops an approach to obtaining the covariance matrix for an estimate when there are multiple input parameters with error, multiple output variables to be estimated, and the functional relationship is non-linear. To accomplish this, a novel two-step procedure is developed that linearizes with respect to the parameters and then with respect to the variables. The method is quite general and is presented in a general form. An example is provided by applying the method to the hyperbolic underwater acoustic positioning model. The accuracy of the method is verified by numerical study using Monte Carlo simulation