Simulation and numerical modeling for sonar systems analysis--An overview

Although somewhat arbitrary, models can be categorized as being analytical, numerical and/or simulation models. Analytical models are those models for which the mathematical expression can be solved in "analytical" or "closed" form. Numerical models are those for which solutions are obtained using "numerical analysis" techniques, usually evaluated using a computer. Numerical models include analytical models which are implemented on a computer for ease in obtaining solutions (and generating results in graphical form) for a variety of alternative conditions. Numerical sonar models generally include analytical submodels which describe the various physical phenomena implicit in the prototype, such as spherical spreading with range and absorption loss with frequency. Numerical models also include those models for which closed-form, analytical solutions to the equations cannot be found for the conditions of interest, and, hence, require numerical techniques to obtain solutions. Simulation Models are those models which include in some sense the dynamics of the prototype being modeled. This includes models which represent dynamic systems that produce outputs which unfold in time in response to time-varying inputs or parameters. It includes models which produce statistical realizations of the response of a system to random inputs or with randomly varying parameters, as in time series generation models for use in single or multiple Monte Carlo simulations. It is noted that simulation models can be constructed from analytical or numerical models which produce closed-form or numerically-derived solutions, respectively, to individual stimuli; however, when the analytical or numerical models are implemented for a contiguous sequence of dynamic stimuli, they become simulation models. Since simulation models are usually sufficiently complex to require implementation on a computer, they generally can be considered a subset within the numerical model category.