This report describes an empirical analysis of a motion model that has been used to generate random submarine tracks for an antisubmarine warfare tactical decision aid. The model describes a submarine's motion as a series of transitions between the square cells of a grid that covers a defined operating region. A 3 x 3 transition matrix is associated with each cell of the grid which determines the submarine's transitions from a cell. The set of transition matrices define a Markov process. Despite its discrete nature, this Markov track generating process has been called a diffusion process in antisubmarine warfare tactical decision aid literature. The transition matrices are determined by tracks generated by an auxiliary stochastic process that is presumed to be of higher fidelity but more costly to implement than the Markov process.