Stability and Interpretation of Autoregressive Models of Terrain Topology

Terrain topology is the principal source of vertical excitation into the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle models over a wide range of terrain, but it is computationally impractical to simulate long distances of every terrain type. A method to characterize terrain topology is developed in this work so that terrain can be grouped into meaningful sets with similar physical characteristics. Specifically, measured terrain profiles are considered realizations of an underlying stochastic process; an autoregressive model provides the mathematical framework to describe this process. The autocorrelation of the spatial derivative of the terrain profile is examined to determine the form of the model. The required order for the model is determined from the partial autocorrelation of the spatial derivative of the terrain profile. The stability of the model is evaluated and enforced by transforming the autoregressive difference equation into an infinite impulse response filter representation. Finally, the method is applied to a set of U.S. highway profile data and an optimal model order is determined for this application.