Developing stable autoregressive models of terrain topology

It is desirable to evaluate vehicle models over a wide range of terrain types, but it is computationally impractical to simulate over measured terrain. A method to characterise terrain topology is developed in this work to group terrain into meaningful sets with similar physical characteristics. Specifically, measured terrain profiles are considered realisations 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 profile. The stability of the model is evaluated and enforced by transforming the AR difference equation into an Infinite Impulse Response filter representation. Finally, the method is applied to a set of USA highway data and an optimal model order is determined for this application.