The concept of simulation-based engineering has been embraced by virtually every research and industry sector (Sinha, Liang et al. 2001; Mocko and Fenves 2003). Engineering and science communities have become increasingly aware that computer simulation is an indispensable tool for resolving a multitude of scientific and technological problems. It is clearly desirable to gain a reliable perspective on the behaviour of a system early in the design stage, long before building costly prototypes (Chul and Ro 2002; Letherwood, Gunter et al. 2004; Makarand Datar 2007; Ersal, Fathy et al. 2008; Mueller, Ferris et al. 2009). Simulation tools have become a critical part of the automotive industry due to their ability to reduce the time and money spent in the development process.

Terrain is the principle source of vertical excitation to the vehicle and must be accurately represented in order to correctly predict the vehicle response in simulation. In this dissertation, non-deformable terrain surfaces are defined as a sequence of vectors, where each vector comprises terrain heights at locations oriented perpendicular to the direction of travel. The evolution and implications of terrain surface measurement techniques and existing methods for correcting INS drift are reviewed as a framework for a new compensation method for INS drift in terrain surface measurements. Each measurement is considered a combination of the true surface and the error surface, defined on a Hilbert vector space, in which the error is decomposed into drift (global error) and noise (local error). It is also desirable to develop a compact, path-specific, terrain surface representation that exploits the inherent anisotropicity in terrain over which vehicles traverse. In order to obtain this, a set of analytic basis vectors is formed from Gegenbauer polynomials, parameterized to approximate the empirical basis vectors of the true terrain surface. It is also desirable to evaluate vehicle models and tire models over a wide range of terrain types, but it is computationally impractical to store long distances of every terrain surface variation. This dissertation examines the terrain surface, rather than the terrain profile, to maximize the information available to the tire model (i.e. wheel path data). A method to decompose the terrain surface as a combination of deterministic and stochastic components is also developed.