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This paper examines the role played by vehicle models and their impact on the performance of sensor-based navigation systems for autonomous land vehicles. In a navigation system, information from internal and external vehicle sensors is combined to estimate the motion of the vehicle. However, while the issue of sensing and effects of sensor accuracy have been widely studied, there are few results or insights into the complementary role played by the vehicle model. This paper has two main contributions: a theoretical analysis of the role of the vehicle model in navigation system performance, and an empirical study of three models of increasing complexity, used in a navigation system for a conventional road vehicle. The theoretical analysis focuses on understanding the effect of estimation errors caused by approximations to the "true" vehicle model. It shows that while substantial performance improvements can be obtained from better vehicle modeling, there is, in general, no definitive "best" model for such complex nonlinear estimation problems. The empirical study shows that an appropriate choice of a higher order model can lead to significant improvements in the performance of the navigation system. However, the highest order model suffers from problems related to the observability of some of its parameters. We show how this problem can be overcome through the imposition of weak constraints.