The development of new stochastic terrain gridding methods are necessitated by new tire and vehicle modeling applications. Currently, grid node locations in the horizontal plane are assumed to be known and only the uncertainty in the vertical height estimates is modeled. This work modifies the current practice of weighting the importance of a particular measured data point (the terrain height at some horizontal location) by the inverse distance between the grid node and that point. A new weighting function is developed to account for the error in the horizontal position of the grid nodes. The geometry of the problem is described and the probability distribution is developed in steps. Although the solution cannot be determined in closed form, an estimate of the median distance is developed within 1% error. This more complete stochastic definition of the terrain can then be used for advanced tire modeling and vehicle simulation.

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