Gaussian Process modeling of large scale terrain

This paper addresses the problem of large scale terrain modeling for a mobile robot. Building a model of large scale terrain data that can adequately handle uncertainty and incompleteness in a statistically sound way is a very challenging problem. This work proposes the use of Gaussian Processes as models of large scale terrain. The proposed model naturally provides a multi-resolution representation of space, incorporates and handles uncertainties aptly and copes with incompleteness of sensory information. Gaussian Process Regression techniques are applied to estimate and interpolate (to fill gaps in unknown areas) elevation information across the field. The estimates obtained are the best linear unbiased estimates for the data under consideration. A single Non-Stationary (Neural Network) Gaussian Process is shown to be powerful enough to model large and complex terrain, handling issues relating to discontinuous data effectively. A local approximation methodology based on KD-Trees is also proposed in order to ensure local smoothness and yet preserve the characteristic features of rich and complex terrain data. The use of the local approximation technique based on KD-Trees further addresses concerns relating to the scalability of the proposed approach for large data sets. Experiments performed on sparse GPS based survey data as well as dense laser scanner data taken at different mine-sites are reported in support of these claims.