Time Series Modeling of Terrain Profiles

Abstract

Every time we measure the terrain profiles we would get a different set of data due to the measuring errors and due to the fact that the linear tracks on which the measuring vehicle travels can not be exactly the same every time. However the data collected at different times from the same terrain should share the similar intrinsic properties. Hence it is natural to consider statistical modeling of the terrain profiles. In this paper we shall use the time series models with time being the distance from the starting point. We receive data from the Belgian Block and the Perryman3 testing tracks. The Belgian Block data are shown to behave like a uniformly modulated process ([7]), i.e. it is the product of a deterministic function and a stationary process. The modeling of the profiles can be done by estimating the deterministic function and fit the stationary process with a well-known ARMA model. The Perryman3 data are more irregular. We have to use the intrinsic mode function decomposition method ([2]). The first few intrinsic mode functions could be modeled in the same way as the the Belgian Block data. The residue part is a very smooth function which we may consider as a deterministic function.