Applying Two Dimensional Kalman Filtering for Digital Terrain Modelling

Digital Elevation Models (DEMs) have been increasingly used to model the terrain surfaces to provide the 'physical bases' for environmental studies. However, DEM is subject to systematic errors, random noise and outliers. In this paper, a newly developed two dimensional (2-D) Kalman filtering approach to generating optimal estimates of terrain variables from a noisy grid DEM is introduced, which comprises a 2-D Kalman processor, a function for outlier detection and removal, and a two-step filtering procedure. The experiment of a simulated surface indicates that after applying the developed 2-D Kalman filtering technique the outliers of a DEM can be efficiently detected and well removed. The standard deviation of random noise of the DEM can be significantly reduced by approximately 70% for elevation and about 85% for the first partial derivatives of elevation, compared with their original values. The experiment of slope calculation shows that using this approach, the effect of random noise and outliers of slope can be efficiently reduced by more than 60% in terms of standard deviation, of the results derived from Arc/Info software using the same simulated DEM data.