Rigorous Propagation of LiDAR Point Cloud Uncertainties to Spatially Regular Grids by a TIN Linear Interpolation

Airborne light detection and ranging (LiDAR) has been widely applied to terrain modeling, but a gridded digital elevation model (DEM) is usually adopted for most applications. The LiDAR point cloud is transformed to grids by interpolation methods, with triangulated irregular network (TIN) linear interpolation most widely used. Both horizontal and vertical uncertainties exist in a point cloud dataset and should therefore be propagated to grid points during spatial interpolation. Studies in the literature have either considered the vertical component only or both components separately. This letter proposes to apply the general law of propagation of variances (GLOPOVs) to estimate vertical uncertainties at grid points for TIN linear interpolation considering both horizontal and vertical uncertainties of the point cloud simultaneously. The experimental results with an airborne LiDAR dataset indicate that underestimation of grid point vertical uncertainties may be derived if only vertical uncertainties of the point cloud are considered; the amount of underestimation depends on the terrain slope. This letter suggests that both horizontal and vertical uncertainties of point cloud should be considered during TIN linear spatial interpolation. The effect of correlated errors between LiDAR points is also examined. It is shown that if significant correlation between points is ignored, the resulting propagated TIN error is underestimated by a factor of almost 2.