Error propagation of stockpile volumetric calculations derived from aerial LiDAR data


Engineering Surveying; LIDAR

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Fritzvan der Merwe, University of Pretoria, South Africa,
Nico Luus, University of Pretoria, South Africa,


In an increasingly push-button driven technological world, it is important to know what errors can be encountered when it comes to calculating the volumes of assets where a monetary value is involved. There are an increasing number of aerial and terrestrial survey companies in Africa that use LiDAR technology to calculate volumes of stockpiles. In very few instances are any thought given to the possible errors in the systems. The general assumption seems to be that the sheer volume of measurements will cause all random errors to cancel out, while checks for systematic errors are performed before and after the surveys. LiDAR survey systems are complex combinations of several sensors.

The different elements of the systems and their precisions are discussed. An error prediction formula is derived by applying the General Law of Propagation of Variances. Using different laser scanner/IMU combinations, the contribution of the individual element errors to the total error in the 3-dimensional point coordinate was calculated to see how a better precision in one element might affect the overall precision. The results are illuminating in terms of the vertical and horizontal precision changes.

The propagation of variances in an interpolated DEM is investigated and combined with the laser precisions and volume calculations to obtain a final probable error which is quantified using vendor data and real measurements. It was concluded that the error can be significant in certain circumstances.

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