When assessing the relative altitude of a small unmanned aircraft system above a digital elevation model, digital terrain model, or digital surface model (henceforth collectively referred to as “model”), there are a number of variables that affect the accuracy of that determination. Inherent “errors” that reside in the variables at play in the interaction, along with the structure of the model, create an environment in which there is an area of positional uncertainty that determines an altitude range wherein the true altitude resides.
Cardinal Geospatial has explored the variables at play – models (DEM/DTM/DSM), sUAS positioning, and altitude conversions – and how errors inherent in each affect the interplay amongst themselves as a sUAS is in flight.
Perhaps the most challenging variable to account for is the positioning of the sUAS. Error in the horizontal and vertical accuracy of sUAS stems largely from the type of equipment being used onboard. The less accurate these systems are, the more error is introduced and the higher the uncertainty of the position of the sUAS. Horizontal position accuracy while the sUAS is in flight is the least documented source of error and is mainly reported in user manuals specific to each sUAS. Unfortunately, due to many manufacturers not providing extremely detailed reports of their products’ accuracy, specific values on sUAS accuracy may be difficult to obtain. However, Transport Canada now has accuracy requirements stating that an sUAS must have lateral position accuracy of at least 10m +/- and altitude accuracy of at least 16m +/- while operating within controlled airspace. This provides us with some amount of guidance as to the maximum amount of uncertainty we can expect to encounter in our sUAS equipment.
Higher resolution data sources for model development tend to yield higher accuracy models with smaller cell size. The cell size of a model represents how many ground truth units squared (e.g. meters squared) each pixel in the raster represents. For example, a very detailed DEM may have pixels that represent less than a square meter in the real world, while LANDSAT data has a pixel size of 30 square meters (usgs.gov). With larger cell sizes, some degree of accuracy is lost due to the fact that the earth does not exist with elevations averaged out among giant 30m squares. Therefore, it can be assumed that there is some degree of variation within each raster pixel beyond the value that it displays. The figure below illustrates a simplified look into how model cell uncertainty (e.g. the uncertainty of which cell the sUAS “occupies”) contributes to our overall minimum requirements for sUAS altitude. We cannot be certain which of the four raster cells presented the sUAS is occupying (note red “bubble of uncertainty” around the drone image). This means that general sUAS error in the XY axis can create an additional layer of uncertainty even if presented with a perfect elevation or surface model.
The sUAS could occupy infinite points within multiple cells within the XY “bubble of uncertainty” for the flight itself. It is important to note that each cell of a raster is merely an interpolated average of the physical location it represents. This suggests that there will be some real-world variation within each raster cell.
In a scenario where the cell size of a given DSM raster is large enough that the sUAS’ XY plane bubble of uncertainty can be assumed to occupy only one cell, then any error present in the model’s creation will be heavily weighted in the overall equation to determine sUAS spatial uncertainty. Higher quality and higher accuracy models will have a smaller cell size and therefore more uncertainty for the sUAS to know for certain which cell(s) it occupies, however, the difference between the smaller cells will be overall smaller. Whereas lower quality and lower accuracy models will likely have a larger cell size and therefore it is easier to determine the cell that the sUAS occupies, but the value of the cell will be a very imperfect representation of the true terrain. Ultimately, the relationship between inter-cell differences and intra-cell error will need to be taken into consideration when flight planning and choosing an appropriately detailed model for obstacle avoidance.
Taking the previously presented sUAS positional uncertainty and occupied model cell uncertainty theory in mind, we can suggest that high quality, high accuracy, and small cell size DSM rasters are the preferred model due to the assumption that the model will be spatially accurate to the ground truth. While the true cell of sUAS spatial occupation will be unknown, as cell size decreases, the error between cells also decreases providing a more accurate and smoother model.
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