UAS Mapping of an Active Gravel Pit: RMSE vs. 95% Confidence
A 40-acre gravel pit expansion is to be mapped by UAS photogrammetry for a 1-ft contour site plan. You fly a DJI Matrice 300 RTK with a 45 MP camera at 250 ft AGL, yielding about 1.1 cm GSD. You place 9 ground control points and 15 independent checkpoints. The bundle adjustment reports horizontal RMSE 0.08 ft and vertical RMSE 0.13 ft at the checkpoints. The client's specification is 0.10 ft horizontal and 0.15 ft vertical at 95% confidence. A stockpile volume is needed to 2% accuracy. The site has 30-ft high walls, a conveyor, and active haul trucks. The flight was at 11:00 with a sun angle of 38 degrees and 8 mph wind. The point cloud shows bowl distortion near the pit walls and a 0.4-ft vertical seam between two flight lines.
1. Does the project meet the stated accuracy specification? Show the reasoning.
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The specification is written at 95% confidence, not as RMSE. For a normal distribution, 95% vertical error is about 1.96 times RMSE = 1.96 times 0.13 = 0.25 ft, which exceeds 0.15 ft. Horizontal 95% is about 1.96 times 0.08 = 0.16 ft, which exceeds 0.10 ft. Therefore the project does not meet the stated 95% specification, even though the RMSE values themselves are below the numbers. If the contract actually meant RMSE, the project would pass; clarify the specification in writing. With 15 independent checkpoints, the estimate is reasonably robust, but the checkpoints must be well distributed and independent of the control points. The 0.4-ft seam already shows a systematic error larger than the vertical RMSE, so the surface is not ready for 1-ft contours.
2. What causes the bowl distortion and the 0.4-ft seam, and what flight or control changes would you make?
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Bowl distortion near 30-ft walls is a classic photogrammetric problem: insufficient oblique views, poor camera calibration, control points concentrated on flat ground, and shadowed or textureless walls. The 0.4-ft seam between flight lines indicates a block-adjustment or strip-alignment problem, possibly from wind, changing light, insufficient overlap, or control points not spanning the site. Improve by adding oblique imagery around the pit perimeter, increasing forward and side overlap to about 80/70, flying cross strips, distributing control points around the perimeter and at elevation extremes, using RTK or PPK and validated targets, and avoiding active haul trucks. Recalibrate the camera and process with independent checkpoints. For 1-ft contours, the vertical surface must be much better than the current seam.
3. How would you design the stockpile volume check to achieve 2%?
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Design the volume check around the stockpile geometry and the required 2%. A 30-ft stockpile with 2% volume tolerance is sensitive to toe and top breaklines; a 0.2-ft vertical bias over the whole surface can exceed 2%. Use the UAS surface for the stockpile, but collect independent checkpoints with total station or terrestrial laser, especially at the toe, top, and steep faces. Compute volumes from the same base surface and breaklines, and compare TIN and grid methods. Remove vegetation and equipment, and do not mix surfaces from different flights. Report the volume, cutoff grade, surface accuracy, and a confidence statement; if the check exceeds 2%, reflight or use a terrestrial laser for the stockpile.