Direct georeferencing of airborne LiDAR data in national coordinates

The topographic mapping products of airborne light detection and ranging (LiDAR) are usually required in the national coordinates (i.e., using the national datum and a conformal map projection). Since the spatial scale of the national datum is usually slightly different from the World Geodetic System 1984 (WGS 84) datum, and the map projection frame is not Cartesian, the georeferencing process in the national coordinates is inevitably affected by various geometric distortions. In this paper, all the major direct georeferencing distortion factors in the national coordinates, including one 3D scale distortion (the datum scale factor distortion), one height distortion (the earth curvature distortion), two length distortions (the horizontal-to-geodesic length distortion and the geodesic-to-projected length distortion), and three angle distortions (the skew-normal distortion, the normal-section-to-geodesic distortion, and the arc-to-chord distortion) are identified and demonstrated in detail; and high-precision map projection correction formulas are provided for the direct georeferencing of the airborne LiDAR data. Given the high computational complexity of the high-precision map projection correction approach, some more approximate correction formulas are also derived for the practical calculations. The simulated experiments show that the magnitude of the datum scale distortion can reach several centimeters to decimeters for the low (e.g., 500 m) and high (e.g., 8000 m) flying heights, and therefore it always needs to be corrected. Our proposed practical map projection correction approach has better accuracy than Legat’s approach,¹ but it needs 25% more computational cost. As the correction accuracy of Legat’s approach can meet the requirements of airborne LiDAR data with low and medium flight height (up to 3000 m above ground), our practical correction approach is more suitable to the high-altitude aerial imagery. The residuals of our proposed high-precision map projection correction approach are trivial even for the high flight height of 8000 m. It can be used for the theoretical applications such as the accurate evaluation of different GPS/INS attitude transformation methods to the national coordinates.