Hybrid TLS–Tachymetry Framework for Geometric Axis Validation of a Steel Lattice Transmission Tower

This study presents a hybrid geodetic validation framework for assessing the geometric consistency of the axis of a steel lattice transmission tower determined from terrestrial laser scanning (TLS) data using an independently established tachymetric reference. Unlike previous investigations that focused on the influence of TLS scanner characteristics, registration strategies, or internal consistency of TLS-derived axes, the proposed approach introduces an external geodetic reference, enabling direct external assessment of TLS-based geometric axis estimation. The reference axis was determined at fourteen height levels, while the TLS axis was estimated from horizontal cross-sections of a point cloud acquired from multiple scanning stations and registered using a cloud-to-cloud method without control points. To enable direct comparison, both datasets were transformed into a common reference system using a seven-parameter Helmert transformation. The transformation was applied solely to remove differences between the independent local coordinate systems prior to the geometric comparison. Axis consistency was evaluated using residual vectors and three-dimensional distances between corresponding points. The mean deviation was 0.031 m, the RMS value was 0.033 m, and the maximum deviation reached 0.078 m. Larger discrepancies occurred predominantly in the upper sections of the structure, in a pattern consistent with the combined influence of TLS registration uncertainty, non-uniform point-cloud coverage, and local geometric conditions. A comparison of TLS axis estimators (centroid, LS-R regression, and PCA) showed that PCA produced an RMS value close to that of the centroid estimator, whereas LS-R produced a higher RMS value; the maximum deviation was lowest for the centroid estimator and highest for PCA. Regression analysis revealed a statistically significant linear trend in the X direction (p = 0.019), indicating residual systematic geometric drift after coordinate-system integration. The obtained discrepancies should be interpreted in the context of a rapid engineering TLS workflow performed without registration targets or a control network, rather than as the intrinsic accuracy of the TLS instrument itself. The proposed hybrid validation framework provides an objective quality-control methodology for evaluating TLS-derived geometric axes against independent geodetic observations and may support reliability assessment of TLS-based inventories and deformation monitoring of slender engineering structures.