Empirical stochastic model of detected target centroids: Influence on registration and calibration of terrestrial laser scanners

The target-based point cloud registration and calibration of terrestrial laser scanners (TLSs) are mathematically modeled and solved by the least-squares adjustment. However, usual stochastic models are simplified to a large amount: They generally employ a single point measurement uncertainty based on the manufacturers' specifications. This definition does not hold true for the target-based calibration and registration due to the fact that the target centroid is derived from multiple measurements and its uncertainty depends on the detection procedure as well. In this study, we empirically investigate the precision of the target centroid detection and define an empirical stochastic model in the form of look-up tables. Furthermore, we compare the usual stochastic model with the empirical stochastic model on several point cloud registration and TLS calibration experiments. There, we prove that the values of usual stochastic models are underestimated and incorrect, which can lead to multiple adverse effects such as biased results of the estimation procedures, a false a posteriori variance component analysis, false statistical testing, and false network design conclusions. In the end, we prove that some of the adverse effects can be mitigated by employing the a priori knowledge about the target centroid uncertainty behavior.