Objective As an emerging technology, terrestrial laser scanners (TLSs) are used in various applications in forest resource surveys, reverse engineering, and measurement modeling. The original observations, distances, and angles of a TLS are easily affected by the external environment and instrument itself during acquisition, so the geometric information of a TLS often contains certain systematic errors in addition to random and gross errors. Thus, a TLS cannot completely reflect the real characteristics of the target objects directly related to the subsequent processing and applications. Therefore, it is necessary to effectively remove or correct the errors contained in the original observations of the point cloud data, which is also known as the calibration methodology. The traditional method usually separates the distance and angle, i.e., using a TLS to measure multiple fixed-length baselines or angles, solving the systematic error based on the theory of least squares. However, the above methods cannot completely remove the random and gross errors located in datasets. In this study, a new TLS self-calibration method was proposed by incorporating random and systematic errors into the function model as unknown parameters via the scanner observation principle and Gauss-Helmert model. The method can effectively consider all kinds of errors in the geometric information, and the results show that this method can efficiently remove random and gross errors with good robustness via simulation experiments and verification analysis of the measured data.

Methods In this study, a self-calibration function model was proposed based on the scanner observation principle and Gauss-Helmert model; the corresponding additional parameters (APs), random errors of the original observations, and exterior orientation parameters (EOPs) were rationally appended to this model. In addition, a stochastic model conforming to the normal distribution was implemented according to the nominal accuracy of the original observations. The functional model was nonlinear; hence, it was first linearized via the Taylor series, retaining the first-order terms, then the Lagrange objective function was constructed based on the weighted total least squares principle, and all unknown parameters, including the terms of systematic and random errors, were solved using the Newton-Gauss iterative method. Thus, considering the gross errors in the original observations, the IGGIII weighting factor function was constructed by normalizing the residuals to realize the reweighting of outliers, and the robust solution of the functional model was obtained.

Results and Discussions In the simulation experiments, the differences between the parameters and true values in schemes 2 and 3 are closer to 0 than those in scheme 1, which indicates the necessity of system error calibration (Fig. 2). The parameter values of the scheme 3 are closer to the true values than those of the scheme 2, which proves that the proposed model can obtain higher accuracy of APs and EOPs (Fig. 2). The root-mean-square error (RMSE) of the parameter estimation of the scheme 3 is the smallest, indicating that the scheme 3 has the strongest resistance to gross errors in the original observations (Fig. 2). The RMSE of the scheme 2 at the translation parameter Δz is greater than that of the scheme 1, indicating that the scheme 2 is sensitive to gross errors in the parameter estimation process (Fig. 2). In addition, the error of coordinate components and median error of point position in schemes 2 and 3 are smaller than those in the scheme 1, indicating that the observations corrected by systematic errors are closer to the real values (Fig. 3). Because the random and systematic errors (even, possibly, gross errors) in the original observations of checkpoints could not be removed in the adjustment process, the RMSE of coordinate components of individual checkpoints in the scheme 3 is larger than that in the scheme 2; however, the final point accuracy of the scheme 3 is optimal (Fig. 3). For the experiments on the measured data, at a common point, each coordinate component and the point median error of the scheme 2 are better than those of the scheme 1, and the point accuracy is improved from 10 ^-4 to 10 ^-11; the point accuracy of the checkpoint is improved by 23.8%. Apparently, the accuracy of the scheme 2 for the x-component of the checkpoint is reduced by 50% compared with that of the scheme 1, because the random error of the checkpoint cannot be removed in the adjustment process (Table 3).

Conclusions In this study, a novel model of scanner self-calibration function is proposed by combining the scanner observation principle and Gauss-Helmert model, and the IGGIII weighting factor function is used to derive its robust solution. Compared with the existing methods, the proposed model can effectively consider the random and gross errors in the original observations, which is more rigorous in theory. The experimental results prove that compared with the existing methods, the parameter solutions can be obtained with higher accuracy via a posteriori weighting of the observations with good robustness. After systematic errors’ correction, the point cloud coordinates are closer to the real ones. Moreover, since the proposed model is nonlinear, its variables need to be continuously updated in the iterative process; thus, how to improve the operation efficiency of the algorithm still needs further studies.