Terrestrial laser scanner geometric error model parameter correlations in the Two-face, Length-consistency, and Network methods of self-calibration

Terrestrial laser scanners (TLSs) are increasingly used in a variety of applications where accuracies on the order of few tenths of a millimeter or smaller are routinely demanded. Self-calibration is a quick and cost-effective way to improve the accuracy of a TLS without the need for calibrated artifacts or reference instruments. In a previous work [1], we outlined three approaches to self-calibration, the Network method, the Length-consistency method, and the Two-face method. In this paper, we lay out the mathematics underlying the total least-squares adjustment process for the three different techniques and also address correlation between parameters calculated from the three methods. We show that while the three methods offer similar uncertainties in the parameters, there are fewer correlations between the calculated model parameters in the Length-consistency and Two-face methods.