Nonlinear least-squares solutions to the TLS multi-station registration adjustment problem

Performing multiple scans is necessary to cover an entire scene of interest, making multi-station registration adjustment a critical task in terrestrial laser scanner data processing. Existing methods either rely on pair-wise adjustment, which leads to drift accumulation and lacks global consistency, or provide an approximate solution based on a linearized model, sacrificing statistical optimality. In this study, using a multi-station stacking model, we propose a method that provides two different nonlinear least-squares (LS) solutions to this problem. We first demonstrate how a nonlinear Baarda’s S-transformation can be used to transform solutions that share the same optimal network configuration. Then, two practically meaningful LS solutions are introduced, i.e., the trivial minimal-constraints solution and the partial nearest solution. Most importantly, we derive a truncated Gauss–Newton iterative scheme to obtain numerically exact solutions to the corresponding nonlinear rank-deficient problem. We validate our method with three real-world examples, demonstrating that (1) global consistency is maintained with no drift accumulation, and (2) our nonlinear solution outperforms the approximate linearized solution. Code and data are available at https://github.com/huyuchn/Multi-station-registration.