## 2 Materials and Methods
### The IMMS Analytical Measurement Principle
In addition to synchronization errors, each one of the above quantities is characterized by measurement errors, whose combined effect propagates onto the final positioning \(\mathbf{r}^{SCs}_{i}\) of the generic point. This error could be estimated by considering every independent contribution, as suggested for MMSs in [14], where they were evaluated at around 20 cm overall at a 30-m distance. In any case, as is logical, error improves with the distance \(\mathbf{r}^{b}_{i}\) of the laser beam, in particular by taking into account the \"level-arm\" effect resulting from angular inaccuracies in the rotation matrix \(\mathbf{R}^{ins}_{tls}\): since the main INSs used nowadays are micro-electromechanical systems (MEMS) with generally limited accuracy, this can produce very large errors in the positioning. Special attention is also required in analysing the accuracy of the \(\mathbf{r}^{SCs}_{gms/ins}\) positioning obtained from the joint use of the satellite receiver and inertial platform, remembering that most applications of IMMS are in closed spaces and tunnels, where GNSS positioning is not available. In spite of this, supposing that both sensors are working, GNSS positioning becomes inaccurate when the available satellites are reduced by obstructions. Therefore, in such cases, the positioning can be estimated by INS accelerometers. The previously mentioned Kalman filter integration of the two navigation sensors allows one to augment and enhance the other: the absolute position (and also velocity) of the GNSS is used to compensate for the errors in the INS measurements, while the stable relative position of the INS is used to bridge over when the GNSS solution is of low quality or is unavailable. To sum up, on one hand, the analytical principle expressed by Equation (1) can be considered as a new dynamic way of perceiving TLS surveying, while, on the other hand, it is an _old_ idea from nearly 20 years ago in aerial laser scanning (ALS) methodology (e.g., [15]). In ALS, although \(\mathbf{r}^{b}_{i}\) could be kilometric with a speed of hundreds of km/h, the accuracy of the positioning is surprising, generally limiting the errors under to 10 cm. If we are to recall the SLAM acronym, the novelty of the IMMS approach is that TLS sensor _localization_ (position \(\mathbf{r}^{SCs}_{tls}\) and rotation embedded in \(\mathbf{R}^{SCs}_{tls}\)), that is, the trajectory/orientation of the TLS system, and the _mapping_ points (\(\mathbf{r}^{SCs}_{i}\)), that is, the 3D point cloud obtained, are considered as a \"starting point\" for the final solution. In this sense, the expression _simultaneous_ localization (of the scanning sensor) and mapping (of the scanned points) is not exactly appropriate, since the simultaneity does not refer to a computational black box like in the SfM photogrammetric approach, where localization and mapping instead really are the output processes. Nevertheless, even if in truth IMMS provides the final cloud in two steps, the output model is so impressive that an extension of the term \"simultaneous\", in the sense of being \"automatic\", is due. An important question instead concerns the contribution of the navigation GNSS/INS (navigation) sensors and the TLS and/or imaging (measuring) sensors to localization and mapping problems. In general, MMS technology uses the former for localization and the latter only for mapping: since navigation and measuring data have complementary strengths and weaknesses, a combination is instead advisable. We presented an example of such an integration [16] in 1998, using the images to solve the position and attitude estimation problem in a low-cost MMS system without INS sensors. On the other hand, nowadays photogrammetry carried out through a SfM approach generally only uses the images for localization and mapping. The originality of the IMMS principle is instead to take advantage of the mapped results to update the navigation results in order to consequently improve the mapped ones.