## 2 Materials and Methods
### \"Ground Truth\" and Dataset Alignment  
As stated in Section 2.1, it is very difficult to analytically predict the accuracy of the final position starting from the IMMS components of instrumental error; therefore, the data assessment presented in this study is produced by comparing each resultant _mapping_ with the \"ground truth\".  
For this, a sub-set of the available point model, previously acquired by Z+F 5010C TLS [28], was assumed. The scan alignment was performed thanks to 155 control points (black and white targets): their positions were defined by topographic measures based on a control network of 40 vertices in the inner part of the fortress. The topographic network and the control points were measured by the geodetic branch of the Italian Military Geographic Institute (IGMI). IGMI estimates network accuracy of less than one centimetre, and target accuracy of about one centimetre. The scan alignment, initially based on such targets, was then optimized by an ICP algorithm (implemented in Cyclone software, by Leica Geosystems), providing a mean absolute error of less than one centimetre. Considering the available data metrics, and the expected accuracy of the IMMS under testing, it is possible to assume the former as a reliable reference.  
A cloud of about 1250 million points was then available as the ground truth: first of all, it was cleaned up by removing cars, passers-by, etc. and, later decimated to clouds with 1-cm resolution (as specified further on), in order to make the resolution not only more regular but more comparable to that of the datasets under examination. At the end, two reference datasets were created, with the data acquired by following the two planned paths: a first dataset of about 67 m \(\times\) 78 m with 69,785,238 points for path 1, and a second of about 43 m \(\times\) 48 m with 33,483,564 points for path 2. In both cases, the maximum elevation difference in the datasets is about 25 m.  
The three examined IMMSs provided data in different reference systems: the Stencil and Zeb-Revo are defined arbitrarily, while the Pegasus produces WGS84 coordinates according to GNSS measurements which are transformed into a local vertical datum. Therefore, all of them needed to be transformed to use the same reference system as the ground truth (a local datum in a Gauss conformal projection that was specifically designed to avoid cartographic deformations). For this purpose, the widely used and open source CloudCompare software [29] was employed. First of all, a rough alignment was obtained from the three IMMS clouds by rotating and translating them, and suitably defining four corresponding points in all of the datasets. These points were chosen as far away from each other as possible in the whole test area: the same natural features were picked up in all the datasets. As a result, the four clouds were roughly pre-aligned, while the final refinement was obtained using the ICP algorithm, again with CloudCompare software. Hence, the ICP algorithm was used in a traditional manner, and not for \"SLAM purposes\" as in Section 2.1.  
As is known, the ICP process randomly considers a sub-sample of the point clouds at each iteration; we noticed that the default value proposed for the \"random sampling limit\" parameter affected the results. Due to the very large point models considered, we increased its value to 2 million points to strike a balance between the computation speed and reliability of the results. Table 1 summarizes the signed distances (RMS Root Mean Square) after ICP alignments of the IMMS clouds.