Evaluation of Three-Dimensional Positional Acuracy of Cartographic Products Using an Elipsoide of Uncertainties

Abstract

In Brazil, the positional accuracy evaluation of cartographic products follows the guidelines of Decree n. 89,817 / 1984. The decree divides positional accuracy into two components: planimetric and altimetric. Three-dimensional products, such as Digital Surface or Elevation Models (MDS / MDE), are often evaluated separately, but some authors, such as Santos (2015) and Li et al. (2005) mention that the most efficient way to evaluate this type of product is through the resultant between planimetric and altimetric components. This work proposes a method for the three - dimensional accuracy evaluation of cartographic products by three - dimensional components of a geometric surface, in this study an ellipsoid, whose dimensions are given by the tolerances described in Decree n. 89,817 / 1984. Subsequently, the proposed method (called EPSI) was confronted with both Decree 89,817 / 1984 methodology and ET-CQDG (DSG, 2016), a Brazilian technical specification. In order to verify the method efficiency, 15,000 discrepancies were simulated and in approximately 83% of cases the proposed method was more restrictive when compared to planimetry analysis, and in 58% of cases when compared to altimetry evaluation. In the remaining cases, the method was equivalent to the separate planimetry and altimetry analysis, described by ET-CQDG (DSG, 2016). Using practical examples, it can be seen that the three-dimensional methodology is more restrictive than the one usually applied.