Finite Mixture Models in the Evaluation of Positional Accuracy of Geospatial Data

Abstract

Digital elevation models (DEMs) are highly relevant geospatial products, and their positional accuracy has demonstrated influence on elevation derivatives (e.g., slope, aspect, curvature, etc.) and GIS results (e.g., drainage network and watershed delineation, etc.). The accuracy assessment of the DEMs is usually based on analyzing the altimetric component by means of positional accuracy assessment methods that are based on the use of a normal distribution for error modeling but, unfortunately, the observed distribution of the altimetric errors is not always normal. This paper proposes the application of a finite mixture model (FMM) to model altimetric errors. The way to adjust the FMM is provided. Moreover, the behavior under sampling is analyzed when applying different positional accuracy assessment standards such as National Map Accuracy Standards (NMAS), Engineering Map Accuracy Standard (EMAS) and National Standard for Spatial Data Accuracy (NSSDA) under the consideration of the FMM and the traditional approach-based one-single normal distribution model (1NDM). For the NMAS, the FMM performs statistically much better than the 1NDM when considering all the tolerance values and sample sizes. For the EMAS, the type I error level is around 3.5 times higher in the case of the 1NDM than in the case of the FMM. In the case of the NSSDA, as it has been applied in this research (simple comparison of values, not hypothesis testing), there is no great difference in behavior. The conclusions are clear; the FMM offers results that are always more consistent with the real distribution of errors, and with the supposed statistical behavior of the positional accuracy assessment standard when based on hypothesis testing.

Keywords

• DEM
• normal distribution
• parametric error models
• Gaussian finite mixture models