A New Method for Positional Accuracy Control for Non-Normal Errors Applied to Airborne Laser Scanner Data

Abstract

A new statistical method for the quality control of the positional accuracy, useful in a wide range of data sets, is proposed and its use is illustrated through its application to airborne laser scanner (ALS) data. The quality control method is based on the use of a multinomial distribution that categorizes cases of errors according to metric tolerances. The use of the multinomial distribution is a very novel and powerful approach to the problem of evaluating positional accuracy, since it allows for eliminating the need for a parametric model for positional errors. Three different study cases based on ALS data (infrastructure, urban, and natural cases) that contain non-normal errors were used. Three positional accuracy controls with different tolerances were developed. In two of the control cases, the tolerances were defined by a Gaussian model, and in the third control case, the tolerances were defined from the quantiles of the observed error distribution. The analysis of the test results based on the type I and type II errors show that the method is able to control the positional accuracy of freely distributed data.

Study of NSSDA Variability by Means of Automatic Positional Accuracy Assessment Methods

“…In the view of such variable results, in his own study Zandbergen [14] focuses his attention on the development of a rigorous characterization of the positional error distribution in four different types of spatial data: GPS locations, street geocoding, TIGER roads, and LIDAR elevation data; concluding that in all cases the positional error could be approximated with a normal distribution, although there is some evidence of non-stationary behaviors resulting in a lack of normality. More recent studies [30][31][32][33][34] follow the line of argument adopted by Zandbergen in his work defending that positional errors could be not normally distributed. Among these last studies, Ariza-López et al [34] argue that there are six main causes of the non-normality of many positional error distributions: (i) the presence of too many extreme values (i.e., outliers), (ii) the overlap of two or more processes, (iii) insufficient data discrimination (e.g., round-off errors, poor resolution), (iv) the elimination of data from the sample, (v) the distribution of values close to zero or the natural limit, and (vi) data following a different distribution.…”

“…More recent studies [30][31][32][33][34] follow the line of argument adopted by Zandbergen in his work defending that positional errors could be not normally distributed. Among these last studies, Ariza-López et al [34] argue that there are six main causes of the non-normality of many positional error distributions: (i) the presence of too many extreme values (i.e., outliers), (ii) the overlap of two or more processes, (iii) insufficient data discrimination (e.g., round-off errors, poor resolution), (iv) the elimination of data from the sample, (v) the distribution of values close to zero or the natural limit, and (vi) data following a different distribution. The presence of any of these cases can have several consequences depending on the degree of non-normality of the data and the robustness of the method applied.…”

Obtaining new resolutions in carnivore tooth pit morphological analyses: A methodological update for digital taphonomy

“…The BWMV (reported as its square-root) is a further nonparametric measurement that additionally presents robustness of efficiency, proving a valuable substitute in non-parametric calculations [85]. NMAD and the square-root of the BWMV have proven to be important variables in accuracy control and system assessment analysis in remote sensing applications [83,[85][86][87][88][89]. Because of this, these metrics were employed as a substitute for standard deviation error calculations where Gaussian distributions were not detected, while the central tendency is reported as the median.…”

Statistical Methods for Thematic-Accuracy Quality Control Based on an Accurate Reference Sample

“…Appendix I in [13] presents an example of the calculation of the p-value of the exact test. It is interesting to notice that [20,21] also applied this exact test for positional accuracy quality control by considering error tolerances.…”