Error Propagation

Disciplinary Context

In the discipline of statistics, the error propagation law is a mathematical formula used to formalize the relationship between input and output error. In surveying data processing, this method is adapted for analyzing error propagation, with a focus on estimating the error in point measurements. In geographic information science, the method of error propagation is relevant to all spatial data processing conducted in GIS. The error generated from any spatial operation will significantly affect the quality of the resulting data set(s). This has led to much research focused on error propagation in spatial analysis, particularly on methods to quantify the errors propagated.

Modeling Approaches

There are two approaches for modeling error propagation: the analytical approach and the simulation approach. These approaches, which can be applied in either a raster-based or vector-based spatial analysis environment, can be illustrated by the error propagation law used in statistics and Monte Carlo simulation, respectively.

[Page 130]In the analytical approach, the error propagation law is one of the most effective methods for analyzing error propagation. To begin, a stochastic function, either in linear or nonlinear form, is identified to describe the relationship of the output of a GIS operation and the input variables. If the function is an online one, either first-order or second-order Taylor series can be applied to evaluate the error.

The error propagation law is normally used for modeling positional error propagation. In terms of the positional error of points, errors can be classified as random error, systematic error, or gross error. The error propagation law is mainly applicable for handling random error.

The Monte Carlo method is an alternative solution for modeling error propagation. With this simulation method, the output result is computed repeatedly, with the values of input variables randomly sampled according to their statistical distributions. Given that the input variables are assumed to follow specified error distributions, a set of statistic parameters to describe the output errors, such as the mean and the variance of the output, can be estimated from the simulations.

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