Estimating positional accuracy of data layers within a GIS through error propagation

The positional accuracy of a GIS layer can be separated into absolute and relative components. Accepted standards for estimating horizontal accuracy in cartographic data quantify absolute positional accuracy only. However, relative accuracy values that describe variability in spatial relationships of coordinate information - such as variance of area, azimuth, and distance computations - can be valuable to research and decision making. This paper presents a technique for quantifying absolute and relative positional accuracy estimated through error propagation from a covariance matrix for affine transformation parameters. This technique was developed and tested with a spatial data set manually digitized from a simulated 1:24,000-scale map whose errors were restricted to those of the electrostatic plotter. A sequence of transformation tests was performed, using from 4 to 40 control points per test. Estimates for combined error associated with electrostatic plotting and manual point-mode digitizing were inversely related to the number of control points up to about 20. Semi-major axes for point certainty regions at a 39.4 percent confidence level ranged from 1.86 to 5.45 metres (0.0775 to 0.227 mm at map scale).