Positional AccuracyFebruary 15, 2006 Geog 458: Map Sources and ErrorsOutlines What is positional accuracy? Components of positional error Statistical statement of positional error Sources of positional error Evolutions of positional standards Testing positional accuracy Documenting positional accuracy measuresWhat is positional accuracy? Closeness to “true” location Positional error means the discrepancy between measured position and the true position Positional error consists of systematic error and random error Systematic error: whole data set is biased ( bias) Random error: each data set has some inherent deviation ( precision)Examples Case A Case BArrows are drawn from measured position to true positionEach points show the same systematic error and no random errorTotal error = systematic errorEach point exhibits the same systematic error with variant random errorsTotal error = systematic error random errorComponent of positional errors Bias is measured from systematic error Sample mean of discrepancy Can be defined both in x-direction and y- direction Precision is measured from random error Sample standard deviation of discrepancy Its called circular errors in surveying and mapping community (Circular Map Accuracy Standard : CMAS)Read DCW error analysis report p. 4-5 for formulaExamples Case A Case BArrows are drawn from measured position to true positionPrecise (=No random error)Discrepancy values exhibit no deviation from biasImprecise (=Some random error)Discrepancy values exhibit varying deviation from bias Statistical statement of positional errors Meaning of RMSE = average error regardless of direction RMSE = 60 feet means that the discrepancy between measured and true position is 60 feet on average In other words, any point in this data set is located average 60 feet around its true location Statistical statement of positional errorsThe point you see on the left is likely to be somewhere around 60 feet radius, but how sure can this be stated?60 feetSince we state errors, it will be convenient to compare the sample distribution of errors to typical distribution of errorsTypical distribution of errors would have a bell shape Statistical statement of positional errors “Tested 104 feet horizontal accuracy at 95% confidence level”104 feet60104 = 60*1.7308where 1.7308 is constant used to derive 104 so that shaded area in the Gauss curve becomes 95% of the total area formed by the curve10444Statistical statement of positional errors “Tested 104 feet horizontal accuracy at 95% confidence level” It reports the likely Maximum Error of positional information at a given confidence level under the assumption that errors will be distributed like Gauss curve It means that the horizontal position of a feature will be within 104 feet of its true location 95% percent of the time It means there is also 5% chance that the horizontal position of a feature will be outside of 104 feet of its trueSources of positional errorsSource Surveying or measurement equipment errors Measurements are of varying precisions Equipments have inherently different resolutions Processing steps Transformation between different coordinate systems Rounding errors when data is stored in different formats Location/accuracy of control points Algorithms used for transformation Better look at a lineage report To fully understand positional accuracy involves first identifying the steps contributing to the determination of the database objects coordinates How do we know which step introduces more errors relative to other steps? Error propagation analysis (then we can go back to the most problematic steps to fix it to improve the accuracy)Evolutions of positional standardsNMAS1947 National Map Accuracy Standards 90% of well-defined points within tolerance ACIC 1962 Aeronautical Chart and Information Center Converts NMAS into a statistical statement Circular Map Accuracy (precision) APS 1985 American Society of Photogrammetry Bias (mean of error) and precision (standard deviation of error) NSSDA 1998 National Standard for Spatial Data Accuracy Adopted by FDGC RMSE 95% of well-defined points within toleranceTesting positional accuracy Rigor of statement Descriptive to quantitative If quantitative, non-statistical to statistical If statistical, which components of errors precision, bias, RMS, in which confidence level Levels of testing Deductive estimate Internal evidence Comparison to source Independent source of higher accuracy Dimensionality of features Point to areaSDTS: Positional accuracy Degree of compliance to the spatial address and coordinate coding standard The description of positional accuracy should consider the quality of the final product after all transformations The information on transformation forms a part of the lineage section Measure