This month's guest columnist, Thad Mauney, Ph.D., is the director of research and development of Geospatial Information Technologies at Baker GeoResearch, Inc. Contact: Thad Mauney, Ph.D., 115 N. Broadway, Billings, MT 59101; Tel: 1-800-GEOLINK, or (406) 248-6771; Fax: (406) 248-6770; E-mail: [email protected]

Q Now that I know about RMS, 2DRMS, CEP, accuracy, precision, and so forth, which one should I use to report the accuracy of my GPS results?

A Two US government standards provide some guidance. These standards are official criteria for many products provided by and to government agencies. And, although they may not be legally required, these standards are widely used as performance specifications by state, local, and private entities, as well.

The Old Standard
The National Map Accuracy Standard (NMAS) published by the Bureau of the Budget in 1947 has been extensively applied by the USGS in the production of its topographic map series. This standard specifies the required accuracy of well-defined points in the final cartographic product.
    Under the NMAS, not more than 10 percent of the well-defined points tested shall be in error by more than a specified tolerance at the printed scale. For maps at scales of 1:20,000 and smaller, the horizontal tolerance is 1/50". For maps at scales larger than 1:20,000, the tolerance is 1/30".
    This means that on a 1:24,000 scale quadrangle, a feature should be within 1/50" x 1'/12" x 24000 = 40 feet (12.2 meters) of the true geographic location. If 90 percent or more of a set of test points are within this distance, it may be stated that the map meets the NMAS.
    The specified values relate to what was realistically attainable in cartographic production in the 1940s. Now, in the era of GIS, this leads to the odd custom of describing the accuracy of digital datasets in terms of scale even if they are never plotted.
    For example, if tests of our GPS results show that 90 percent or more of the features lie within 2m (6.56') of their 'true' position, we might specify the accuracy by stating the largest scale at which the data would meet NMAS criteria. So, we would compute that 6.56' x 12"/1' / (1/30)" = 2362. We can round up the non-significant digits and state that this dataset would meet NMAS when plotted at scales up to 1:2400, but why couldn't we just say that the accuracy of the dataset is 2m?

The New Standard
The National Standard for Spatial Data Accuracy (NSSDA), endorsed just last year by the US Federal Geographic Data Committee (FGDC), specifies a standard way to state the accuracy of spatial datasets, whether these are plotted or not.
    The NSSDA states, "The NSSDA uses root-mean-square error (RMSE) to estimate positional accuracy. RMSE is the square root of the average of the set of squared differences between dataset coordinate values and coordinate values from an independent source of higher accuracy for identical points."
    Furthermore, "Accuracy is reported in ground distances at the 95 percent confidence level. [This] means that 95 percent of the positions in the dataset will have an error with respect to true ground position that is equal to or smaller than the reported accuracy value. The reported accuracy value reflects all uncertainties, including those introduced by geodetic control coordinates, compilation, and final computation of ground coordinate values in the product."
    Notice that the percentage criterion differs from the NMAS. The new standard requires that 95 percent be within the specified distance rather than just 90 percent. To state accuracy, there must be a reference used as 'truth,' and the geodetic datum in use for the project is that reference. But, since a geodetic datum is really a mathematical surface (an ellipsoid positioned to closely fit the surface of the Earth), we need test points to represent it within the project area.
    For data testing to be valid, these points must be: well defined, independent, and of higher accuracy than the data being tested. When a test with such points is completed, we can compute an accuracy value. If the horizontal error is normally distributed, and the x and y components are approximately equal, we can compute that Accuracyr = 1.7308 * RMSEr.
    The multiplier 1.7308 derives from the two-dimensional normal distribution, calculating the 95 percent confidence interval when error is measured radially. When working with a one-dimensional error distribution to compute vertical accuracy, a multiplier of 1.96 is used to obtain the 95 percent confidence interval. Naturally, the horizontal and vertical accuracy of a three-dimensional dataset may differ, and these are typically stated separately.
    Only when a dataset has actually been tested by comparison to an independent source of higher accuracy shall the accuracy be stated, "Tested ___(meters, feet) horizontal accuracy at 95 percent confidence level." If the data are produced by procedures that have been demonstrated to comply with a particular accuracy level, but the dataset is not itself tested, it should instead be stated, "Compiled to meet ___(meters, feet) horizontal accuracy at 95 percent confidence level."
    The NSSDA method of stating accuracy is consistent with the FGDC standards for metadata so that these values can travel with the GIS dataset. Unlike the NMAS, the NSSDA does not specify accuracy values that datasets must meet. Instead, it provides a consistent means of reporting accuracy. Ultimately, the data provider determines what accuracy exists in their data, and the data user determines what accuracy values are acceptable for their application.

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