ABSTRACT
Global positioning systems (GPS) without differential correction may now be accurate enough for many forestry applications. We present accuracy estimates for point locations and a method of stating area accuracy so that potential GPS users can decide whether the accuracy is sufficient. The results show that GPS without differential correction is more accurate than traditional methods of location and area calculation, short of actual surveying. Compass-and-pace is less accurate than GPS, and lines and points at customary map scales are as wide as typical GPS errors. If differential correction is not necessary, practitioners can use the inexpensive, light, and easily operated consumer-grade receivers and simple software.
Keywords: geospatial technologies; inventory; mapping
A global positioning system (GPS) is becoming a necessity for effective forestry fieldwork. Locating boundaries and calculating area, for example, can be done more accurately with GPS than with traditional forestry field methods. Unfortunately, GPS has not been available to everyone. The expense and steep learning curve of mapping-grade receivers have kept many from taking advantage of this new technology. GPS software with differential correction capability-necessary because of the up to 100-meter error (Liu and Brantigan 1995) caused by selective availability (SA)-can also be expensive and difficult to learn.
When SA became history on May 1, 2000, however, possible location error immediately dropped by a factor of 10. We now have a choice whether to use differential correction or not. Is GPS without differential correction accurate enough for professional work? If the answer is "yes," we can use consumer-grade receivers and software.
Consumer-grade receivers, intended for use by hikers, hunters, and boaters, are inexpensive, light, and easy to use. The software is also easy to master and even less expensive than the receivers, and it is designed for people without training in specialized computer programs. Many receivers and programs are available.
Professional-grade receivers and software allow more flexible data collection, organization, recording, and transmission to a GIS database, but cost and ease of use may outweigh these factors if accuracy is sufficient. To determine whether accuracy is sufficient for an application, we require two things: a method of stating point location accuracy and a method of stating area accuracy.
Point Location Accuracy
Point location accuracy is a measure of the distance between the true location and the GPS reported location. Direction is not considered: One can be 2 meters north of true or 2 m south of true and have the same point location accuracy. Many authors have addressed point location accuracy. For example, Wilson (2000) presents 50 percent, 68 percent, 95 percent, and mean horizontal error distances between a known location and single GPS observations of that location without differential correction for two common consumer-grade receivers (table 1). Using the Garmin eTrex as an example, 50 percent of GPS estimated observations were within 2.7 m of the true location, 68 percent were within 3.8 m, 95 percent were within 6.7 m, and the average error was 3 m. These values are specific to the conditions in which they were collected, but they can serve as a guide to what can be expected.
Based on table 1, the location accuracy of the Garmin III+ is very similar to that of the eTrex. The slightly greater errors reported for the III+ should not be interpreted to mean the eTrex is more accurate: The differences could be the result of the conditions on the days the measurements were obtained, the physical location of the units, the density of the ionosphere, and a dozen other factors. In fact, what the results show is how consistent accuracy is among receiver types. We would expect that any consumer-grade receiver, regardless of manufacturer, would have about the same accuracy as those shown in table 1.
The mean number of satellites and the mean and 68 percent horizontal dilution of precision are also shown in Wilson (2000). No specific information on number of satellites, satellite distribution, or dilution of precision for any individual reading is given, so there is no correlation reported between these factors and error. Presumably, the distribution of error includes these factors implicitly. Practitioners can develop an error distribution for their own conditions and equipment using the procedures described by Wilson.
We can interpret the table 1 accuracies in the aggregate and by point. Officially, we are betting on aggregate results, but practically we must work by point. In the aggregate, if we take 100 GPS observations, the assumption is that 50 will be within 3 m of true location, 68 will be within 4 m, and 95 will be within 7 m. This is the usual confidence interval interpretation. These are not certainties, however, so we should not be surprised if 100 points do not fall out exactly this way.
By point, we're betting that the single GPS observation we just made has a 50 percent chance of being with 3 m of true, a 68 percent chance of being within 4 m, and a 95 percent chance of being within 7 m. These odds and distances form a bull's-eye of accuracy around a GPS-based point (fig. 1). The next location (and the next, and the next) will have the same odds and distances. We must attribute long-run probabilities to single events. This approach allows a probability to be associated with a distance error for a single point.
Some people are surprised at a possible error of 7 m or more, but there are practical considerations that make this error unimpressive. First, being as wrong as 7 m would be unlikely. The likelihood of being within 4 m is two and one-half times that of missing by 4 to 7 m, and more than 10 times that of missing by more than 7 m. Instead of looking at what might happen in the extreme, we should look at what is most likely to happen.
Second, a 0.5 mm pencil line on a 1:24000 USGS topo map is 12 m (40 feet) wide at map scale, larger than the 95 percent errors shown by Wilson (2000). A large map scale for forestry use would be 1:8000 (about 1 inch = 10 chains, or 1 cm = 80 m), which makes the pencil line 4 m wide. We have accepted errors like these in the past. We assumed we were accurate because we could not tell otherwise. With GPS, for the first time we can actually determine the errors.
Third, GPS navigation error is independent of distance, topography, and vegetation between start and end. Going from Florida to a point in California will have the same location error probability at the end as starting just a mile from the destination. The location of any point is not influenced by location errors in other points, so errors do not accumulate, as they do if we run a line by compass and pace, and any errors made at the beginning carry forward to and perhaps beyond the end of the line. With GPS, in contrast, the start and the end have the same error probabilities.
Fourth, individual GPS observations can be averaged to reduce the effect of extreme observations. The errors in table 1 apply to single GPS observations, not averages. Averaging observations reduces the influence of any one observation. Commonly, 20 to 60 observations at one point are averaged. It should be noted that averaging observations increases precision, not accuracy. Observations averaged over many days would be very accurate, but over a 20- to 60-second interval any biases due to satellite arrangement, ionospheric density, and other factors contributing to error will change little. Averaging over a short interval minimizes the effects of extreme errors. Table 2 (p. 26) shows error distances for the average of 20, 30, and 60 successive individual observations taken by the authors. Note that averaging more observations reduces maximum error and increases minimum error.
Area Accuracy
Expressing area accuracy with GPS is different from the error of closure used in traditional surveying (Liu and Brantigan 1995). Error of closure assumes a starting point with subsequent errors accumulated as the boundary is traversed. Successive points are not independent. Errors in locating point A affect the errors in point B and so on around the traverse back to point A. Error of closure is the ratio of the distance required to make the start and end points meet to total traverse length. A good error of closure has a small ratio, such as 1:2000; a bad error of closure has a large ratio, such as 1:200. Steep slopes and long lines contribute more to error than flatter terrain and shorter line lengths.
