GPS Consumer Series: How is the Accuracy of a GPS Receiver Described?
By Chuck Gilbert

The GPS Consumer Series is a column that explores the issues associated with GPS data collection. This column explores the benefits provided by various GPS receiver features on today's market. Issues commonly encountered in differential GPS data capture are examined from the user's perspective.

Introduction
If you were to simply read the advertisements of several GPS manufacturers, you could become very confused. Worse yet you could be mislead to think that you understand more than you really do.
      Whether intentional or otherwise, advertisements often do not convey an intelligible picture of GPS accuracy. In defense of the manufacturers, GPS accuracy is a complex topic involving a variety of technical factors. In an advertisement, a detailed outline of these factors would be, at best, out of place, and at worst, completely meaningless to many readers. The inherent complexity of the topic coupled with the desire to show the product in its best light results in most advertisements simply glossing over several important points. This month's column will discuss a few of these points, in an attempt to increase your awareness of what the GPS manufacturers are trying to convey.

General differences in style
If the same GPS system were to be described by different manufacturers, you would probably end up with varying descriptions; such differences may be attributed to what I will refer to as "style." Some manufacturers may use an aggressive style and state the best accuracy that they were able to achieve under optimal conditions (even though such an accuracy may have been achieved only 50 percent of the time). At the other extreme, some manufacturers may be overly conservative. A conservative manufacturer may characterize the receiver under difficult or extreme circumstances, then state an accuracy that reflect the observed results at 95 percent probability. The same receiver, described in two different ways could have two very different accuracy values. For example, imagine that a certain GPS receiver collected 1000 data points under ideal conditions. It is conceivable that the best data point could be accurate to better than 0.01 meters, and the worst, accurate to only 15 meters. Now imagine that the same receiver collected 1000 data points under difficult GPS conditions (such as the multipath rich environment typical of an urban city center) and under these difficult conditions, it is conceivable that the resulting accuracy varied from 1 meter to 5 meters. How would you describe the accuracy of this receiver given, say, 20 words in a small ad?

How long is long enough?
One of the more common "gotchas" in describing GPS accuracy is the occupation time required to achieve the claimed accuracy. Be wary if the ad does not explicitly state how long you must occupy a location in order to achieve a particular accuracy. In the best case scenario, the required occupation time might be as little as one second. However, several systems that tout sub-meter accuracy are only able to achieve this after a stationary occupation of at least several minutes.

Expression of accuracy
How are the accuracy values represented statistically? The accuracy can be expressed in a manner that describes the 50th percentile (e.g. half the data is better than the stated value, half the data is worse than the stated value). Alternatively, the accuracy may be described at the 95th percentile (95 percent of the data is better than the specification). The list below states the more common terms used to describe GPS accuracy:
• CEP (Circular Error Probable) - Values stated as CEP apply to horizontal accuracy only. Half of the data points fall within a circle of this radius centered on truth, half lie outside this circle. (As a nifty approximation, you may multiply CEP by 2.5 to obtain 2dRMS.)
• SEP (Spherical Error Probable) - Applies to combined horizontal and vertical accuracy. Half of the data points fall within a sphere of this radius centered on truth, half lie ou side this sphere.
• 1dRMS (or RMS) - Approximately 68 percent of the data points occur within this distance of truth. It should be expressed clearly whether the accuracy value refers only to horizontal or to both horizontal and vertical. (Note that 1dRMS can be double or tripled to obtain 2dRMS or 3dRMS.)
• 2dRMS - Approximately 95 percent of the data points occur with this distance of truth. It should be expressed clearly whether the accuracy value refers only to horizontal or to both horizontal and vertical.
• 3dRMS - Approximately 99.7 percent of the data points occur with this distance of truth. It should be expressed clearly whether the accuracy value refers only to horizontal or to both horizontal and vertical.

With or without Selective Availability
The vast majority of GPS-based data collection systems for GIS utilize the civilian C/A code (as opposed to the military P code). The U.S. military runs a program that almost always degrades this GPS C/A code. This governmental degradation of the GPS signal (known as Selective Availability, or S/A) has an equal impact on all C/A code GPS receivers. The specified accuracy of positions under the influence of S/A is that the horizontal coordinates will be within 100 meters of truth 95 percent of the time. This specification will hold true regardless of the manufacturer or model of C/A code receiver.
      It is true that the effects of S/A can be removed by using a process known as differential correction. However, without the benefit of differential correction all C/A code receivers are essentially the same accuracy, less than 100 meters 95 percent of the time. A less common, but very misleading, tactic is to advertise or display the hypothetical accuracy of the GPS receiver as if there were no S/A in effect. Some systems will display such a hypothetical accuracy even when S/A is in full force. When researching accuracy claims, compare the accuracy after differential correction - this is the only meaningful accuracy value. Don't forget that statements regarding the uncorrected accuracy when there is no S/A, are essentially meaningless since the user cannot "turn S/A off."

Upgrade Costs
Watch for accuracy claims that require the purchase of upgrades at additional cost since it is quite common that the standard system may have a limited accuracy. Generally this is not a big problem, however, the necessity of the upgrade should be made clear in the advertisements and literature.

Maximum baseline length
Differential correction requires at least two receivers. The distance between these two receivers will have an impact on the accuracy of your differential correction. Consider your application and whether your source of base data (usually a GPS base station) will typically be nearby or whether your source of base data will be located at a significant distance from where the rover data is collected. If your base station is typically more than 10-20 kilometers from the site of your rover data collection, you should consider this factor in your purchasing decision.
      The degradation of accuracy with distance is known as spatial decorrelation. Spatial decorrelation is often expressed in terms of parts-per-million (ppm) of the distance between the base and rover receivers. For example, if the distance between your base and rover is 200 kilometers, and the decorrelation of your GPS system is specified at 10 ppm; you may experience as much as 10 millionths of 200 kilometers of accuracy degradation, or 2 meters. On the other hand, using the same 200 kilometer example, with a decorrelation of only 2 ppm; your error will be limited to 2 millionths of 200 kilometers, or 0.4 meters. Spatial decorrelation values of GPS systems on the market today range from 1-2 ppm to as much as 20 ppm. Spatial decorrelation was discussed in more detail in the November 1995 issue.

Memory requirements
When GPS data is going to be used in a post-processed differential correction, it is necessary to store much more information than merely position records. As a result, there is a relationship between desired accuracy and the amount of memory you will require to store that data. This is not the most common problem, however, it has stung a few GPS purchasers in past years. I mention this issue only because there has been historical precedent. There have been manufacturers who proclaim that their system can store many hundreds of thousand of positions. What the advertisements did not say was that in the operating mode that can store hundreds of thousands of positions, your data is limited to (uncorrected) 100 meter accuracy. The same system could store differentially correctable data (for 2-5 meter accuracy), however, in the correctable mode, the same amount of memory could only accommodate a few dozen positions.

Summary
The issue of GPS accuracy can be complex. There is rarely enough room in an advertisement to show the necessary detail for a complete picture of GPS accuracy. An ideal description of GPS accuracy will have reference to several factors. The most common factors that should be included in a complete description of accuracy include the following:
• Required occupation time
• Type of data recorded (phase or pseudorange)
• Type of processing (phase or pseudorange)
• Environmental conditions
• Maximum allowable PDOP
• Minimum allowable signal strength
• Maximum allowable distance between base and rover receivers
• Horizontal accuracy versus vertical accuracy
      In summary, do not use advertisements as your guide to GPS accuracy. Whenever possible refer instead to independent technical reports, or manufacturers technical data sheets that feature the system of interest.

About the author:
Chuck Gilbert has over a decade of experience as a GPS user. He has been employed as an applications engineer for Trimble Navigation since 1989.

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