GPS Consumer Series: Averaging GPS Data Without Applying Differential Correction
By Chuck Gilbert

The GPS Consumer Series is a monthly 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 walk outside right now, turn on a GPS receiver, then read the position on the screen, the answer will almost always be inaccurate. Any one GPS receiver, operating on its own, will be accurate to better than 100 meters 95 percent of the time. In my book, that's not very accurate. It's not that the GPS system itself is that error prone. The vast majority of this error is due to intentional degradation of the GPS signal by the U.S. Department of Defense (DoD). The DoD cites reason of national defense. I do not intend to debate the wisdom or effectiveness of this policy. I merely wish to elaborate a little on how this degradation impacts the typical GPS user.
      My thanks to Paul Malley and Rob Peterson, two astronomers in Texas, who have pressed for more information, and inspired these words. While their application may be esoteric, their data collection needs are not atypical. I will use their application as an example. These astronomers go to remote locations to observe and record solar eclipse data. It is important that they are able to determine relatively accurate geographic coordinates for their telescope locations. In the interest of simplicity, I will not state precisely what their accuracy requirements are - that is not relevant. Suffice it to say that their fundamental needs are not very different from that of any biologist, geologist, or any other worker in the field who desires spatial coordinates for their 'things' in the field.

It Takes Two (or More) to Tango
If the GPS signal were not degraded, the accuracy of one receiver, operating on it's own (or autonomously) would typically be about 10-15 meters. The error in excess of this 10-15 meters is a result of the DoD policy to degrade the GPS signal for non-military users. (This degradation is known as Selective Availability or S/A.)
      Fortunately there is a relatively easy way to subjugate this degradation. If two or more GPS receivers collect data at the same time, it is possible to use the data from one receiver to remove most of the error from any number of other receivers, providing that a few simple criteria are met.
      The main criteria for differential correction are listed below:
a) Both receivers must record data at the same time.
b) One receiver must be stationary at a location of known coordinates. This stationary receiver is usually referred to as a base or reference receiver.
c) Both receivers must record the cor- rect type of information (positions only are not enough). A variety of details about the satellites and their orbits are required for successful correction.
d) The two receivers should be in the same geographic region. Usually, two receivers within 500 km (300 miles) of each other are close enough together.
      The process of using two receivers at the same time to remove errors is known as differential correction. After differential processing the accuracy of GPS data can be improved to better than one centimeter with survey grade GPS receivers, and to accuracy better than one meter with mapping grade GPS receivers.
      For a more thorough discussion of the requirements and details of differential correction refer to this column in the October 1993 issue of Earth Observation Magazine. Alternatively, reprints of the October 1993 issue can be obtained from Trimble. For more detail still, I recommend the book Global Navigation, A GPS User's Guide, by Neil Ackroyd and Robert Lorimer, ISBN #1-85044-232-0.

Double or Nothing?
For the majority of applications, the 100 meter accuracy available under the influence of S/A is not good enough. In fact, even without S/A, the resulting 10-15 meter accuracy is still not good enough for many applications. It is the superior accuracy of differential GPS that makes GPS a viable solution for innumerable applications.
      The cost of acquiring differential accuracy is that users require either an additional GPS receiver to serve as a reference receiver or they must obtain GPS base data from another source. An alternative source of base data may not be readily available (particularly in remote areas), leaving the user only one choice, to buy yet another GPS receiver. Obviously, this adds to the cost of using GPS. In some cases, acquiring a second receiver will immediately double the cost of using GPS because users must buy two receivers (base and rover) instead of just one.

Cheating the Hangman?
Some users try to get around this dilemma by simply using one receiver, collecting more than one position at each site, then averaging together multiple positions. The premise is that the average of many positions is likely to be better than any individual position. This is correct. However, the big question is, "How long must you average to obtain some particular accuracy?"
      The answer is...
      "It depends.
      " The severity of Selective Availability varies with time. During periods of severe degradation, you must average for a longer time than when S/A is mild. To illustrate, let's examine the GPS data for a 24 hour period selected at random.
      Figure 2 illustrates the result of averaging position data for varying periods. The data represented here was collected continuously over a 24 hour period at a high precision geodetic control point. Positions were collected once per second for a total of more than 86,000 positions. The X-axis represents the amount of time over which the positions were averaged. The Y-axis represents the distance from truth of the resulting average position.
      For example, the graph indicates that after averaging data for two hours (7,200 positions), the average location of these 7,200 positions was 41.73 meters from the true location. Since there were 24 hours of data to choose from, and because the average for one 2 hour period could be different from the result at another, the full 24 hour data set was divided into as many unique two hour data sets as possible (12 two hour sets). All 12 of the two hour data sets were averaged to generate 12 different answers, then the 12 answers were averaged together to provide a single representative value for the time "2 Hours." The table on page 44 (Figure 1) summarized the 12 data sets that were combined to produce the value on the graph in Figure 2.
      Note the wide variability of the 12 two hour averages. After averaging over 7,000 positions the answers range from as much as 82 meters from truth to as little as 7 meters from truth. It is important that users recognize the unpredictability of averaging data without differential correction.
      The same procedure was used for all of the time periods on the graph. Thus, the value in the graph representing 15 minutes (0.25 hours) was derived from 96 different 15 minute samples. On the other hand, the values in the graph representing 16 and 24 hours were derived from a single set of 16 hours and 24 hours of data respectively.
      It is interesting to note that the first data point (15 minute average) is more accurate than the 30 minute and the one hour averages. This also is indicative of the large variability of uncorrected, averaged data. It is conceivable that, once in a while, a user could obtain a very accurate position by averaging only a few hours of data. This is merely luck, the problem is that the user never knows when the average was lucky and when it was not.
      It is important to be aware that the results plotted in Figure 2 are specific for only that particular 24 hour period. It is very likely that other 24 hour periods would be similar in that they would show error decreasing with time, however, the magnitude of the error could vary significantly from day to day.

What If You Keep On Going?
What happens if you average data more than 24 hours? Several data sets have been collected ranging from 1,500,000 to 14,000,000 positions. In general, the average wanders around within about 5 meters of truth for about three weeks (or about 1,500,000 positions at once per second). After three weeks to as much as six months the average position does not improve beyond about 1-2 meters from truth.

Summary
The previous data indicate that averaging uncorrected data is not a reliable way to generate dependable, accurate positions. Be aware that after position data is averaged together in the field, it is no longer differentially correctable. For a successful differential correction, GPS receivers must store much more information than just position. Therefore, if a single averaged position is stored in a GPS receiver, it will not have the details that are required to correct it later via post-processing.
      There are many GPS systems on the market today that allow users to average position data while in the field. This is a very dangerous feature. I advise extreme caution in using any such averaging features. Consider the two points below if you require reasonably accurate data, and you plan to average while in the field. There are two ways that position averaging and differential correction can be used together. First, if ALL of the position data is stored and the positions are first differentially corrected then the corrected positions are averaged together. Alternatively, if the differential corrections are being performed in real-time via a telemetry link with your base receiver. This real-time correction scenario is useful primarily when users plan on using the GPS receivers to navigate accurately while in the field. If either of the two techniques described above are used you can have the best of both worlds.

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. If you have a suggestion or request for a future article, please drop a line to Chuck care of Earth Observation Magazine.

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