GPS Consumer Series: Doing Differential Correction "By Hand"
By Chuck Gilbert

Introduction
GPS is a very powerful tool. The productivity that can be achieved with GPS is mind-boggling. In some situations, when used for the collection of GIS data, it can boost productivity not by only two or three times, but by an order of magnitude! However, despite the benefits of using GPS, there are some short comings.
      When you allude to the deficiencies of GPS most people who are familiar with GPS will immediately think about Selective Availability. Selective Availability (S/A) is the intentional degradation of the GPS signal for national security reasons in the United States. Despite many other more serious issues, people seem fixated on S/A. This strikes me as a great mystery.
      Why? I doubt that our obsession with S/A is due to the magnitude of the errors. Although the specification of S/A is within 100 meters 95 percent of the time, the reality is that many uncorrected positions are within 20 meters of truth. The problem is that you just dont know when your position is good and when it is not. Maybe people have become so disturbed by S/A because it is an intentional degradation? I dont think this is the reason either, although it is troubling to see something so pure and beautiful being intentionally sullied, people tend to grow accustomed to seeing ugliness. After a while they dont notice any more. Perhaps this reaction is merely an understandable frustration of having the government meddle with our lives? Well, although we tend to forget, they are the governments satellites after all.
      S/A is remarkably easy to remove from GPS data. There are other error sources that cannot even be easily detected, much less removed. (Some error sources cannot be removed even if you have detected their presence.) There are quality control issues and industry standard issues, however, none of these other issues are as widely discussed. Why should everybody get so excited about S/A?

How to get rid of S/A
The process of removing the effects of S/A is trivial. In the most difficult scenario, you basically just tell some differential post-processing program the names of your data files and click on the Okay button. After your computer clicks and whirrs for a few minutes, you have a corrected file ready for your viewing pleasure. (See the sidebar for more details about differential correction.) In one of the simplest scenarios, you can subscribe to a commercial service that will transmit the differential corrections directly to you, 24 hours/day. You can receive these corrections to S/A by simply carrying a small personal pager and connecting it to your GPS receiver.
      There are other commercial services that transmit the corrections via communications satellite over entire continents. Even the United States government is in on the act. While the Department of Defense is continually degrading the GPS signal, the United States Coast Guard and the Army Corp of Engineers are continually transmitting the corrections to all who are interested! Additionally, many other national governments transmit these corrections to their own citizens as well. There is a theme that binds all of these different types of differential correction. Money. To do differential post-processing, you have to buy a program. For the commercial services that transmit the corrections, the key word was subscribe. Even to receive the free transmissions from the government, you have to buy a special radio receiver that can receive the transmissions.
      It seems that everybody wants to find a way around the system. More specifically, everybody wants to find a cheap way around the system! I have recently encountered several people wh think that they may have invented a good way around differential correction. I dont get out much. If Ive encountered so many people with this idea, then there must be an enormous number of people (who I have not met) that have reached the same conclusion.
      I can understand the allure of finding an inexpensive way to remove the scourge of S/A. However, what you save in money now will often be paid later in inconvenience and in erroneous data. Lets examine this clever little ploy to remove S/A.
      The more crafty GPS user might ask (as indeed he has), If I just record position data in one receiver at a fixed, known location, cant I examine these positions later to determine the errors associated with S/A? (Simplified, the answer is Yes.)
      Assuming that both receivers had common errors, can I simply subtract these errors (that Ive computed at the fixed receiver) from the other receivers that were roving about collecting positions at unknown locations? Would this process remove the effects of S/A from my other receivers that were roving at unknown locations? Sound simple? The answer is, Yes, you can, if you're careful, lucky, and have a lot of time on your hands.
      In order for this little trick to be successful, there are two important issues that you must keep in mind. First, the data in both receivers must be collected simultaneously. Second, both receivers must choose to use exactly the same satellites at exactly the same time for position computation. If either of these rules are violated, then the technique described above cannot be used to remove any errors.

Got the time?
Time is the first issue that must be considered in answering the question above. If you observe the position data collected by a receiver at a stationary, known location, you will find that the position changes continuously. Therefore the position error is also constantly changing. Therefore, to successfully apply the corrections from one receiver to another, you must have collected the data simultaneously on both receivers.
      It will not be viable for you to simply compute one correction value that can be used for an entire day of data. In fact, if the correction and the position to which it is applied differ by more than a few seconds, the corrections could be incorrect by meters. In fact, most receivers that collect data for differential processing actually make it a point that the data at multiple receivers is collected absolutely simultaneously. So for example, if two receivers are both set to record data every 5 seconds, they will both always record at an absolute time of 5, 10, 15, etc. (No matter what time they were turned on, neither would ever record at 7, 12, 17... or at 9, 14, 19, 24, etc.) This helps to ensure that the data is collected simultaneously at both receivers.

Pick a satellite, any satellite
The second issue to be considered has to do with satellites. The time and orbital data from the satellites is how errors are imparted by S/A. The data from every satellite is erroneous. Furthermore, the error on every satellite is unique and changes constantly. Therefore the error associated with any given position is a direct result of which satellites were used to compute that position. For example, a position computed using satellites 1, 2, 3, and 4 will have completely different errors from a position computed from satellites 2, 3, 4, and 5.
      Recall that to effectively correct positions both receivers must have encountered similar errors. This will be true only if both receivers were using exactly the same satellites at exactly the same time. It takes a minimum of four satellites to compute an accurate GPS position. (Positions can be computed from more than four satellites, but four is the minimum that we will consider.) At any location on Earth, there are typically about eight to 12 satellites visible. So, for example, if there are 10 satellites visible that makes 848 possible satellite combinations that might have been used to compute a position!
      If both receivers are situated where they have an unobstructed view of the sky, it is quite likely that they will both select the same satellites, especially if they are the same brand of GPS receiver and thus use the same satellite selection algorithm. Unfortunately, this is not a very likely scenario because the roving GPS receivers are usually encountering buildings and trees that intermittently block various parts of the sky. These local sky obstructions are very common and thus results in the two receivers using different satellites a great deal of the time.

Do you have what it takes?
There is still another obstacle to consider. What information from the GPS receiver was recorded in the data files? I think you see now that a record of which satellites were used is vitally important. Was the satellite information recorded for all the position data? Generally it is not. Note that in the more sophisticated GPS that is designed for differential GPS, such information would always be recorded automatically. However, in the low-cost GPS receiver (that was not designed to do post-processed differential GPS) it is very unlikely that any information would have been recorded about which satellites were used. Therefore, it is likely that the only way a user could obtain a record of which satellites were used for which positions would be to station a user at the receiver and to keep a constant log of what satellites are being used at what times. (Assuming, of course, that there is a screen that provides such detail.)

Summary
There are several GPS receivers on the market today priced as low as a few hundred dollars. The least expensive GPS receivers that are designed to do differential GPS are generally priced in the thousands of dollars. Users who attempt to apply differential corrections by hand generally have underestimated what it takes to do an accurate, reliable differential correction.
      The risk of grossly incorrect position data and the labor intensive nature of this manual differential correction make it a highly impractical solution. The additional cost to buy a well designed, professional GPS data capture tool (as opposed to a low cost consumer oriented receiver) is well justified by the consistently superior accuracy and reliability.

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.

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