Figure 1. The Earth and two atmospheric layers. Point C represents the center of the Earth; point P is the location of the GPS receiver; and point D is where the low-altitude signal from B enters the troposphere. Using this chart, we can construct a right triangle where side CP, the hypotenuse, is 6,372 + 12 kilometers, or 6,384 kilometers. Using the Pythagorean theorem, we find that side DP, the distance the signal travels through the troposphere, is 407 kilometers. (Note: The height of the troposphere and ionosphere are exaggerated compared to the size of the Earth.)

Q:Why do we mask satellites near the horizon? And why do experts treat signals from satellites near the horizon--even if they are above the elevation mask--as contributing to a weaker solution than signals from satellites that are more or less directly overhead?

A:The short answer is that low-angle satellite signals travel much greater distances through the atmosphere than signals from satellites directly overhead and are thus subject to more effects of refraction. To help you understand the geometry, remember that there are several layers to the atmosphere. The layer closest to the Earth’s surface--the part we live in--is called the troposphere. It generally varies in height between 7 and 17 kilometers. For the purpose of this discussion, we’ll use the average of those heights, which is 12 kilometers.

Figure 1 shows the Earth with a couple of the layers of the atmosphere that affect the GPS signals--the troposphere (at an average height of 12 kilometers) and the remainder of the atmosphere, which is considered by most to be between 100 and 120 kilometers. When it comes to GPS signals, we also often talk about the ionosphere, which extends from about 50 to 1,000 kilometers above the earth.

For a particular GPS receiver location on Earth, imagine satellite signals coming from satellite A and satellite B. Satellite A is almost directly overhead, and the signals travel through about 1,000 kilometers of ionosphere and about 100 kilometers of atmosphere, of which the last 12 kilometers is considered the troposphere.

For satellite B, which is near the horizon, we can see that the distance the signals must travel through each band of the atmosphere and ionosphere is much greater, even though the thickness of the ionosphere and the atmosphere is greatly exaggerated in this figure compared to the diameter of the Earth (approximately 6,372 kilometers). A simple calculation of a right triangle shown in Figure 1 reveals that the distance the low-angle satellite signal travels through the ionosphere is about 3,707 kilometers, and even the distance traveled through the 12-kilometer-thick troposhere is 407 kilometers--more than 32 times the troposhere’s height. Thus, any effects on the signal will be at least this order of magnitude greater.

The simplified diagram shown here is not accurate because the signal from the satellite starts curving downward once it is refracted. This movement further increases the distance traveled through the atmosphere.

Q:When using RTK GPS in or near a heavily wooded area or even near a tree with heavy canopy, I will often find that if I walk in at a “normal” speed to the point I’m interested in surveying, I have lost lock by the time I get my antenna pole in place and leveled. When I either walk in very slowly or run in, that seems to prevent the loss of lock. I’ve been told by a seminar speaker that this is at best an erroneous position and at worst a procedure that might be called unprofessional because it is an inappropriate use of the surveyor’s tools. What do you think?

A:Sorry to say that the procedures you are following are an inappropriate use of RTK GPS. GPS, whether RTK or not, is predicated on obtaining good reception from an adequate number of satellite signals. The receiver electronics and associated firmware use those signals to make the measurements that are required to determine the baseline from the base station to the rover. If the satellite signals are “iffy” for whatever reason, then the measurements are either not accurate or not possible. In the former case, you might get a low-accuracy position of the point you are trying to measure; in the latter case, you will get no position at all.

It is hard to say exactly what happens when you walk in slowly. If you lose lock when you walk in at a normal speed, you should also lose lock at a slower walking speed. Perhaps in your second attempt you weren’t blocking some of the low-angle satellite signals visible between the edge of the canopy and the horizon. It is also possible that the GPS receiver is having a hard time tracking the signals, and by slowing down you gave it the ability to avoid losing lock. However, you must be careful not to assume that not having a state of “loss of lock” is equivalent to high-quality positioning.

In the case of running in to get a position, you are probably experiencing a latency between the measurements and the actual display of your coordinate or, more likely, a latency between the measurements and the message that lock has been lost. The position you record in these circumstances may be the position when the system last had a good measurement, which could be quite a distance from where you finally placed your antenna pole.

In situations with heavy tree canopy, it is generally recommended that you locate a pair of points near high-quality positions and then occupy one of them with a total station and backsight the other to locate the problematic point with optical technology. When you do this, be sure to evaluate the quality of the position you wish to have when you locate the point under the trees. You should also space your pair of points so that your azimuth will be of the desired quality while keeping in mind the uncertainty of positioning with RTK for the particular situation.

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