Trilateration: A must for NextGen and ADS-B

This is the seventh in a series of articles looking at the impact of NextGen on GA pilots.

Last post we discussed where GPS came from and how its implementation was successfully completed by using ground base pseudolites.

We also reviewed how triangulation was used for navigation. Triangulation basically emulates what we in aviation have used for years with VORs and ADFs. Pick two or more transmitters, home in on their intersection and, boom, you found your location.

Now we will home in on GPS a bit more and begin to see what role GPS will play in the Next Generation Air Transportation System (NextGen) and Automatic Dependent Survelliance-Broadcast (ADS-B), the cornerstone of NextGen.

Besides triangulation, GPS uses time, distance, and a fixed known value to calculate its location by using this easy algebraic equation: Distance = Speed of Light x Time of Signal Arrival.

Satellites are spaced at particular distances apart and travel on different orbits around the Earth so that there is always at least four birds that have a direct line of sight to our GPS receivers (See Figure 1A).

Figure 1B demonstrates that each bird must be at least 11° above the horizon for the GPS to use it correctly. The higher you fly your airplane, the more birds you get to use. If you were to stand directly under a GPS satellite, which is 18,000 kilometers (or about 11,184 miles) above the Earth, the time it would take the RF (Radio Wave Signal) to reach you from the satellite would be approximately .065 seconds. By using this simple algebraic equation and solving for the appropriate unknown, you can determine distance or time.

Remember those spheres we discussed last post? These spheres bring on a different type of data retrieval called Trilateration. Now this gets pretty cool. Check out Figure 2a: The green sphere represents Earth and the blue sphere makes up the distance between Satellite 1 and our GPS receiver on Earth, depicted as a red X. This means that our GPS receiver’s location can be located anywhere along the arc of the sphere’s intersection with Earth.

Add another satellite, called Satellite 2 (Figure 2b), which creates yet another sphere’s radius (shown in pink) whose size is defined by the distance from our GPS receiver and Satellite 2. You can see that each sphere literally overlaps each other and sits inside the other. A white line defines their point of intersection.

By adding the second satellite, our GPS receiver can see two spheres, providing a more defined point of intersection. In Figure 2c we rotated all the objects in Figure 2b to the left, putting Satellite 2’s sphere in front of Satellite 1’s. The white circle formed here is the intersection between the two spheres as a white line in Figure 2b, just where they are touching each other. We can see our GPS receiver located somewhere on this white circle.

Now bring in Satellite 3, which builds another sphere where it intersects into the first two spheres, plus a fourth sphere, which is the Earth. The third satellite’s sphere adds an additional green intersection line showing a red X intersection at the bottom or yellow X intersection at the top. The GPS has some intelligence where it knows it is on the Earth side of the sphere and uses the lowest point. Four or more satellites allows for pinpoint accuracy, along with elevation or altitude.

Modern day GPS satellites must have within them atomic clocks that produce precision time-coded signals transmitting a kind of almanac to keep all the satellites synchronized, up to date, and on time with each other. But there are other factors that still have to be attended to in order to keep these clocks in sync.

This is where our old friend Albert Einstein comes into the picture. He predicted that objects in orbit run at different speeds than objects on the Earth’s surface. The reason is gravity. The closer you are to the Earth, the stronger the gravitational field and the slower time moves. Conversely, the further you are from the Earth, the weaker the gravitational field and the faster time moves. The link between both time and gravity is caused from heavy objects in space, like the Earth and the Moon, that actually bend space. Since time is directly linked to space, these heavy objects bend time also.

Satellites orbiting above the Earth at 18,000 kilometers have far less gravity than what is on Earth, causing their clocks to run a bit faster. Because of this, there are monitoring stations around the Earth that periodically reset these clocks to keep them exactly synchronized with each other. If not, this error would cause GPS systems to drift as much as 12 kilometers (about 7.5 miles) a day.

Still, other time-related errors occur due to Earth’s atmosphere. Similar to light bending (or refracting) when traveling through glass, radio signals that travel though Earth’s atmosphere also bend the RF signal. Although somewhat small, this bend (Figure 3) can cause further delays that influence a GPS location. To correct for these errors, a function known as Differential Correction is used. Satellite reference stations are positioned on the Earth’s surface. They are set at precise locations and receive the same GPS signals that your GPS receives. These stations calculate the amount of delay that is coming from these satellites and sends correctional data signals to your GPS, typically by using beacons of transmission.

However, a far more accurate state-of-the-art system that uses stationary satellites (Satellite #135 and Satellite #138) to get the message out is a system known to us in aviation as WAAS or Wide Area Augmentation System. This system increases accuracy, availability, safety and reliability for the aviation sector of GPS. Accuracy is improved from 20 meters to 1.5 meters. If there are any abnormalities within the WAAS GPS system, it will report this information directly to the cockpit.

There are 38 ground base reference stations, two master stations, two geosynchronous satellites, four uplink stations, two control centers, and a WAAS terrestrial communications network that pools all this information and gets the word out.

Can it get any better? Next month we dive into ADS-B. You will begin to see the direction NextGen will take us as these technologies became available.

Jeffrey Boccaccio is a private pilot and chief engineer at MatchBox Aeronautical Systems. You can reach him at NextGen@GeneralAviationNews.com or Jeff@Matchbox-Systems.com.

 

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