1. Flight Planning and Navigation
GPS Navigation
Aerospace Engineering
© 2011 Project Lead The Way, Inc.

2. Global Positioning System (GPS)

3. Global Positioning System (GPS)
Cloud of 24 GPS satellites orbit the Earth
Satellite positions are accurately known
GPS device receives satellite signal with ‘time-sent’ information
Device calculates distance to satellite
Intersection point of multiple satellites defines device location
Image source: National Coordination Office for Space-Based Positioning, Navigation, and Timing (2013). Retrieved from
A global positioning system utilizes multiple satellites that orbit the Earth. The triangulation of the satellites is based on extremely precise timing of radio waves that are received from the satellites. Since the satellites are not stationary but moving through space at thousands of miles per hour, the radio waves are slow. They bend and bounce their way from satellite to receiver.
With the challenges that arise from the satellites orbiting the Earth, it is easier to examine how the GPS works in smaller bits. How does GPS really work, how is the accuracy challenged and maintained, and how are technical and engineering techniques used to overcome those challenges to make GPS the most readily available, accurate, and truly global navigational system available?

4. Satellite Precision One satellite
limits possible GPS receiver location to a spherical location
A GPS system calculates the distance from every satellite that a receiver can see above its local horizon. With one distance you can determine that you are somewhere on a tremendously large sphere that is visible from the satellite. When a second satellite is available and the distance is known, you have a second sphere that intersects with the first sphere. Since the GPS receiver must be on a sphere and not inside or outside of it, the intersection of the two spheres is a huge circle in space. This circle can be enormous, with a diameter much larger than the entire planet Earth.
Two satellites
limit possible GPS receiver location to a circular location

5. Satellite Precision Simplified diagram Three satellites
limit possible GPS receiver location to two locations
If a third satellite is provided, the intersection of all three is reduced to two locations in space. One location is illogical as it is in outer space somewhere or it is moving at an incredibly high speed. The GPS receiver can be programmed to ignore this point and assume that the other one is where you are located. Of course, you could just as easily use a fourth satellite measurement to confirm this decision.
One location is impossible due to location and speed

6. GPS Orbital Configuration
24 satellites
20,000 km (Approximately 12,500 mi) above Earth
Orbits take 12 hours
Cover entire Earth
Image source: National Coordination Office for Space-Based Positioning, Navigation, and Timing (2013). Retrieved from

7. GPS Orbital Configuration
Satellites orbit the earth in a uniform path; however, the Earth moves underneath the path. This is the reason why the ground track is always changing, as shown in the image.
Unfortunately, knowing just the distances from the satellites doesn’t really help us find our location. The satellites are very far away and constantly moving. We are XX miles away from where? In order for our GPS to work, we need to know the location of the satellites much more accurately than we need to know our actual location.
GPS satellites orbit very high above the Earth. This makes their future flight path very predictable. Therefore, it is easy to calculate an “ephemeris” for the satellite. An ephemeris is a table indicating future positions of an object. The ephemeris data for every GPS satellite is confirmed and updated by using very powerful and accurate ground-based radar measurements of the satellite’s current position and velocity in space. The ephemeris is constantly changing due to the gravitational pull of objects (Sun and Moon) as well as drag caused by the solar wind.
The Department of Defense broadcasts this information to the satellite, which sends its ephemeris data out along with its unique Psuedo-Random Code.
Measuring the distance to an orbiting satellite is a daunting task using physical means. However, radio satellite broadcasts make this a simple task. After all, radio waves travel at a known speed, the speed of light.
Imagine seeing a marathon runner during a race. The runner always runs at 10 mph. When you stop the runner and check his or her wrist-stopwatch, you find that the runner has been running for 2 hours. If you use the distance formula (Distance = Rate * Time) you can determine that they must be 20 miles into the race.
Rate (10 mph)  x   Time (2 hrs) = Distance (20 miles)
For a radio signal, the rate is about 186,000 miles per second. At speeds this high, the calculated distance is only as accurate as your ability to accurately measure time. If your stopwatch is off by one second, your distance is off by 186,000 miles.
Challenge:
How accurate must the stopwatch for light be in order to achieve an accuracy of less than 52.8 feet (1/100th of a mile)? How about 5.28 feet?
Back to the runner. You wanted to know how far the runner had run. You were able to determine this by checking the stopwatch to determine how long he or she had been running. It makes sense that you must check the stopwatch to determine how far the runner had traveled, but who started the stopwatch in the first place? If you looked in the newspaper, you could look up the fact that the marathon was supposed to start at noon. Using your own watch, you could measure the time of arrival and determine the travel time of the runner. The problem is that you can’t know whether the race really started on time, and you need to have a very precise time measuring tool on your wrist.
A GPS system avoids this issue by having a satellite broadcast the same short phrase over and over again. Remember the message does not need to be very long as the speed of light is very fast; the message arrives at the receiver very quickly. The short phrase that is used by the satellite is called the Pseudo-Random Code (PRC). It is an engineering breakthrough even though it is really just a pattern of digital 1s and 0s, or “on” and “off” pulses. The pulses are very complex, almost random noise, designed to guarantee that the receiver can identify the satellite that is broadcasting the signal.
The complexity of the process allows the system to use the same frequency for all satellites and makes it difficult to jam the system to degrade its accuracy. This is an important concern considering the system was originally developed by and for the military.
The other reason the PRC is an engineering breakthrough is its ability to allow the satellites to use very weak signals and the receivers to use very small antennas. This makes the system affordable and portable. The miracle is in the noise, the real noise—real noise IS random. Thus, if you compare the 1s and 0s in noise with the PRC’s 1s and 0s, they will match only half the time. If you declare a +1 every time the two signals match and a -1 every time they mismatch, the sum of all signals will provide a net result of zero no matter how long you compare the signals.
If you were to compare the PRC to another signal with lots of noise (i.e., weak signal and small receiving antenna) and the same PRC signal embedded in it, the longer you compare the signals, the more the sum drifts positive. The weaker the signal or the longer you collect the signal, the outcome is the same. You can amplify the signal and confirm the match. 
All of this is important in order for the receiver to compare its internal repeating phrase to that from the satellite. The two signals start out in sync, but the satellite’s phrase is delayed by exactly the travel time to the receiver. If you measure that time delay and multiply it by the speed of light, the result is the distance to the satellite.
On GPS satellites, the timing for the start of the PRC broadcast is synced to a tremendously precise onboard atomic clock that cost tens of thousands of dollars. You can’t afford this technology for timing on the receiver side. How do you start the internal PRC phrase of the receiver to work at the right time?
It is safe to assume that the receiver’s cheap internal clock is not in sync with atomic clock accuracy. However, the inaccuracy creates a predictable error. Let’s assume that the receiver clock started its PRC phrase a little late. Using a simple example, assume the receiver was a second late and remember that real travel times for waves are on the scale of 0.1 second or less. Since the receiver doesn’t know its clock is late, it would just assume that every time delay it measured was 1 second shorter than it really is. This shortens the distance to each satellite by 1 second or 186,000 miles, which drastically shifts the predicted location of where the signals from three satellites signals could intersect. The receiver doesn’t know that it has a problem. However, add in a fourth satellite, and the signals can’t possibly overlap at the same place.
This is where computers really shine. The receiver’s computer chip can simply try different time corrections for all four satellite signals until it finds one that makes them all pass through a single point in space. If it then actually applies this correction to its internal clock,—the clock is now synced to the atomic clocks on the satellites for dollars rather than tens of thousands of dollars.
The secret is the fourth satellite signal. Most GPS units have at least a four-channel receiver so that they can process the signals simultaneously.
Track Across the Earth

8. GPS Accuracy Within 100 meters (328 ft) Original GPS
Within 15 m (49 ft)
Selective availability removed
3-5 m (10-16 ft)
Differential position (GDPS)
< 3 m (10 ft)
Wide Area Augmentation System (WAAS)
Selective Availability was the military degradation of the GPS accuracy for defense purposes. More information is available at the National Executive Committee for Space-Based PNT website:
The PRC and ephemeris signals from four satellites should provide an absolutely accurate position to the precision of the atomic clock on the satellite. The key word is “should” as there are many problems associated with timing the signal’s travel time. Remember even a thousandth of a second is a huge error!
Problems include the reduction in the speed of light as it enters the atmosphere (error to greater distance), signals that reflect off of multiple objects and create echoes that arrive at different times, purposeful errors, and even atomic clock errors.
We can correct for the atmospheric problems by using more advanced technology. If the receiver can monitor dual frequencies, then it can compare the amount of variation between a low-frequency (slowed more) and a high-frequency (slowed less) signal to deduce the error and correct for it. The GPS system broadcasts on two different carrier frequencies called L1 and L2. Unfortunately, this requires a very sophisticated receiver. Only the military has access to the L2 carrier channel. The other option is to build in atmospheric models so that “typical” corrections can be made to all incoming signals.
Receivers can deal with the multi-path errors by employing signal rejection analysis software. The basic principle is that the first signal to arrive will have traveled along the shortest route and thus any signal that arrives later is most likely an echo and should be ignored.
Before May 1, 2000, the government purposely degraded the timing data of the satellite’s clock by adding noise to the signal. They may also have introduced slight inaccuracies to the ephemeris data. Military GPS receivers made use of a decryption key to obtain the full accuracy information. This Selective Availability (SA) was disabled, which improved the accuracy of GPS positions by a factor of 10.
All of these errors combined introduced errors of about 10 meters. With SA active, this led to errors of hundreds of feet. Without SA the basic GPS receiver is capable of measuring positions to within 30 or 50 feet. This is accurate enough for an aircraft approaching a runway, but unfortunately it isn’t accurate enough to land the aircraft on the centerline of the runway.

9. GDOP - Geometric Dilution of Precision
GPS accuracy is influenced by the visibility and wide angles to the satellites.

10. GPS Augmentations Systems to increase GPS accuracy
Nationwide Differential GPS System (NDGPS)
Wide Area Augmentation System (WAAS)
Continuously Operating Reference Station (CORS)
Global Differential GPS (GDGPS)
International GNSS Service (IGS)
The key to the improved accuracy of the DGPS system (meters for a moving receiver, better yet for a stationary one) is the presence of a fixed local GPS station. If the fixed station is fairly close to our mobile DGPS unit (within hundreds of miles), it should share the same errors in its signals. If the location of the fixed station is accurately surveyed, the errors in its GPS position can be transmitted to the mobile unit to correct its position. The fixed station measures the errors in all visible satellite data.
These corrections can be broadcast live to the receiver if extreme accuracy is essential. Corrections can also be applied later when the GPS unit returns to base for corrections. Another method is called “inverted differential” GPS where each mobile unit broadcasts its positions back to a base station for immediate correction. All methods improve the accuracy to a few meters.
The ultimate accuracy of the system is based on timing. If we could use an even more accurate timing method, the accuracy of the system would be improved. Normal GPS is based on “code phase” by sliding the psuedo-random code from the receiver back until it matches that from the satellite. But the frequency of the code is very low, which means that a 1% error in matching up the timing is a significant meter error.
By switching to a “carrier-phase” system, the GPS unit can pay attention to the much higher frequency carrier code in the 1.57 GHz range. The entire wavelength is in the centimeter scale. This makes the phase errors that are possible in the few millimeter range. This is 1000 times more accurate than the traditional GPS system.
The Wide Area Augmentation System (WAAS) is based on using a geostationary satellite that broadcasts on the GPS frequencies to transmit alerts that a particular satellite has errors and should be ignored. More importantly, the system broadcasts differential correction data from about 25 stations scattered all across the country. WAAS enabled GPS units have allowed aircraft to commit to “category 1” landings in which they can use the unit to navigate very close to the runway before they must obtain visual references for the final landing.
If we place the differential receiver stations on the airport near the runway, this Local Area Augmentation System (LAAS) would be capable of such extreme accuracy as to allow “category 3” landings where the GPS unit is trusted all the way to touchdown in even zero visibility.
Challenge: How would you extend this level of accuracy to the entire globe?

11. NDGPS – Nationwide Differential GPS System
Accurately surveyed locations used for reference
Corrects GPS for increased accuracy for users on land and water
Developing system for cm accuracy
HA-NDGPS (High Accuracy NDGPS) intended to be accurate within cm.

12. WAAS - Wide Area Augmentation System
Operated by FAA (U.S. Federal Aviation Administration)
Aircraft navigation for all phases of flight

13. Benefits of WAAS Primary means of navigation More direct routes
Approach with vertical guidance
Decommission older equipment
Simplify onboard equipment
Increased capacity
Primary means of navigation (Takeoff, enroute, approach, and landing).
More direct routes. Not restricted by location of ground-based navigation equipment.
Approach with vertical guidance at any qualified US airport.
Decommission older equipment.
Reduce maintenance costs of expensive equipment.
Simplify onboard equipment.
Increased capacity due to reduced separation of aircraft. Improved accuracy allows this.

14. References
Federal Aviation Administration (2009). Retrieved from iStockphoto (2011). Retrieved from National Aeronautics and Space Administration (2009). Retrieved from National Coordination Office for Space-Based Positioning, Navigation, and Timing (2013). Retrieved from