From Earth’s Atmosphere to Zero Mean Noise
By Ben Segal CTO at Navmatic
Photo by NASA
93 million miles away, the Sun ejects a large volume of charged particles that hurtle towards Earth. While you stare at the blue dot on the map application on your phone, you may not realize that in just a few hours or days, those particles will arrive at Earth, wreak havoc on GPS signals, and incorrectly cause your blue dot to jump across the street. Understanding the error caused by these particles (and from other sources) is the key to unlocking great positioning performance and a blue dot which accurately represents where you’re located.
As described in the previous blog post, Introduction to GPS, determining location using GPS requires:
- distance measurements to (at least) four satellites
- locations of (at least) four satellites
Any error in either the distance measurement or location of the satellite will affect the accuracy of the estimated position. The distance measurement is computed by receiving and processing signals from a GPS satellite.
The precise GPS signal containing bits of data is generated deep inside the GPS satellite. Then, it passes through various electronic hardware components and finally escapes an antenna pointed at Earth at 299,792,458 meters per second, the speed of light. As the signal travels towards Earth it gets slowed by the free electrons of the ionosphere as well as the air and water vapor molecules of the troposphere. At the last minute, the signal bounces off of nearby buildings and lands in your cell phone.
Each of these impediments causes an additional amount of error in the GPS signal that can result in poor GPS accuracy. Some of these errors are more or less prominent depending on the application and the environment. In this blog post, we’ll cover some of the most prominent GPS errors and how to mitigate them.
Space weather and Earth weather can both dramatically interfere with GPS signals.
The ionosphere is a component of Earth’s atmosphere, located roughly a few hundred kilometers above the Earth. During the day, the sun’s energy causes gas molecules in the atmosphere to lose electrons, a process known as ionization. As these free electrons
Photo by NASA
accumulate, they start to interfere and delay the GPS signal. At night, as the rate of ionization decreases, the GPS signal error decreases, which corresponds to a more accurate estimated position. During a normal day, this delay can be on the order of a few meters of error. The delay also depends on the season and location on Earth.
The ionosphere is also heavily affected by solar weather. Solar storms release large amounts of energy that can cause rapid, unpredictable fluctuations in the ionosphere and corresponding severe, rapidly changing signal delays.
The troposphere is also a portion of the atmosphere, but located much closer to the surface of the Earth and is composed of air and water vapor molecules. These molecules slow down the GPS signal as well, but not as significantly as the ionosphere. Typically this error is on the order of a few meters.
3. Satellite Errors
Knowing precisely where each satellite is located as well as what time the satellite thinks it is are critical for good positioning performance. Each satellite broadcasts its estimated location in a data message known as the ephemeris. For a quick explanation of the ephemeris message, check out Introduction to GPS. These ephemeris messages are not perfect, so there is some error due to where the
Photo by NASA
satellite thinks it is relative to where it actually is. Similarly, although each satellite contains multiple atomic clocks, these clocks can also have slight errors that need to be compensated for.
Atmospheric and Satellite Error Mitigation
Although atmospheric delays and satellite specific errors can be significant, they can also be mitigated in a few ways. We’ll cover some, but not all, of the most common techniques.
A simple, but coarse method for removing some of the ionosphere and troposphere error involves using empirical models. These models exploit the fact that the ionosphere and troposphere can be modeled roughly as a function of time of day, day of year, and location on Earth. More sophisticated models might incorporate solar weather data or local temperature and humidity observations.
Due to the underlying physics that governs how the ionosphere delays the electromagnetic GPS signal, the ionospheric error is a known function of the frequency of the signal. Therefore, if GPS signals are tracked on two different frequencies, they can be combined using a specific mathematical relationship to remove almost all of the ionosphere delay. However, this technique doesn’t work for the troposphere.
Another method of eliminating atmospheric and satellite specific errors involves using correction data transmitted from a third party. There are many possible implementations, but two common ones are RTK (Real Time Kinematic) and PPP (Precise Point Positioning). With RTK, raw GPS signal observations from a GPS base-station are transmitted and then received by nearby receivers to subtract off many error sources that are seen in common. With PPP, correction data to remove specific error sources individually are transmitted to receivers globally. Newer techniques such as PPP-RTK seek to fuse the wide-area coverage of PPP with the precision of RTK corrections.
Receiver Specific Errors
One of the most severe and trickiest error sources also occurs most frequently in dense urban environments. Multipath occurs when a GPS signal bounces off of a building, car, or anything else. This reflection can be small or large and there can be many of them as the signal bounces off of multiple objects. In the worst case, a satellite might be blocked from view by a building, but the signal may deceptively bounce around a corner, providing an erroneously large measurement.
Photo by Kenta Kariya
Each GPS signal has noise, some of which is related to thermal noise and some of which is due to the properties of the GPS signal structure.
Receiver Specific Errors Mitigation
Multipath errors are specific to each receiver and also highly dependent on the local environment which makes them difficult to eliminate using models or corrections. Often, multipath is most easily eliminated before it gets to the position computation, using specific antennas or signal processing techniques in the GPS receiver electronic hardware.
Some more advanced mitigation techniques include using local environment data (such as 3D building models) to evaluate whether to include or reject various GPS signals from the position computation.
In addition to the United States’ GPS, multiple additional Global Navigation Satellite System (GNSS) constellations exist such as Russia’s GLONASS, China’s Beidou, and Europe’s Galileo. Using multiple constellations can help mitigate multipath by providing additional signals free from reflections or obstructions. In addition, using multiple satellite constellations allows for taking advantage of more modern signal structures that reduce noise.
This table shows the approximate magnitude of each GPS error source, but the exact error is highly dependent on the use case, application, environment, location, and time.
Similarly, which mitigation technique works best also depends on the use case and environment.
These five GPS error sources show why something as simple as a blue dot is actually quite complicated to pin down.
Sources & Additional Reading: