GPS, How does it work? | ICT #12

Summary

The video script delves into the fascinating world of GPS technology, explaining how it utilizes a constellation of 24 satellites and the concept of trilateration to pinpoint locations. It highlights the critical role of atomic clocks and Einstein's theory of relativity in ensuring accuracy, as even tiny time discrepancies can lead to significant location errors. The script clarifies that GPS doesn't require an internet connection but can benefit from it for faster startup. It concludes by emphasizing the importance of these complex technologies in our everyday lives, from food delivery tracking to car navigation.

Takeaways

• 🌐 GPS is a critical technology that relies on a network of 24 satellites to provide location services worldwide.
• 📍 To accurately pinpoint a location, GPS uses a minimum of four satellites, employing the mathematical concept of trilateration.
• ⏱️ Atomic clocks on satellites are crucial for GPS as they provide precise timekeeping, essential for calculating distances based on signal travel time.
• 📱 The time error of mobile devices is a significant concern in GPS accuracy, as even a tiny error can lead to substantial location inaccuracies.
• 🔄 Albert Einstein's theory of relativity is integral to GPS, accounting for time dilation effects due to the speed and gravity experienced by satellites.
• 📊 Trilateration in 3D space requires three satellites to narrow down a location to two possible points, with a fourth satellite used to determine the correct one.
• 📶 The GPS system measures the distance between the satellite and the receiver by sending a signal with a timestamp, which the receiver uses to calculate distance.
• 🕰️ Receivers in smartphones use crystal clocks, which are less accurate than atomic clocks, necessitating a correction for the time offset in GPS calculations.
• 🌌 GPS does not require an internet connection to function, but internet assistance can speed up the GPS startup process by providing satellite information more quickly.
• 🛰️ Modern GPS receivers often use a combination of GPS and other navigation systems to enhance location accuracy and reliability.

Q & A

How many satellites are required for GPS to track a location?

At least four satellites are required to track a location using GPS.

What is the role of trilateration in GPS technology?

Trilateration is a mathematical technique used in GPS to determine someone's position by measuring distances from at least three satellites to the receiver.

Why do GPS satellites carry atomic clocks?

GPS satellites carry atomic clocks to provide highly accurate time measurements, which are essential for calculating distances and positions with precision.

How does the speed of light affect GPS calculations?

The speed of light is crucial in GPS calculations because the time it takes for a signal to travel from a satellite to a receiver is used to calculate the distance, and any delay, even in microseconds, can result in significant location errors.

What is the significance of Albert Einstein's theory of relativity in GPS?

Einstein's theory of relativity is significant in GPS because it accounts for the time dilation effects on the atomic clocks due to their high speed and the weaker gravitational field at the satellites' altitude, ensuring more accurate positioning.

Why do GPS receivers need at least four satellites to determine a location?

GPS receivers need at least four satellites to determine a location because, in addition to the three spatial coordinates, they also need to calculate the time offset of the receiver's clock, which requires an extra measurement.

How does the GPS system compensate for the inaccuracies in a smartphone's clock?

The GPS system compensates for the inaccuracies in a smartphone's clock by using the fact that the time offset is the same for all satellites, treating the time offset as an additional unknown to be solved along with the three spatial coordinates.

Does GPS require an internet connection to function?

GPS does not require an internet connection to function. However, an internet connection can speed up the GPS startup process by downloading satellite location information more quickly.

What is the impact of special relativity on the GPS satellites' atomic clocks?

According to special relativity, the atomic clocks on GPS satellites moving at high speeds slow down by about seven microseconds every day due to their motion.

How does general relativity affect the GPS satellites' atomic clocks?

General relativity causes the atomic clocks on GPS satellites to tick slightly faster at their altitude due to experiencing a weaker gravitational field, resulting in a faster rate by about 45 microseconds every day.

What is the net effect on the atomic clocks in GPS satellites due to relativity?

The net effect on the atomic clocks in GPS satellites due to relativity is a daily offset of about 38 microseconds, which is accounted for by adjusting the clocks' rates using a relativity equation.

Outlines

00:00

📡 Understanding GPS Technology

The first paragraph introduces GPS as an essential technology in our lives, utilizing a network of 24 satellites to determine location. It explains the concept of trilateration, which requires at least four satellites to pinpoint a location by measuring distances. The paragraph also touches on the significance of atomic clocks and the impact of time errors on GPS accuracy. It highlights the role of Einstein's theory of relativity in GPS, adjusting for time dilation caused by the satellites' speed and gravity. The summary emphasizes the need for precise time measurements and the practicality of using four satellites to determine location without an atomic clock in mobile devices.

05:01

🌌 The Role of Relativity in GPS

The second paragraph delves into the nuances of GPS accuracy, emphasizing the importance of Einstein's theory of relativity. It discusses how the theory of special relativity accounts for time dilation in fast-moving atomic clocks aboard satellites, and how general relativity corrects for the slightly faster ticking of these clocks due to weaker gravity at their altitude. The paragraph clarifies that GPS does not require an internet connection but can be augmented by it for faster startup. It also mentions that modern receivers use multiple navigation systems for enhanced accuracy. The video concludes by stressing the importance of relativity and other mathematical concepts behind the functioning of GPS.

Keywords

💡GPS

GPS stands for Global Positioning System, which is a satellite-based navigation system that provides geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. In the video, GPS is the central theme, as it explains how the system uses satellites to track and determine locations, making it integral to modern navigation and location services.

💡Satellites

The term 'satellites' in the script refers to the 24 GPS satellites that continuously orbit the Earth. These satellites are crucial for the functioning of GPS as they send signals that are used to calculate distances and, ultimately, the location of a receiver on Earth. The video emphasizes that at least four satellites are needed to pinpoint a location accurately.

💡Trilateration

Trilateration is a mathematical technique used to determine the position of a point in three-dimensional space by measuring distances from it to known points. In the context of the video, trilateration is used to explain how GPS calculates location by measuring the distance from a GPS receiver to multiple satellites and then determining the point that best fits these distances.

💡Atomic Clock

An atomic clock is a timekeeping device that uses the vibrations of atoms to measure time with extreme precision. In the video, it is mentioned that GPS satellites are equipped with atomic clocks to ensure the accuracy of time measurements. These clocks are essential because even a tiny error in time measurement can lead to significant inaccuracies in position calculations.

💡Relativity

Relativity, specifically Einstein's theory of relativity, is discussed in the video as it plays a critical role in GPS accuracy. The theory of special relativity accounts for time dilation in fast-moving objects, like GPS satellites, while general relativity accounts for the gravitational time dilation experienced by satellites due to weaker gravity at their altitude. The video explains how these relativistic effects are corrected for in GPS to maintain accuracy.

💡Time Offset

Time offset refers to the difference between the actual time and the time measured by a device, such as a smartphone's clock. In the video, it is highlighted that GPS receivers do not have atomic clocks and thus have a time offset. This offset must be calculated and corrected for to ensure the accuracy of GPS positioning, which is why a fourth satellite is needed to determine both the location and the time offset.

💡Speed of Light

The speed of light is a fundamental constant in physics, approximately 299,792 kilometers per second in a vacuum. In the context of GPS, the speed of light is used to calculate the distance between a GPS receiver and a satellite by measuring the time it takes for a signal to travel from the satellite to the receiver. The video emphasizes the importance of this measurement for accurate location determination.

💡Assisted GPS

Assisted GPS, or A-GPS, is a system that uses data from the internet or cellular networks to supplement the GPS signal. The video mentions that while GPS does not require an internet connection, A-GPS can speed up the startup process by downloading satellite location information from the internet instead of relying solely on direct satellite downloads.

💡US Department of Defense

The US Department of Defense developed the GPS system, as mentioned in the video. This highlights the origins of GPS as a military technology that has since been made available for public use. The video underscores the significance of GPS as a tool that has transitioned from military applications to widespread civilian use.

💡Navigation Systems

Navigation systems refer to the various technologies and methodologies used to determine position and navigate from one location to another. The video discusses how modern receivers can use multiple navigation systems, including GPS, to enhance accuracy. This highlights the evolution of GPS as part of a broader ecosystem of location-based services.

Highlights

GPS is an integral part of our lives with various applications.

GPS uses 24 satellites orbiting Earth, requiring at least four for location tracking.

GPS technology employs atomic clocks for precise timekeeping.

Einstein's theory of relativity is crucial for accurate GPS functioning.

Trilateration is the mathematical technique used to determine location in GPS.

Two satellites are needed for 2D trilateration, and three for 3D.

Satellites measure distance to the receiver to determine location.

The Earth's surface is used as a third reference to eliminate incorrect location possibilities.

Four satellites are required to account for the time offset of the receiver's clock.

Receivers use the time difference between sent and received signals to calculate distance.

Time measurement must be extremely accurate due to the speed of light.

Smartphones use crystal clocks which are less accurate than atomic clocks.

Time offset is a significant factor in GPS calculations and is mitigated by using four satellites.

GPS receivers do not need an atomic clock due to the use of four satellites.

GPS systems must account for time dilation effects described by relativity.

GPS compensates for relativity effects to maintain accuracy.

GPS was developed by the US Department of Defense and is free for public use.

Modern GPS receivers use multiple navigation systems for enhanced accuracy.

GPS does not require an internet connection for operation.

Assisted GPS uses internet downloads to speed up satellite location information.

Transcripts

- [Narrator] GPS has already become

an integral part of our lives,

And you can see a few useful applications

from these examples.

(upbeat music)

GPS is really an interesting technology.

It uses a system of 24 satellites

continuously orbiting the Earth,

and requires at least four satellites

to track your location.

It uses at atomic clock,

and the time error of your mobile phone

is also a matter of great concern.

Moreover, Albert Einstein's theory of relativity

plays an important role in GPS technology.

Finally, a real-life application

for the theory of relativity.

Let's put aside all these complications,

and understand the technology of GPS

is a step-by-step and logical manner.

Let's assume that your friend

wants to find out your location,

and you have a mobile phone

which has an integrated GPS receiver.

In GPS, an interesting mathematical technique

called trilateration is used to locate someone's position.

Let's first understand trilateration

in a two-dimensional way.

At least two satellites are required

to find out your position in two-dimensional trilateration.

Using some engineering techniques,

the satellites measure the distance

between you and the satellites.

We will see the techniques for doing this later.

Now things are easy.

The first satellite knows you are at a distance of R1.

So, you should be somewhere on this circle.

The second satellite knows you are at a distance of R2,

so you should be on this circle as well.

This means your actual location

should satisfy both these circles.

In short, you should be on the intersection points.

Now there is a small issue.

There are two intersection points.

So, which is your final position?

For this you take the Earth's surface as the third circle,

and eliminate the improbable solution.

In the three-dimensional world,

you can also use the same approach.

Here, instead of two satellites, we need three satellites.

In the three-dimensional world

the satellite knows you are somewhere on a sphere.

With the use of a second satellite

your position narrows down to a circle.

Note that the intersection of two spheres gives a circle.

Now, with the help of a third satellite,

you will be able to narrow down your location

to just two points.

Here, the intersection of a circle

and a sphere gives two points.

Just like in the previous case,

using the Earth as the forth surface

we find the correct point, the three spacial coordinates.

Now, let's see how the distance between you

and the satellite is measured.

All the satellites are equipped

with a very accurate atomic clock.

The satellite sends an intermittent

radio signal down to Earth.

This radio signal will contain the exact time

the signal was sent, and the position of the satellite.

Assume the receiver also has a very accurate clock.

The receiver on Earth receives the signal.

A typical smartphone GPS receiver is shown here.

Since radio waves travel at the speed of light,

your receiver receives the signal

after a certain time duration.

By finding out the difference

between the sent and received times,

and multiplying it by the speed of light,

you will be able to find out

the distance between you and the satellites.

Since the satellite has already sent you its coordinate,

you can easily build a sphere

around the satellite's center point,

and find out your position, as explained before.

One thing to note here,

is that the time measurement has to be very accurate.

Even an error of microseconds will give an error

in the range of kilometers,

since the speed of light is so huge.

Here comes the main issue.

Your receiver does not have a highly accurate clock.

Your mobile phones or laptops,

work on crystal clocks that are not accurate

when compared to atomic clocks.

Having an atomic clock in a smartphone,

is simply impractical.

You can easily see how inaccurate

your smartphone clock is compared to an atomic clock,

by checking the time settings.

We call the difference between to actual time,

and the time measured by your mobile phone, as time offset.

This time offset will cause a huge error

in GPS calculations.

How do we overcome this issue?

The good news is that the time offset of your smartphone,

with all three of the satellites is the same,

since the satellites all keep the same time.

The time offset value of your device

becomes the new unknown.

This means, apart from the three spacial coordinates,

we have to solve the time offset value

of your receiver as well.

We need an extra satellite measurement

to solve this fourth unknown,

and that is why we need four satellites

to measure your location.

This way we avoid the need of an atomic clock

in your mobile device.

If you check your current GPS constellation,

it will be clear that at least four satellites

can see your location at any point in time.

Please hold on, this video is not yet over,

we have one more issue to solve.

Even with all these advanced technologies,

this GPS system will not give you the right location.

Here comes the importance

of Einstein's theory of relativity.

Time is not absolute,

it depends upon many other factors.

According to the theory of special relativity,

a fast moving clock will slow down.

The atomic clocks,

which are moving at speed of 14,000 kilometers per hour,

will slow down by seven microseconds every day, due to this.

At an altitude of 20,000 kilometers above the Earth,

the satellites experience one quarter

of the Earth's gravity,

thus, according to Einstein's general relativity theory,

the clocks will tick slightly faster.

In this case, around 45 microseconds every day.

This means a net 38 microseconds offset

is created every day in the atomic clock.

To compensate for this,

a theory of relativity equation is integrated

into the computer chips,

and adjusts the rates of the atomic clocks.

Without this application of the theory of relativity,

the GPS would have produced an error

of 10 kilometers every day.

GPS is navigation system

developed by the US Department of Defense,

and is completely free for the public.

However, there are accurate alternatives

available in many countries nowadays.

Modern receivers simultaneously make use of GPS

and other navigation systems,

to get the most accurate position.

Now, a quick question.

Does GPG require an internet connection?

GPS does not require an internet, or cell phone signal.

However, with their help,

GPS startup can be greatly speeded up.

Satellite location information

can be downloaded by the internet,

rather than direct satellite downloads, which are very slow.

Such GPS systems are known as assisted GPS.

So, the next time you track your food delivery,

or navigate your car,

please keep in mind how important the theory of relativity,

developed by Einstein,

and the other mathematical ideas are, behind GPS.

Thank you for watching the video,

and please, don't forget to press the support button.