# Do GPS receivers use trilateration or distances between satellites?

My main question is whether GPS receivers use trilateration or the distances between satellites. On GPS.gov and their videos, it says you receivers use trilateration. But, I have seen people say that they use the distances between satellites. I would like to know which is correct, I have a question if GPS receivers use trilateration. How do GPS receivers get time synchronization if they need to use how long it takes for a signal to make it to them to calculate their location (I know it has been explained in other threads (Here) but none have been real clear to me how it does it (Explain it if you can please.))?

This is my other question if GPS receivers use the distance between satellites, how does it do it? A diagram would be useful if anyone has it. Also, why would GPS.gov say that receivers use trilateration if they actually don't?

Again, I know this is a 'duplicate thread' but no other threads have explained to me in a way that I can understand it.

• Can you clarify what you didn't understand about the other question and its answers? Just asking for another explanation won't help much. – Nathan Tuggy Jan 3 '16 at 1:55
• @NathanTuggy Wether GPS receivers use trilateration or distance between satellites to calculate its position on Earth. – Hawkeye Jan 3 '16 at 1:58

While PearsonArtPhoto answered this correctly the discussion on his answer shows real question seems to be how it works.

Lets start with a simple case here on Earth. You have a bell in the town square that rings at noon. You hear the bell, look at your watch and it says 12:00:02. (I'm assuming perfect timepieces and zero reaction time here.) What can you conclude from that?

A reasonable value for the speed of sounds is 1125 ft/sec. You heard it 2 seconds after it rang, you can conclude that you are somewhere on the circle 2250 feet from the bell--not very useful unless you want to know how long it will take to walk to the town square.

Now lets add another bell to the picture. This bell is placed 2000' from the original bell and rings at the same time but on a different frequency so you can tell them apart.

The bells ring. You hear the first bell at 12:00:02 and the second at 12:00:03. Now we have something useful. We know we are 2250 from the first bell and 3375 from the second. Take a map, draw both circles on it. You are standing where they intersect. Two circles inherently intersect at exactly two points (assuming they intersect at all, something we know will happen if everybody's timepiece is accurate.) You are on one of those intersections, although you can't tell which without additional data.

Now, lets make it more complex--you're a bird instead of a person. The bells ring, you get the same measurements. Now, however, instead of drawing circles around each bell you have to draw spheres. The intersection of two spheres is a circle--we are back to the same problem we had on the ground with one bell. Once again, we fix it the same way--add another bell. Now we are looking at the intersection of that circle with the third sphere--once again, two points.

Note, however, that this requires everyone to have an accurate timepiece. Since the GPS system requires time accuracy on the order of a few nanoseconds for normal civilian accuracy that's a tall order. You don't put such timepieces in your pocket!

How do we fix this? The same way we keep fixing it as we add dimensions--add another bell. We don't know how big to draw the spheres anymore but we still do know the differences between their sizes. We start out assuming the sound we heard first was right there and try to solve the problem--of course we can't. Keep increasing the size until we do find a solution. We will end up with four spheres that intersect in exactly two points.

Now, the GPS system uses a radio broadcast instead of a bell but other than the vastly higher transmission speed the math is exactly the same. Yes, the GPS system produces two possible answers for your location but we do have one more piece of data available that resolves it--your receiver assumes you are on Earth. The satellites are 12,550 miles up--which puts the second solution roughly 25,000 miles up. The receiver discards this obviously bogus answer and gives you the one that's somewhere near the Earth's surface.

Now, the real system is more complex than this because lightspeed is only constant in a vacuum. Thus the satellites also transmit an atmospheric weather report (not sun/wind/rain, but how much slowing is going to happen) and your receiver listens to these reports and figures out how to correct for this slowing. (These weather reports are on a 30 second cycle which imposes a 30 second minimum time for your GPS to acquire after it's turned on. In practice the acquisition time is longer because of the games they play to allow the system to work at space-transmitter power levels while using simple omnidirectional antennas on the receivers.)

Mil-spec GPS systems use a different approach. There are actually two signals being broadcast by every GPS satellite, your civilian unit ignores the second. A military unit has the crypto keys to read that second signal. This is on a substantially different frequency than the primary signal and thus is affected differently by the atmosphere. The mil-spec receiver can use the difference between the two signals to figure out it's own atmospheric corrections without waiting for the weather report. This also allows the government to deliberately introduce error into the civilian signals while not messing up the military signals--useful in wartime if you want to deny the enemy accurate navigation. This capability has never been used, though--too many soldiers had their own civilian GPS units in Desert Storm.

• Would you happen to know how GPS syncs there atomic clocks to the receivers to make sure that distance it gets is as accurate as possible? – Hawkeye Jan 3 '16 at 4:22
• "We will end up with four spheres that intersect in exactly two points" this scenario almost never happens, and if it does - considering the speed of the satellites - it can't last more than a fraction of a second. But you are basically right, except that you dont need the fourth satellite to match two points, but just one to sync time on receiver. – Vlastimil Ovčáčík Aug 13 '16 at 10:07

Each satellite provides the receiver with a time value $t_s$ and its (the satellites) position, $x_s, y_s$ and $z_s$. Consider that you are receiving data from $4$ such satellites.

The time value will be larger the further away the satellite is. Using the time values, you can find the difference in delays between the satellites. If you know the difference in delays between the satellites and know the position of each satellite, you can accurately calculate your own position.

This process does not require being perfectly synced to the timing of a satellite, since it's the time differences that are the key.

As explained in the Wikipedia articles on GPS, trilateration, and multilateration, it basically boils down to this:

Mathematically, your position is described by three unknowns (three dimensions). You could solve for it using three simultaneous equations incorporating distances from three known positions. However, you only have values for differences in arrival time; to compute distances, you need to know actual time-of-flight which means you need to know what time it is - a fourth unknown. So, solution requires four simultaneous equations in four unknowns (x,y,z, and time). When a GPS receiver picks up signals from four satellites, the four relative arrival times together with the position of each satellite at the emission time of each signal allows the receiver to compute both its own position and the actual time.

GPS receives use the distance between the user and the satellite, not the distance between satellites. In fact, the name for this is trilateration.

If time isn't well known, then one can use an additional satellite to figure out the time, much in the same way that 3 satellites gives the position in 3 axis, the 4th allows for figuring out the time, the 4th dimension.

• Then my second question is how GPS satellites sync their atomic time to a receiver? – Hawkeye Jan 3 '16 at 2:00
• By using more satellites. 3 satellites gives 3 degrees of freedom, 4 gives 4. The 4th is time. – PearsonArtPhoto Jan 3 '16 at 2:01
• Can you explain that in greater detail on how it syncs? I heard that the 4th satellite allows for timing but now exactly how. Also, why would other threads say it uses distances between satellites? – Hawkeye Jan 3 '16 at 2:08
• All I can really do is say the math works out. The other thread doesn't mention satellite-to-satellite distances, only satellite-to-receiver distances. – PearsonArtPhoto Jan 3 '16 at 2:17
• I guess my next question would be do receivers use their time to find the distance using the speed of light (not including the formulas to remove the time delay due to Earth's atmosphere)? – Hawkeye Jan 3 '16 at 2:21