Thank you. I've been saying for a long time that "corporate personhood" is unnecessary for doing corporate business, only to get lots of arguments like those above.
Corporations were around since before this country was formed, and there was nothing "person" about them, except the ability to own property.
"You can't set constraints to these values, they're determined by the relative positions between the satellites and the GPS receiver."
Additional information:
My memory was roughly correct about the civilian "4th fix" to improve the accuracy of GPS. But it wasn't perfect. What I did not realize -- or remember -- is that this 4th input is typically a ground installation (the U.S. Coast Guard maintains a nationwide set of longwave transmitters), which sends out a corrective signal. So it is in fact used by the military. I must assume that the situation is similar in Europe and other places.
So the discussion involving whether 4 satellites are necessary is rather moot, since their positions are actually calculated precisely by ground-based stations, and the 4th, ground-based signal(s) correct for variances.
"You can't set constraints to these values, they're determined by the relative positions between the satellites and the GPS receiver."
But this is what everybody keeps forgetting: it isn't just a timing (distance) signal. You have more information than that. The relative positions of the satellites themselves are known.
Remember that the solution to each of the timing equations is not a line or a circle, but a surface. At the intersections of the 3 surfaces, you may technically have an infinite number of solutions, but in practice they will all fall within a certain range.
Granted, you will improve your accuracy with more satellites (and as you say, if they were all in a plane relative to you, that would introduce complications.) But my point was that as a practical matter it is theoretically possible with only 3... within certain limits of course. Many here seem to think I did claim it was perfect, but I have explicitly stated several times now that you will clearly get better results with 4.
But there is information missing here: the locations of the satellites themselves. You are assuming the use triangulation using nothing but the timing of the signals. But there is actually more information than that.
If you know the satellite locations -- but not your own -- you can calculate your position in 3-space from only 3 points.
Each time signal gives you a semi-sphere of known dimensions. There is only one place where those surfaces will all intersect. (Technically there are two, but only one of them is on Earth.)
As I have stated elsewhere, I know that 4 are typically used to improve the timing. But it isn't absolutely necessary to get an approximate position, including altitude.
"My point is the above poster doesn't understand why 3 points is not perfect."
And this is where the misunderstandings lie. I did not say it was perfect. In fact, in a number of different places in this thread I mentioned how 4 satellites are used to improve the accuracy.
However, in an ideal theoretical situation 4 would not be necessary.
"With 3 satellites there are 2 possible solutions to the equations. Since we know we are on earth and not in space one solution can be discarded. So in theory 4 satellites are required in practice not."
I mentioned this myself elsewhere. But as you of course know, one of those solutions is clearly nonsense, so there is no ambiguity.
"... we can say with confidence that when we solve the navigation equations to find an intersection, this solution gives us the position of the receiver along with accurate time thereby eliminating the need for a very large, expensive, and power hungry clock. The very accurately computed time is unused in many GPS applications, which use only the location."
Note the phrase: "computed time". Not measured time.
"You can't carry atomic clocks in your pocket, they're a tad too big for that. There is no way to know the time on the satellites from the ground, because you don't know where you are, and hence how far the satellites are from you, and hence the delay added to the signals."
Proof you are a moron.
These can be CALCULATED from 3 satellites. You don't need to know them in advance, and you don't need a value from outside the satellites themselves.
Repeat: the military GPS system was designed to operate on 3 satellite locks. Sorry if your tiny brain can't wrap itself around the concept that there is more information here than simple geometry.
3 satellites are all that are necessary to pinpoint you in any 3D position. Period.
(Technically they can only put you in 1 of 2 positions, but the other one is off in space so not very likely.)
The 4th satellite is only necessary for civilian systems to correct for timing that was very much intentionally made ambiguous for civilian receivers, since GPS was made by and for the military.
" Is the fourth satellite a solution to a geometric problem, or a timing/measurement/accuracy problem? If it's a timing problem, why does the fourth satellite need to be the timekeeper?"
Haha! A thoughtful and good question, and from an AC. No offense meant.
The other people in this thread would have you believe that #4 is necessary geometrically. But -- as I have been trying to explain -- that is simply false.
You are quite correct that it is a timing issue. The civilian GPS signal is not very accurate, so civilian manufacturers use a 4th satellite to correct for timing, which results in a fairly accurate position from a system that was designed (quite intentionally) to be rather rough for non-military receivers.
This was actually quite clever on their part. But it is the sole reason for the 4th satellite.
The encrypted part of the GPS signal is far more accurate. The military (well... military contractors) designed it to work robustly with only 3 satellites. There is NO geometric problem here... you are getting transmissions from 3 satellites that know their own positions in time and space... therefore you know your position. In full 3D. With only 3 satellites.
Once again: the 4th is only necessary for civilian operation, to correct for the sloppiness of the civilian-receivable GPS data. There is no geometric need for a 4th position.
I am replying to you, but this is really aimed at these other dimbulbs who are arguing with me.
Listen up, folks. I don't claim to be the brightest bulb in the universe myself, but I do pretty good and I remember my recent history, which many of you seem to have (forgotten; never learned; didn't pay attention... pick your answer).
GPS has been around for a long time. But it was only pretty recently that we civilians learned about it, and it became something useful. Why? Well, that's a story.
Much of the GPS signals are encrypted, for use by the military. The high-precision part. When people saw potential for civilian use, they were somewhat dismayed, because the un-encrypted part of the signal was pretty inaccurate. Your location could only be found within a few tens of meters. Not good enough.
So a few electronics companies -- at about the same time -- came up with the idea of using a FOURTH satellite to correct the sloppy timing they got from the USUAL 3, used by the military.
And thus practical, consumer GPS was born.
But make no mistake: GPS was designed to work -- does work, still works very well -- for the military with only 3 sats visible. That is the way it was designed, that is the way it works.
So stop giving me all your theory about how it "needs" 4. You are just plain wrong.
"No, you're not correct. The 3D information that you'd get without the fourth satellite would be so inaccurate as to be meaningless. You need the fourth satellite for a 3D fix that puts you in the right city, let alone the right street. That's qualitatively different from 'only for precision'."
Then why do the military only require 3 satellite locks? Eh? Answer me that, you fucking genius.
The real answer -- which I already gave earlier -- is that the additional lock is for error correction. Nothing more. It is NOT essential for location, including elevation.
"Simple geometry states you need three satellites for an accurate 2D fix, and four satellites for a 3D fix, not whether you have access to the encrypted P(Y) code."
Um... Duh... simple geometry doesn't apply here, because these are TRANSMITTERS THAT KNOW THEIR OWN LOCATION IN SPACE AND TIME.
"Farm machinery has grown in size and complexity over the last couple of decades."
Why? Are you saying it's because GPS was there? That's pretty stupid. It might be true, but it's pretty stupid.
"GPS is now REQUIRED for many machines."
Then get different machines. I still don't give a damn. You can put up some reflectors at the edge of your field and use a goddamned laser. There are about 100 ways to get around this "requirement".
And you can think I'm trying to be a douchebag all you like. What I'm doing is giving my honest opinion. If you don't like it, that's fine; ignore it. But I *DO* know something about it. I live in an area that is mostly rural, and mostly farms (where the terrain is not prohibitive, that is). So FOAD yourself.
"The 4th sat is for elevation. 3 to fix you in 2D. 4 to fix you in 3D."
No. That's with GPS, and that's after the fixes for precision that are necessary because the "high precision" part of U.S. GPS is restricted to military.
With an open system, it should require no more than 3 visible sats to fix your position in 3D.
Somebody tried to argue this point with me a couple of weeks ago, and it's simply false. You can get a rock-solid 2D position with only 2 observation points. 3 (and even just the first 2, if they are transmitting the appropriate data) can establish elevation.
"Galileo is much more precise than GPS. And that's just for starters."
No, it isn't. It's just that unlike GPS, the precise part is open to the general public.
Also, I think OP is incorrect. The only reason for a 4th lock using GPS is to get the precision you would normally get with 3, if you were military. If the new system is open and precise, 4 sats should probably not have to be visible.
Slashdot Mirror
To improve work / life balance, just do all your astronomy during regular business hours.
"In my fairly rural highschool nearly a decade ago they even had (hidden!) cameras in the bathrooms..."
I don't know about most states but that would be illegal as hell in mine.
Some shopping malls tried it and got into serious trouble.
Thank you. I've been saying for a long time that "corporate personhood" is unnecessary for doing corporate business, only to get lots of arguments like those above.
Corporations were around since before this country was formed, and there was nothing "person" about them, except the ability to own property.
Yes. Computed from at least four sat signals.
Well, guess what? We were all wrong, to varying degrees.
My memory that the 4th signal is used just to improve accuracy was correct. However, that 4th signal is not a satellite at all, but a ground station.
"You can't set constraints to these values, they're determined by the relative positions between the satellites and the GPS receiver."
Additional information:
My memory was roughly correct about the civilian "4th fix" to improve the accuracy of GPS. But it wasn't perfect. What I did not realize -- or remember -- is that this 4th input is typically a ground installation (the U.S. Coast Guard maintains a nationwide set of longwave transmitters), which sends out a corrective signal. So it is in fact used by the military. I must assume that the situation is similar in Europe and other places.
So the discussion involving whether 4 satellites are necessary is rather moot, since their positions are actually calculated precisely by ground-based stations, and the 4th, ground-based signal(s) correct for variances.
"You can't set constraints to these values, they're determined by the relative positions between the satellites and the GPS receiver."
But this is what everybody keeps forgetting: it isn't just a timing (distance) signal. You have more information than that. The relative positions of the satellites themselves are known.
Remember that the solution to each of the timing equations is not a line or a circle, but a surface. At the intersections of the 3 surfaces, you may technically have an infinite number of solutions, but in practice they will all fall within a certain range.
Granted, you will improve your accuracy with more satellites (and as you say, if they were all in a plane relative to you, that would introduce complications.) But my point was that as a practical matter it is theoretically possible with only 3... within certain limits of course. Many here seem to think I did claim it was perfect, but I have explicitly stated several times now that you will clearly get better results with 4.
But there is information missing here: the locations of the satellites themselves. You are assuming the use triangulation using nothing but the timing of the signals. But there is actually more information than that.
If you know the satellite locations -- but not your own -- you can calculate your position in 3-space from only 3 points.
Each time signal gives you a semi-sphere of known dimensions. There is only one place where those surfaces will all intersect. (Technically there are two, but only one of them is on Earth.)
As I have stated elsewhere, I know that 4 are typically used to improve the timing. But it isn't absolutely necessary to get an approximate position, including altitude.
"My point is the above poster doesn't understand why 3 points is not perfect."
And this is where the misunderstandings lie. I did not say it was perfect. In fact, in a number of different places in this thread I mentioned how 4 satellites are used to improve the accuracy.
However, in an ideal theoretical situation 4 would not be necessary.
"With 3 satellites there are 2 possible solutions to the equations. Since we know we are on earth and not in space one solution can be discarded. So in theory 4 satellites are required in practice not."
I mentioned this myself elsewhere. But as you of course know, one of those solutions is clearly nonsense, so there is no ambiguity.
It doesn't work by "triangulation", dimbulb.
Jesus, spare me.
"... we can say with confidence that when we solve the navigation equations to find an intersection, this solution gives us the position of the receiver along with accurate time thereby eliminating the need for a very large, expensive, and power hungry clock. The very accurately computed time is unused in many GPS applications, which use only the location."
Note the phrase: "computed time". Not measured time.
Bozo.
"You can't carry atomic clocks in your pocket, they're a tad too big for that. There is no way to know the time on the satellites from the ground, because you don't know where you are, and hence how far the satellites are from you, and hence the delay added to the signals."
Proof you are a moron.
These can be CALCULATED from 3 satellites. You don't need to know them in advance, and you don't need a value from outside the satellites themselves.
Repeat: the military GPS system was designed to operate on 3 satellite locks. Sorry if your tiny brain can't wrap itself around the concept that there is more information here than simple geometry.
"So some of the military only need 3."
Nice conjecture, but not correct.
3 satellites are all that are necessary to pinpoint you in any 3D position. Period.
(Technically they can only put you in 1 of 2 positions, but the other one is off in space so not very likely.)
The 4th satellite is only necessary for civilian systems to correct for timing that was very much intentionally made ambiguous for civilian receivers, since GPS was made by and for the military.
" Is the fourth satellite a solution to a geometric problem, or a timing/measurement/accuracy problem? If it's a timing problem, why does the fourth satellite need to be the timekeeper?"
Haha! A thoughtful and good question, and from an AC. No offense meant.
The other people in this thread would have you believe that #4 is necessary geometrically. But -- as I have been trying to explain -- that is simply false.
You are quite correct that it is a timing issue. The civilian GPS signal is not very accurate, so civilian manufacturers use a 4th satellite to correct for timing, which results in a fairly accurate position from a system that was designed (quite intentionally) to be rather rough for non-military receivers.
This was actually quite clever on their part. But it is the sole reason for the 4th satellite.
The encrypted part of the GPS signal is far more accurate. The military (well... military contractors) designed it to work robustly with only 3 satellites. There is NO geometric problem here... you are getting transmissions from 3 satellites that know their own positions in time and space... therefore you know your position. In full 3D. With only 3 satellites.
Once again: the 4th is only necessary for civilian operation, to correct for the sloppiness of the civilian-receivable GPS data. There is no geometric need for a 4th position.
"That's not unique to the military signal. It's just a matter of how much money you want to throw at the problem."
The U.S. military GPS system was designed to work properly with only 3 visible satellites.
Put that in your pipe and smoke it, or do whatever the hell you want with it. I didn't invent the system. But I do know just a little about it.
I am replying to you, but this is really aimed at these other dimbulbs who are arguing with me.
Listen up, folks. I don't claim to be the brightest bulb in the universe myself, but I do pretty good and I remember my recent history, which many of you seem to have (forgotten; never learned; didn't pay attention... pick your answer).
GPS has been around for a long time. But it was only pretty recently that we civilians learned about it, and it became something useful. Why? Well, that's a story.
Much of the GPS signals are encrypted, for use by the military. The high-precision part. When people saw potential for civilian use, they were somewhat dismayed, because the un-encrypted part of the signal was pretty inaccurate. Your location could only be found within a few tens of meters. Not good enough.
So a few electronics companies -- at about the same time -- came up with the idea of using a FOURTH satellite to correct the sloppy timing they got from the USUAL 3, used by the military.
And thus practical, consumer GPS was born.
But make no mistake: GPS was designed to work -- does work, still works very well -- for the military with only 3 sats visible. That is the way it was designed, that is the way it works.
So stop giving me all your theory about how it "needs" 4. You are just plain wrong.
"No, you're not correct. The 3D information that you'd get without the fourth satellite would be so inaccurate as to be meaningless. You need the fourth satellite for a 3D fix that puts you in the right city, let alone the right street. That's qualitatively different from 'only for precision'."
Then why do the military only require 3 satellite locks? Eh? Answer me that, you fucking genius.
Which, by the way, your own references say very clearly.
Nevertheless, I am still correct. The 4th sat is only for precision. It is not necessary for location.
The real answer -- which I already gave earlier -- is that the additional lock is for error correction. Nothing more. It is NOT essential for location, including elevation.
"Simple geometry states you need three satellites for an accurate 2D fix, and four satellites for a 3D fix, not whether you have access to the encrypted P(Y) code."
Um... Duh... simple geometry doesn't apply here, because these are TRANSMITTERS THAT KNOW THEIR OWN LOCATION IN SPACE AND TIME.
Get that?
"Farm machinery has grown in size and complexity over the last couple of decades."
Why? Are you saying it's because GPS was there? That's pretty stupid. It might be true, but it's pretty stupid.
"GPS is now REQUIRED for many machines."
Then get different machines. I still don't give a damn. You can put up some reflectors at the edge of your field and use a goddamned laser. There are about 100 ways to get around this "requirement".
And you can think I'm trying to be a douchebag all you like. What I'm doing is giving my honest opinion. If you don't like it, that's fine; ignore it. But I *DO* know something about it. I live in an area that is mostly rural, and mostly farms (where the terrain is not prohibitive, that is). So FOAD yourself.
"The 4th sat is for elevation. 3 to fix you in 2D. 4 to fix you in 3D."
No. That's with GPS, and that's after the fixes for precision that are necessary because the "high precision" part of U.S. GPS is restricted to military.
With an open system, it should require no more than 3 visible sats to fix your position in 3D.
Somebody tried to argue this point with me a couple of weeks ago, and it's simply false. You can get a rock-solid 2D position with only 2 observation points. 3 (and even just the first 2, if they are transmitting the appropriate data) can establish elevation.
"Why can't we all be friends?"
Because some of those "friends" will eat your lunch.
Don't be paranoid... but don't be a fool, either.
--
Peace through superior firepower.
"Galileo is much more precise than GPS. And that's just for starters."
No, it isn't. It's just that unlike GPS, the precise part is open to the general public.
Also, I think OP is incorrect. The only reason for a 4th lock using GPS is to get the precision you would normally get with 3, if you were military. If the new system is open and precise, 4 sats should probably not have to be visible.