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Galileo: Europe's Version of GPS Reaches Key Phase
another random user sends this quote from the BBC:
"The third and fourth spacecraft in Europe's satellite navigation system have gone into orbit. The pair were launched on a Russian Soyuz rocket from French Guiana. It is an important milestone for the multi-billion-euro project to create a European version of the U.S. Global Positioning System. With four satellites now in orbit — the first and second spacecraft were launched in 2011 — it becomes possible to test Galileo end-to-end. That is because a minimum of four satellites are required in the sky for a smartphone or vehicle to use their signals to calculate a positional fix."
There has been far, far too many delays and political fuckery with this. I'm glad to hear it is finally going online.
Satellite navigation is just very important to everything these days (it is the primary nav method for all planes, ships, etc). Having everything rely on GPS, and thus on the budget the US chooses to spend keeping it working, is not a good idea.
This will make things much more reliable since, after an initial hissing match, the US and EU settled down and the systems play nice together and you'll be able to get devices that use both for better accuracy and reliability.
So now there's GPS, GLONASS, and Galileo. Is there going to be cooperation between the different sets of satellites, or will a given device only talk to its own set of satellites? It sucks, for example, when I'm hiking and can't get a GPS fix because I'm in a canyon with a view of only part of the sky. Ditto when all the visible satellites are near the horizon, so the vertical position's accuracy goes to hell, like a couple of weeks ago when I was at 7000' and it told me I was at 14000'. If we had a large number of satellites all in the sky at once, and could use them in any combination, it would be really cool.
Find free books.
because a minimum of four satellites are required in the sky for a smartphone or vehicle to use their signals to calculate a positional fix.
Lets be more accurate here. A minimum of 4 satellites are required to be in the sky that can be observed at the same time from the same point on earth. Hopefully these satellites are relatively close together, because otherwise they might never all be visible at the same time. And if they are, since they are in low earth orbit they will pass by relatively quickly and only be briefly useable during each orbit. So, if the orbits are close this may allow a little bit of testing, but the "system" is still too satellite poor to be of any real use for navigation (at least unless you combine the signals with info from other U.S. or Russian satellites).
I'm an American. I love this country and the freedoms that we used to have.
because US can turns off the GPS.
Well, the US did have selective availability enabled for a while. Perhaps European civilians don't want to be affected by US decisions.
Why is Europe spending billions to create their own GPS constellation when the US government already went through the hassle and expense? The GPS system is free and open to use by anyone with a GPS receiver. This strikes me as nothing but a political move, as if to say "We're independent and don't need America to provide anything for us". This is a completely redundant and pointless project by the EU.
Sigh,
It is a measure of trust. No one, trusts that the US will not screw with GPS if it would give them a military or economic advantage. Sure they say right now that they won't, but who knows what will happen in 5, 10 or 15 years in the future. And trust me, the value of an accurate navigation/timing system makes it well worth the efforts the Europeans, the Russians and the Chinese are making to field their own versions.
Why can't we all be friends?
They'll arrive. There are already devices that can receive both Soviet GLONASS and GPS (e.g. Galaxy SIII) to get better positional accuracy. Soon the new devices will receive Galileo as well, for triple redundancy and improved accuracy.
That must be exactly what Russians think about us not wanting to use their fine space launch services indefinitely.
The US also has the ability to disable GPS for certain areas and has in the past degraded the quality of data for national security reasons ( http://www.gps.gov/systems/gps/modernization/sa/ ). Though this has been changing (new satelites don't have it, though really it's just a software update), it puts pressure on other places to put up their own systems that are either compatible or at least non-interferring so that should the US ever do anything like that again, they cannot be impacted by it. It's a bit like MAD but instead of destruction, nobody can ever get degraded service (assuming enough players). This also raises the question of who should pay for it all, since with three systems now going that all work, it could let each place share only a part of the costs (eventually).
I wonder, since you can pretty much figure out what city you are in through ordinary radio and wifi beacons, not to mention the help you could get from having a clock and a sun locator, couldn't you really use GPS on the road with just two or three satellites?
When your international reputation is at an all-time low you should expect things like this... Galileo was started way before the US popularity took a nose dive, but the last decade or so are only going to make projects like this *more* likely. To the civilised world, the US is not one of the good guys any more, they're not in "bad guy" territory yet, but they're sure headed there fast.
Basically the world no longer trusts the USA. Simple as that.
Simon.
Physicists get Hadrons!
Are there any consumer gear that can receive Galileo?
I don't see how this could possibly be called a Chicken and the Egg type problem, as the satellites are are already in space to support consumer devices. They obviously didn't need consumer device support to get things started at all.
Article did not answer: If Europeans don't have GPS yet, how do their existing sat-navs work? And why is this new system only for Europe?
The Europeans do have GPS, it's publicly available and "global" is in the name. There is also the Russian GLONASS, which is basically the same. The EU doesn't have it's own network, though, which is important for political reasons (and only political reasons). Although there are some technical improvements Galileo makes over GPS, they certainly don't justify a new system. It's also available for everyone, or at least will be, if it ever gets operational (again, global).
"None can love freedom heartily, but good men; the rest love not freedom, but license." --John Milton
"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.
In Asia China's Beidou/Compass should be interesting now, and we'll see how quickly the next phase comes along.
And Japan's QZSS is easily usable by GPS receivers with the right software.
Why is Europe spending billions to create their own GPS constellation when the US government already went through the hassle and expense? The GPS system is free and open to use by anyone with a GPS receiver. This strikes me as nothing but a political move, as if to say "We're independent and don't need America to provide anything for us". This is a completely redundant and pointless project by the EU.
Even as an American I can see the value in having a completely separate system for satellite navigation. Even ignoring the ability of the USA to reduce the accuracy (or completely shut off) the system, the system is still a potential single point of failure subject to software problems or a rogue agent controlling the ground stations. Much better to have a completely separate redundant system with no common elements.
Hint: the G in GPS means global for a reason.
They're there in their room. You're on your own.
"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.
Why did the US spend billions to create their own HST when Gallileo build a telescope 400 years ago ? The gallileo telescope can be rebuild for 10$ and used by anyone with a least one eye.
Your comment is short-sighted.
GPS, whether American, Russian, or EU, is first and foremost, a military asset for their respective owners.
The US military can elect to disable or cripple civilian GPS service to all devices other than their own when they deem it necessary to prevent its use by hostile forces. Presumably, GLONASS and the EU systems have the same capability.
History repeatedly shows that international political alliances vary over time. Just because we currently are at relative peace with the EU and Russia, that does not mean it will always be so in the decades to come. I'm not saying we will be in a hostile situation with either in the future, but it's not out of the realm of possibility, either.
The EU is building their own system not because they want to win a "pissing match" with the US or Russia. It would be foolish of them strategically to depend on a GPS that is under someone else's control.
Let's play Four Horsemen of the Apocalypse. I'll be Pestilence.
I love how position is often triangulated by connecting points to form something other than a triangle.
I thought the "triangulation" name came from forming a triangle between yourself and each remote point (and depending on the accuracy you desire, there could be many remote points)
It's not that you're drawing one big triangle on a map, you're using many (or at least several) triangles to known points.
"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.
"Nose dive"? That is bullshit from the socialist fantasy bubble! Now here's a summary of objective benchmarks by which a country's reputation can be judged...
USA is #1 in overall National Brand ranking, and #1 in international tourism receipts (in spite of really shooting itself in the foot with all the post-9/11 security theater). USA gets more foreign investment than any other country - more than twice as much as the runnerup. It has the world's most respected universities, and some of the most admired and best managed companies. USA's credit rating went down a bit under Obama, but only a handful of countries rank higher. It ranks higher among preferred immigration destinations than most of Europe (sadly too many survey respondents thought France was a romantic destination, even though most people who visit it are disappointed) (and justly behind small Economic Freedom champs like SG and NZ).
USA's reputation was at an "all-time low" shortly after the Revolution, when it was seen as a pirate nation of rootless migrants and uncivilized wilderness. USA's reputation gradually went up and up during the 19th century, leapt upward as it became a superpower and a powerful anti-colonial influence after WW1, and went further up in the civilized world after WW2 and during the Cold War.
--libman
Jesus, tunnel vision much ?
Look it's nothing to do with GPS vs Galileo. It's to do with the USA, a nuclear power, declaring war left, right and center, & invading other countries basically because it can. No-one likes that; international reputation suffers, trust is lost, and consequences ensue. There's no point in getting pissy about it, you brought it on yourselves.
I don't think Europeans are innately superior. I think people are just people, wherever you are. I'm married to an American woman, whom I love dearly. I do think the USA is fucked though, the society is (IMHO) past the tipping point and heading down, and I can't see myself staying around much longer, as I've said before on this site. At some point, the money just ain't worth it.
Simon
Physicists get Hadrons!
Right, I'm talking about a cop executing a handcuffed helpless suspect [warning. Graphic.] and the lack of respect for the law that "peace officers" show; about the TSA, just the very fact of its existence; about the demagoguery that passes for news and its knock-on effects on society; about the constant military action taken to divert attention from problems; about the massive debt and crippled economy; about the shameful lack of a decent for-all healthcare system; about the proliferation of lethal weapons that for some reason is enshrined in the country's constitution!, and the horrendous murder statistics that it produces; about the general sense inherent in US society that "everything's ok as long as *I'm* ok, screw you guys" ... I could go on... and on.... and on...
And your point is that the "national brand" is good. Well whoopy-do. That's all right then. Phew! Glad *that*'s sorted out! .... Fuck me, it's worse than I thought :(
Simon.
Physicists get Hadrons!
You need at least one other sat to fix you in time. The receiver doesn't have an atomic clock and so needs an extra point of data for the extra unknown.
Simple logic might win an argument, but that doesn't make you correct.
Apparently, there are units available that will track 120 simultaneous channels across all the available systems (this comes from Dave Wells). Not having a unit in my possession (and never having messed with Rinex before), I'll have to take his word for it.
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.
http://gis.stackexchange.com/questions/12866/gps-positioning-why-four-satellites
http://www.cmtinc.com/gpsbook/chap5.html
http://www.gpsnuts.com/mygps/gps/technical/ed.htm
Note that the final reference I list is written by someone who is a GPS analyst and has worked for the DOD on the GPS system since 1975.
Selective availability can be turned on by geographic region, in order to degrade the civilian signal. This allows you to only degrade the middle-east, while still maintaining precision position determination for the rest of the world. If the US wants to deny position determination, they would just jam Galileo. I supposed the EU could always send the US a sternly worded letter if that were to occur.
I bet the US is already working on finding a way to scramble Galileo and other GPS satellite signals.
-- Cheers!
Yeah, except that jamming Galileo would provoke a vastly different response from the EU than the US turning some switches off on their own positioning system. You know, this isn't a computer game where the only thing that counts is what you can *technically* do.
Sternly worded letter? Fights happen in economy today, not on the battlefield. US citizens like to think they're safe just because no country is stupid and suicidal enough to drop bombs on them.
The EU sees the US as far less trustworthy than you do, and expects to come into conflict with it again - war is unlikely but economic and policitical spats are quite common between the two. In addition to that galilleo lets them have greater accuracy than the US will allow with GPS, and ensures that they don't have a strategic dependency on the US in space.
Strange how myopic and solipsistic the view from the US is sometimes.
and there are also systems that use geo stationary satellite data, for example Egnos.
Excuse me, but please get off my Pennisetum Clandestinum, eh!
There are also navigation systems that use geostationary satellites, e.g. Egnos and Inmarsat.
Excuse me, but please get off my Pennisetum Clandestinum, eh!
Basically it is as follows:
The first satellite just gives a reference time. By itself, it is completely useless for positioning.
Each further satellite effectively allows you to determine one coordinate. Since you need three coordinates in order to specify a coordinate in space, you ultimately need four.
The Tao of math: The numbers you can count are not the real numbers.
Seeing how the USA are the biggest bully on the planet, it is a smart choice for no country to depend on them, even for the EU, itself made of big bullies.
The USA have already misbehaved with their "friends" and there is no reason to believe that they will not do it again. Therefore seeking independence from them is the sane thing to do.
And Galileo will be the most accurate of them.
I think destroying the satellites would be the equivalent of a declaration of war. I'm not sure the U.S. would want to declare war on its allies.
Of course should the U.S. and Europe no longer be allies at the time that happens, then if the U.S. kills the Galileo satellites, I guess Europe's answer would be to kill the GPS satellites. Again, not exactly what the U.S. wants.
The Tao of math: The numbers you can count are not the real numbers.
You can reduce the error margin of a 3 satellite 3D fix by using more accurate clocks. That's not unique to the military signal. It's just a matter of how much money you want to throw at the problem. Qualitatively, this still means you can only get meaningful 3D position data with at least 4 satellites, because the cost of a sufficiently accurate local time signal is prohibitive, especially considering that you can get a 2D fix instead or just use a fourth satellite, because they're really not that scarce.
they're not in "bad guy" territory yet
Just speaking for myself here: they most certainly are, although discussing the reasons is out of scope and would take ages.
I get the impression that many people see the USA as a necessary evil. Apparently everybody thinks that there has to be domination by one nation over the others; in this perspective, the USA are the least bad option (alternatives such as China or Russia aren't that exciting).
If they are standing on solid ground or on a ship they don't care too much about elevation. ...
The air force on the other hand
So some of the military only need 3.
For the civilian stuff the more that can be seen the better to cope with the randomising that the military don't have to deal with. I think that also applies to everyone at high lattitudes, but since I don't know how high these things are and in what orbit I don't know how much of an effect getting the signal through a bit more atmosphere has.
No, that's just plain wrong. It is not sufficient to know the exact time at three transmitters to get a 3D fix. You'd also need to know the exact time when the signals are received, which is a very difficult (read: costly) problem. The accuracy of the positioning information is limited by both the precision of the satellite clock signal and the accuracy of the receiver clock signal. The latter can be removed from the equations by using a fourth satellite signal, but not by providing better satellite clock signals. And you really need to stop calling people names, especially when you're so obviously out of your depth.
You can't solve a four variable system (3D position and local time error) with just three equations. Perhaps you and the military think they can bomb math into submission, but that doesn't make you right, nitwit.
If you know the distances between yourself and 3 satellites then you can trilaterate your position. However, with GPS you don't know the distances, or even the transit times (from which the distances could be trivially determined), you only know the time the signals were sent and the time offsets at which you received them (i.e. you know you got satellite A's signal Xmicroseconds after satellite B's). This is not the same as knowing the transit times, since you don't have a clock accurate enough to tell you the actual time you received the signals. So you need a 4th satellite in order to produce this extra piece of data. This is GCSE level maths - if you have 4 unknowns you need to solve 4 simultaneous equations in order to find them.
http://blog.nexusuk.org
Yes it is a nose dive. Years back there were rumours about rogue CIA idiots torturing people in Central America - some believed it, but most didn't, and those that did believe mostly didn't think it was standard operating proceedure. Then Baby Bush made it very clear that torture was now fully accepted as a tool and not an atrocity for the first confirmed time in the USA since the American Revolution. That's just one thing, abducting other countries citizens for torture (extreme rendition) is another, so that's a reputation loss that far exceeds Reagan's "bombing starts in 15 minutes" moment or anything Nixon ever did.
It sent a message that the US government could not be trusted to stick to the values it had for the last two centuries, so people wondered if it was going to be as untrustworthy as a place built on "might makes right" such as China or Putin's Russia. Hillary didn't help recently by demanding that agents find out the credit card details of all foreign diplomats in the USA so that they can be easily framed and pressured when needed or whatever she wanted it for.
GPS satellites are already being replaced. So far, three IIF sats have made it into orbit. As usual with US military operations, things happened late and extremely over budget, but things are happening and the chance that the system fails due to not enough operational sats is rather small.
I was promised a flying car. Where is my flying car?
Please hand over your geek card if you can not understand why there are different systems. Compare it to operating systems:
There is one closed system coming from America that has a monopoly and can do whatever it likes.
Then there comes an open system from Europe that breaks that monopoly and is intended to be used by the people made for the people.
(See what I did there?)
Don't fight for your country, if your country does not fight for you.
"Hm, what was the last time Congress declared war? Or are we just making shit up now?"
Note the "invading countries left, right, and centre" part of his argument too, the US has been doing this basically without a single break since World War II in one way or another, whether it's drone strikes in Pakistan, or the CIA pulling off defacto coups across the world. His point is that America spends far too much time and far too much money meddling with other nations, rather than keeping to itself, and that often leads to greater instability. Case in point, by ousting Saddam, the US removed the only credible counterbalance in the middle east to Iran, and since then Iran has been able to carry out proxy attacks everywhere from Iraq, to Lebanon, from Afghanistan, to the Philippines. They couldn't do this shit when Saddam was around, because Saddam would then be given the international blessing he needed to do the exact same thing in Iran proper. By trying to make things better for the oppressed minorities in Iraq, the US ended up making things worse for everyone in Iraq, and people in many other countris too. So when you stop avoiding the point he was making by focussing on a specific intentionally mis-used part of that, tell me, are you disagreeing that America consistently meddles in the dealings of other nations?
"Well, a lot of your countrymen do"
Well, ignoring the fact Europe is a country, what Europeans thinks is not that they have any kind of innate superiority - that's simply not in the European mindset- Europeans are simply much more rational than that, they recognise their fallibility in part because they have thousands of years of history of it to learn from. Some European nations did have this mindset- the French and British at the height of their empires for example, but as their empires fell they realise it was simply a load of bullshit. Ironically, the reason you most likely claim it is because it IS something that's in the US mindset, there's even a term for it - "American exceptionalism", it's something America hasn't, like Europe, grown out of yet.
What many Europeans do believe however, that you're getting confused with, is the fact that currently, Europe is at least governing itself just a little bit more sanely than the US, and that is what Europeans are happy to point out to you. The terms you mention are nothing more than banter, and if you believe any use of them implies some perceived superiority then it simply demonstrates that you, as an American, haven't got out of this absurd mindset that some nations and their people are simply inherently superior to others. Europeans know full well they have their problems, and this is ironically why the current global economic instabilities focus on the Eurozone's issues - because Europe is the only one really openly admitting they have a big problem and trying to deal with it, in contrast to for example America's insanely massive deficit, see here for example, and sort by worst to best, note how insanely large the US figure is in the negative compared to even the closest member on the list?
http://en.wikipedia.org/wiki/List_of_sovereign_states_by_current_account_balance
The only reason you believe there's some kind of belief about inherent superiority is because you have that mindset yourself, until you lose that you wont be able to get over this stupid idea that Europeans think they are innately superior. Believing they are doing some things better that lead to for example, lower infant mortality, longer life expectancy, higher levels of personal happiness, etc. does not in any way imply this is because of some innate superiority or belief in such.
Please stop voting this guy up, while simultaneously voting down the numerous posts that are correct.
Four satellites are required because there are four unknowns, and only one measurement per satellite available, irrespective of precision or lack thereof.
Here's some quotes from Global Positioning System so we can all stop agreeing with the loudest person instead of the facts:
"About nine satellites are visible from any point on the ground at any one time, ensuring considerable redundancy over the minimum four satellites needed for a position."
"The receiver uses messages received from satellites to determine the satellite positions and time sent. The x, y, and z components of satellite position and the time sent are designated as [xi, yi, zi, ti] where the subscript i denotes the satellite and has the value 1, 2, ..., n, where n >= 4."
"Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known, a receiver can determine its position using only three satellites. For example, a ship or aircraft may have known elevation.
The time precision required for a fix of any reasonable accuracy requires atomic clocks. 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. You can use three satellites to figure out where you are, if you know what time it is, but you don't. Adding a fourth satellite in the mix lets you solve for all four unknowns in the equation. Note the exception in the wiki article applies only in some rare cases, like the GPS units used by ships, not the GPS units handed out to most military personnel.
THIS HAS NOTHING AT ALL TO DO WITH SELECTIVE AVAILABILITY.
The military encryption simply reduces the precision of the solution, it doesn't actually change the number of unknowns and hence the equations in any way. A civilian marine GPS could locate itself with just 3 satellites even with selective availability enabled, as long as it assumes that it's at 0 elevation. In all other cases, four satellites are required, even for military units.
Just quoting someone else without knowing what you are talking about doesn't make you right. Come up with scientific reasoning using trigonometry and publicly available specs for GPS to prove your point, or keep your mouth shut, please.
Triangulation (without altitude) works with three points if you have one unknown transmitter and three known receivers. This is the other way around. Using just two receivers would give you two possible locations, without altitude. The other way around, in a real life situation with moving sats and a round planet, you need more data sources to get anything near to accurate results. It may very well be that given enough time, you can get somewhat accurate lat/long information from just 3 transmitters, but you'll be suffering to get altitude positioning correct if they are all in more or less the same horizontal plane. The trajectories of GPS sats are such, that you will in practice need more than three sats to accurately determine your position and still have global coverage with less than 30 sats orbiting the planet.
So in theory, using one location and stationary sats, aided with other navigational means, you may be able to get lat/long with just 2 sats and alt with 3, but in practice, you need 4.
I was promised a flying car. Where is my flying car?
"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.
The US military system is, these days, no different to the civilian system. The system was descrambled in the 90s because it became apparent that it was just too expensive to keep building more complex and relatively low-run GPS chips for the military, when what they wanted to do was put them in bombs and things.
By and large though, even the airforce doesn't need GPS elevation data since laser altimeters are faster and very standard on all aircraft.
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.
It has nothing to do with trust. There is nothing the U.S. or any country could do to gain the trust of other countries with a crucial technology like GPS. If Galileo had been developed first, the U.S., Russians, and Chinese wouldn't want to be reliant upon it either, so this has nothing to do with the U.S. being less trustworthy. The US-haters and the US-hater-haters are just casting it as a trust issue to troll and have something to argue about
GPS is just a technology which has become so pervasive and useful that it's become essential to modern life. And any country that's capable will want to make sure it controls anything essential which it's dependent upon. If you need a car to get to work, and you neighbor has an extra car which he says you're free to use any time, you're still gonna buy your own car. Not because you don't trust your neighbor, but because you'd feel awfully stupid if you could afford a car but didn't get one, and one day your neighbor through no fault of his own were unable to lend you his car. The exceptions (e.g. Panama and Suez canals) are only where cost or physical constraints limit the number of essentials which can be built.
And all of these systems work as accuracy enhancers and fully capable backups to each other. So it's not like a lot of duplicated effort is being put in with no gain.
No, the obfuscation layer on GPS has been deactivated for almost a decade now. Before then you just needed a terrestrial correction signal which any GSM tower could send. The un-obfuscated signal of GPS is still a lot less precise than Galileo, though GPS planed for upgrades that would put them on par.
Redundancy improves reliability. It's the same reason why you should keep backups, even though it's a redundant copy of the data.
Dilbert RSS feed
Speak for yourself. I don't trust either.
Dilbert RSS feed
what Europeans thinks is not that they have any kind of innate superiority - that's simply not in the European mindset- Europeans are simply much more rational than that
LOL! Read through that and see if you can spot the contradiction.
Shutting down free speech with violence isn't fighting fascism. It IS fascism!
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.
That's not how I learned it, but I want to change my mind on this if you're really right. But if what you're saying is true, then what exactly is wrong with the following reasoning:
The GPS receiver gets signals from 3 satellites telling the exact time and position of each satellite at the exact moment the signal was sent. Let's call (xi,yi,zi,ti) the position ant time of satellite i (i=1,2,3), and (x,y,z,t) the position and time of the GPS receiver when the message was received. We want to find out the position of the GPS receiver, that is, x, y and z (we don't care about t).
From the data we get from the satellites, we can make an equation like this for each satellite:
Where c is the speed of light, and i is the number of the satellite (i=1,2,3). This equations simply says that the time it will take for the signal to leave the satellite and reach the receiver, multiplied by the speed of light, is equal to the distance between the satellite and the receiver.
Now, we have 3 equations and 4 unknowns (x,y,z,t). Granted, we're not interested on the value of t if all we care about is position. Still, if you allow t to be free, there are an infinite number of possible values for (x,y,z) that satisfy these equations. Obviously we can discard a lot of silly values for t, like any value less than any of the ti (i.e., the time the signal was received must be later than the time it was sent), and also t can't be much more than any of the ti (i.e., we know the satellites aren't to too far from the receiver). Which means you can get a range of possible values for (x,y,z), but that's not very precise.
If you have 4 satellites, however, there's only one solution (x,y,z,t) for the system of 4 equations.
So, in the end: what's wrong with this reasoning? Or, alternatively, What extra information the GPS satellites could send that would change things?
(By the way, the method I described is -- possibly -- the easiest way to describe the problem, but not the way it's usually stated. See for example this paper for a more realistic approach)
Erm, I messed up the equation. It should be:
That doesn't change the reasoning, though.
they're not in "bad guy" territory yet
They are in "bad guy" territory at the latest with Guantanamo. This incarceration and torture of people without enough evidence to start a trial is way past the limits of civilisation. If they are shocked about it like about Abu Greibh and abolish it immediately but no they continue it shameless for years after years.
Guantanamo is only the most visible tip of the iceberg. The whole war in Iraq was against international law and without any evidence of this "weapons of mass destruction" (the whole non-US world was laughing about the presentation of the pretended "facts"). Abduction and torture of foreign citizens also is not a attribute of "good guy".
I could ramble about so many "bad guy" things the USA have done lately, my keyboard would drown in the froth forming at my mouth. I'm not sure the EU would be acting better in the same position, but the USA are doing it right now in reality before our eyes.
The US is a very young child. American state of the art scientific experiments keep affirming the thesis of continental philosophy that spans 2000+ years. (Which arguably travelled from the East.)
To be fair, we should wait at least a millennium before passing judgment on the American outlook.
(I do think, though, we will see USA become SA within 150 years.)
Defining Statistics and Social Research
Let's go one satellite at a time...
First satellite: You know approximately what time it is because the satellite tells you. You know the position of the satellite, and all of the other satellites, because it tells you in its signal. However, you don't know how far away the satellite is because you don't know the difference in time between when it sent its signal and when you received it. Thus, while one satellite tells you a lot, it does nothing at all to narrow down your position.
Second satellite: Now you know the difference in time between when you heard the two satellites, and thus, you know how much further you are from one of them than you are from the other. So in 3D space, you can use this information to narrow down your position to a point that lies on a sphere. This sphere intersects the earth, forming a circle. Thus, you know a lot of place where you might be, but you still really don't know much.
Third satellite: Now you're able to cut that huge sphere down to a circle. Where this circle intersects the earth, are two points. One point is flying around at high speed, the other relatively stationary. Thus, you kind of know where you are now. ...but only kind of. While the earth is a sphere and we intersected that with a circle to get two points, the places on the earth you might be aren't an infinitely thin mathematical sphere. There's thousands of feet of elevation in which you might exist. ...and worse than that, even if you don't care to know your elevation, the intersection of that circle with the atmosphere isn't straight up and down -- it's at some bizarre and slowly changing angle -- thus you can't ignore it because it isn't just your elevation you don't know, but rather, you're equally uncertain about your latitude and longitude. You know your position to within a mile or so, but if you want to be more accurate than that, you need to either know your elevation or find another satellite.
Fourth satellite: That circle of possible locations is now narrowed down to two points. One is flying randomly through space, the other is near earth. You don't even need to find an intersection with the surface of the earth, unless by some odd chance you're having difficulty figuring out which of those two points is you.
Fifth satellite: No longer any questions, you know exactly which point is you. ...but still, the math is only narrowing you down to about a 10 ft. radius...
Sixth satellite: ...and so it's nice to have some additional data to average together for a slightly more accurate result.
Seventh satellite: ...and it's nice to have some spares for when some become obstructed by trees or tall buildings.
But I do know just a little about it.
Which seems to be the amount you know about everything.
That's not helpful.
GPS recievers indeed solve a 4D problem (3D space + time) which requires
4 sats. As expensive as the military units are, they may be able to bridge reception
gaps by keeping time by themselves for a while, so may for a while work with
only three sat signals.
But without a local timer with the precision of an atomic clock, that's the digital
equivalent to dead reckoning, and will only get you so far until you need your fourth
sat again.
Of course, if you are the Navy, one of your coordinates is known by default (at least
plus or minus a couple of meters), so maybe their gear is permanently set to a dedicated
2D mode. That would indeed work with 3 signals - but you still need four inputs for a 3D
position, it's just that in this case one of those inputs doesn't come from space, but from
looking out the window.
Maybe you will believe the Los Alamos Labs' GIS unit?
"If you require 3-dimensional coordinates (northerning, easting, and elevation), a minimum of four satellites is needed."
Note the phrase: "computed time". Not measured time.
Yes. Computed from at least four sat signals.
Bozo.
Nice sig.
Nevertheless, I am still correct. The 4th sat is only for precision.
No it's not.
It is not necessary for location.
Yes it is.
Quoting the Navy: "Therefore there are 4 unknowns at each timeline where a solution is computed, 3 for position and 1 for time. This is why the minimum number of satellites for a solution is 4."
Technically it's not - being better in one thing does not imply inherent superiority. Otherwise, I'd be inherently superior to most Americans in that I'm better at German than they are while they are inherently superior to me in that their American English is better.
For the record, I don't really suvbscribe tothat rationality argument, eithar. At the very least I don't think we are inherently more rational, although we might be effectively more rational. Our advantage is that we're not a superpower. Given that people will usually do things they can get away with (depending on one's moral framework), that top politicians tend to have few scruples and that people like to believe that they aren't doing evil I think it's a reasonably safe assumption that more powerful countries will tend to be more delusional about their status in the world and the possible consequeces of their actions.
If Europe should make it to superpower status (which seems iffy given that we'll have to compete with China, India and possibly the US and Russia) we'll become just as much of an overbearing sociopath as all superpowers in recorded history have been. And boy, will we feel good about ourselves.
USE HOT GRITS WITH STATUE OF NATALIE PORTMAN (NAKED AND PETRIFIED)
Amazing, isn't it? As long as the European Parliament is the US's pet dog we will never be a superpower.
-- Cheers!
Only three if the speed of light was instant :) The time of transmission from each satellite is not equal since they are in different places a very long way apart and timing is critical in this situation.
But we can jam the US's system now without any damage to Galileo, so it's a win/win situation!
-- Cheers!
While "selective availability" (the intentional degradation of civilian signals to roughly 100m accuracy) has been disabled for a while and the new satellites don't have the capability for implementing it, the military does indeed have separate signals for civilian and military users.
Referring to the wikipedia, the civilian signal ("C/A") is only transmitted on the L1 band at 1575.42 MHz. The encrypted precision codes (for the military) are transmitted on both L1 and L2 at 1227.60 MHz. The military signal is indeed quite a bit more accurate than the civilian signal: by itself, the civilian GPS signal is only accurate to around 3 meters. The military signal is accurate to around 30cm.
With current civilian signals only transmitted on a single frequency, receivers cannot correct for ionospheric conditions (which composes a major part of the current uncertainty in measurements) as doing so requires two frequencies. Military signals are transmitted on two frequencies so receivers can correct for ionospheric delay. The military signal is also transmitted at a much higher rate (10x the civilian rate), yielding proportional increases in accuracy.
Currently there are systems like WAAS (North America) and EGNOS (Europe) that provide augmentation in the form of corrections for ionospheric delays (and some other information, like current "health" status of the satellites). This can improve accuracy even more (my handheld civilian unit is able to compute position with an uncertainty of 2 meters). EGNOS also provides an internet feed of the augmentation data so one doesn't have to have a clear view of the geostationary satellites that provide the augmentation. WAAS only augments GPS, but EGNOS augments GPS, GLONASS, and Galileo (for what it's worth at present).
The GPS upgrades will add more detailed signals (the civilian signal will be broadcast on L1 and L2 as well as safety-of-life signal on L5 at 1176.45 MHz). The military codes will also get an upgrade as well, but that won't really matter for civilian users. With the civilian signals being transmitted on a total of three frequencies it will be possible for receivers to account for ionospheric delay and other factors. Overall, things will get considerably more accurate.
Is there any practical way of shooting down satellites in medium earth orbit? GPS satellites orbit around 20,000km -- that's a long way for any anti-satellite missile.
There are also navigation systems that use geostationary satellites, e.g. Egnos and Inmarsat.
EGNOS augments other satellite navigation systems (GPS, GLONASS, Galileo) by providing ionospheric correction data and other relevant information. It is not a full-fledged navigation system in its own right -- it cannot be used for navigation on its own.
How about if you require t1 = t2 and t2 = t3 ? Then you have five equations and four unknowns.Maybe this would break due to special relativistic effects.
Oh dear, I think you're having real difficult with the rather simple word "innate".
In this context the word innate would mean that there was a belief that Europeans are born with some kind of natural superiority, the fact that I stated that Europeans tend to be much more rational and not believe in such hogwash doesn't conflict with this, because the rationality spoken about in case is a learnt trait taught into European culture through are many lessons from history we can draw on to understand why that belief is stupid. As I say, some Europeans used to have this exact belief - the British, the French, the Germans, but we also eventually learnt that wasn't true.
In contrast, many Americans do actually believe that being American gives you some kind of natural superiority, which simply isn't true. Americans have yet to learn the same lesson that Europeans have learnt in regards to this mindset, because, like the afformentioned European countries at the height of their power, they were blinkered by that power and that resulted in their eventual downfall.
So now that you understand the word 'innate' in this context, perhaps you can go back and re-read the posts in this thread and begin to understand why people are in disagreement with you and why there is no contradiction in what I said, merely a lack of understanding of a rather simple term on your part.
Quick, notify JFK, Romney, Limbaugh, and whoever's hosting "Coast to Coast" these days.
This calls for derp-rage.
Village idiot in some extremely smart villages.
*facepalm*
I'm sure you knew what I meant. That'll teach me for being pedantic about the GP's post!
Oh, right, ti is the time at which the signal was sent, sorry.
Assume you know the difference in time between the receipt of the signals, you can solve for the time at which the second satellite sent the signal.
The receipt time difference
dt1i = ti' - t1'
Where t1', ti' is the time when you received the signal i, on some arbitrary clock.
Then this is the equation for t2:
t2 = c*sqrt( (x-xi)^2 + (y-yi)^2 + (z-zi)^2 ) - c*sqrt( (x-xi)^2 + (y-yi)^2 + (z-zi)^2 ) + dt12.
This second order equation in lets you solve for either x,y or z as a function of the other y and z. Now do the same for satellites 1 and 3, and 2 and 3, and you have two more equations.
Does that make sense?
Now do the same for satellites 1 and 3, and 2 and 3, and you have two more equations.
Only two equations. Strike that "2 and 3"
The "high precision" part of the GPS system was opened up to the public by Clinton back when he was president. Birds launched since then lack the capability to restrict civilians to the lower quality fix.
"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.
They have accurate clocks?
I don't know, maybe I'm not a "fucking genius" enough for that to be the right answer.
You can't set constraints to these values, they're determined by the relative positions between the satellites and the GPS receiver.
You will only have t1=t2 when the distance between the satellite 1 and the GPS receiver is the same as the distance between the satellite 2 and the GPS receiver.
"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.
This is the second time you've brought this up. The US stopped deliberately degrading the signal for civilian uses years ago, mostly because it was simply pointless to keep doing it since most civvy receivers were able to overcome the problem with assisted GPS and other methods.
You are technically correct that you only require three satellites to get a 3D position but *only* if you know your local time extremely accurately. It has nothing to do with only three satellites being "deliberately bad" at positioning on civilian equipment - it's the laws of physics.
"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?
They know their location in space and time, but they cannot tell you what it is before it changes. The speed of light is not instant.
You have four unknowns - x, y, z and time. You can't solve those with only three equations, unless you can make a reasonable guess about one of them, thus either you need an extremely accurate clock (an atomic one) or you need to know either x, y or z to high accuracy - laser altimeter, being at sea level, knowing a point due to a separate beacon that knows its position (eg, a phone mast or a battlefield command post with a transmitter).
There's simply no way around this. There is plenty of information about the maths behind the GPS system. You might want to check it out before you start insulting people for correcting you; it just makes you look foolish.
How about if you require t1 = t2 and t2 = t3 ? Then you have five equations and four unknowns.Maybe this would break due to special relativistic effects.
It does. The clocks in the satellites themselves have to be continually adjusted to account for relativistic effects. That's what the GPS master ground station is for. You can't assume they are all the same.
The US will focus on a trade war with Asia. An interesting attrition war from which Europe and Africa would benefit a lot.
Ah bloody hell there's so much wrong in my post. I think the idea is valid, that you can use the difference of time between when the signals were received as an additional constraint. The quadratic equations have a two-fold ambiguity, so I don't know if both solutions would be physically valid, but at worst you've narrowed your position down to one of two (maybe four) points in 3D.
You can't carry atomic clocks in your pocket, they're a tad too big for that.
Actually, it seems you can. And even older generations weren't that huge - certainly too big to carry in your pocket, but not impossible to mount in a vehicle, aircraft or ship. E.g. this HP 5071A which can be yours for the bargain basement price of just $27.500.
So maybe some GPS receivers can indeed get a 3D fix with 3 satellites, when combined with (or including) an atomic clock.
Proud member of the Ferengi Socialist Party.
Please lay out your mathematical solution to this positioning problem using only 3 birds. Until and unless you can do that you're not going to convince anyone here.
And if you *can* do that it's worth big money, so you should file for a patent immediately.
You perfectly made my point with your reply, and I don't think you were even trying. Without attacking a single merit of what I said, all you did was reflect 'anti-US sentiment' and failed to site a single economic reason to spend the billions of dollars Galileo will cost.
My point stands, this is nothing more than a redundant multi-billion dollar pissing contest with no real economic benefit.
I don't understand what you're trying to say; all the signals are received at exactly the same time (which I called t). If you receive the signals at different times, than the whole thing doesn't work, because then the relative positions of the satellites will have changed -- and the whole point is to use the relative positions of the satellites to determine your position.
As for the rest of what you wrote: no amount of manipulation on the equations can change the fact that you have only 3 independent equations and 4 variables. Any equation you derive by manipulating the initial equations (by substituting variables, etc.) will not be independent, so it changes nothing.
But if you want to play with GPS equations, I suggest reading the paper I linked to. It has the equations that are actually used by GPS devices; what I wrote is a simplified version just to show an overview of how the process works.
I wish Europe would rather develop its owns operating system (Linux, hint hint). than its own GPS. Simply because GPS seems fine to me.
The chips can receive some or all of GPS, GLONASS, Galileo, COMPASS (AKA China's Beidou or Big Dipper), QZSS (Japan) and SBAS augmentation services.
For hardware hackers, companies have put the chips into easier to use modules. Two examples are the Telit Jupiter SL869 and the uBlox NEO-7, which are even footprint compatible with each other.
They'll arrive. There are already devices that can receive both Soviet GLONASS and GPS (e.g. Galaxy SIII) to get better positional accuracy. Soon the new devices will receive Galileo as well, for triple redundancy and improved accuracy.
It's already happened. There have been modules for GPS+GLONASS+Galileo on the market for quite some time.
Ezekiel 23:20
I could be wrong, but I'm pretty sure you can figure out your t from 2 satellites, as long as you know their relative position to each other.
Meaning you only need three for a full fix as long as you know where the sats are.
No, it isn't. It's just that unlike GPS, the precise part is open to the general public.
Still a pretty good reason for launching then... since if public GPS can't be accurate... the public can't have accurate GPS...
Selective availability can be turned on by geographic region, in order to degrade the civilian signal. This allows you to only degrade the middle-east, while still maintaining precision position determination for the rest of the world. If the US wants to deny position determination, they would just jam Galileo. I supposed the EU could always send the US a sternly worded letter if that were to occur.
You don't see the difference between the US changing the delivered accuracy of a system they own, and intentionally screwing with others (ie getting close to an act of war)?
Yes, you can figure out t from two satellites if you know your location. I showed how to solve for x above, and then, with your known position, you can solve either of the original equations for t. If you don't know all of your location, then t remains dependent on the remaining variables. In the 2D reduction above, there is a hyperbola comprised of all possible positions that result in the given time difference t2-t1 between the signals from the two satellites. The points on this hyperbola are not at a constant distance from either of the satellites, so the time t can not be computed from the time difference alone.
If you have trouble visualizing the shapes of the solution spaces, which admittedly isn't easy, just remember that a system of n variables needs at least n equations for a unique solution. If this is news to you, please refresh your middle school math knowledge. More equations may not be enough if they're not independent. For example, the equation we got by subtracting equation two from equation one is dependent and doesn't add new information. But no matter how you combine equations, fewer than n equations can not provide a complete unique solution to an n-variable problem. Two separate n and m variable problems may pose as an n+m variable problem and you may be able to find a unique solution for some variables, but in the case of GPS, the problems aren't separable.
If you have information that fixes variables, the principle doesn't change. For example, if you write the problem above with variable altitude y and then decide you know that the altitude is 4, you effectively add another equation y=4 to the equation system, resulting in a three equation system of three variables. Of course you could just as well simply substitute 4 for every occurrence of y and get a two equation system of two variables. That's why having accurate local time information (e.g. from an atomic clock) allows for a 3D fix from just 3 satellites. With t fixed, it's a three variable problem and each of the three satellites contributes one equation. The remaining ambiguities result from the non-linearity of the equations and are easily solved with application knowledge.
Only three if the speed of light was instant :) The time of transmission from each satellite is not equal since they are in different places a very long way apart and timing is critical in this situation.
If the speed of light was instant, GPS wouldn't work. You would receive n identical time stamps from n satellites and would be stuck.
I don't understand what you're trying to say; all the signals are received at exactly the same time (which I called t). If you receive the signals at different times, than the whole thing doesn't work, because then the relative positions of the satellites will have changed -- and the whole point is to use the relative positions of the satellites to determine your position.
Not a big problem, if the times are close together. If you receiver four signals at t, t + 1 microseconds, t + 2 microseconds, and t + 3 microseconds, then even the last satellite has only moved for 3 microseconds, just a few centimetres.
Don't need "your" location - just that of the sats.
time difference from 2 sats + known time difference between the two sats would allow you to solve for t (your time).
meaning you wouldn't need a 4th sat to solve for t.
No, it isn't. It's just that unlike GPS, the precise part is open to the general public.
Correct. The L5 intermediate-precision Galileo signal will be freely available to the public. However, this signal is not as precise as the GPS encrypted "precise acquisition" (aka military) signal.
The freely available L1 signal has essentially an identical format as the GPS "coarse acquisition" signal, and is therefore expected to offer broadly similar performance.
The advantage of having 2 distinct frequencies available to the public is that it is possible to correct for atmospheric dispersion. Within the ionosphere, the propagation velocity of the signals from the satellites can be altered by prevailing "space-weather" conditions; this is actually the major source of error in GPS. As different frequencies are affected differently, using a multi-frequency receiver makes it possible directly to measure this dispersion. Single-frequency receivers must either use a model based upon satellite ascension, or utilise a correction obtained from another source (e.g. DGPS or SBAS).
The galileo service plans to offer a paid-for premium service, offering another signal technically equivalent to the GPS "precise acquisition" signal, and encrypted using commercial cryptography. This service is also expected to provide high-bandwidth downlink for rapid acquisition of satellite ephemeris and differential-correction data (if conventional terrestrial based assisted GPS techniques are not available), as well as a guaranteed level of service, with guaranteed OTA alerts if a satellite malfunction is detecte, allowing a receiver immediately to drop a bad satellite rather than attempt to solve the location problem with bad data. As this signal will be transmitted on a 3rd frequency - triple frequency receivers which could perform an even more precise measurement of atmospheric signal dispersion are possible.
I see the difference; I'm just saying its a very small difference.
The US has gone into sovereign nations to execute individuals we're at odds with; you think jamming a location based service is going to chill our spines?
What is the US going to do if a European country starts jamming the US GPS system? Beg them to attack themselves? They sure as hell can't afford to attack Europe.
Pay Gazprom a higher rate for their gas, depriving Europe of warmth in the dead of winter.
The iPhone 4S and 5 can use GLONASS as well. But agreed, once the Galileo project gives the thumbs-up, we should see mobile device support shortly thereafter.
"You can't carry atomic clocks in your pocket, they're a tad too big for that."
Well, that *used* to be true!
http://www.symmetricom.com/products/frequency-references/chip-scale-atomic-clock-csac/SA.45s-CSAC/
I have never let my schooling interfere with my education. - Mark Twain
With what, money borrowed from China? The US isn't all-powerful, they rely on the cooperation of other nations, we all do. Push it too far and they'll find out.
You seem to assume that you somehow know the distances to 3 satellites. But you don't. What you got is three time-signals. From that you can only infer two distances. Two is only enough for a 2D-fix.
That is what people have been trying to tell you. You need one satellite to be your time-fix.
The satellites will all send out a signal at exactly the same time. Because of the speed of light you will receive each signal slightly delayed and with a different delay for each satellite. When you receive the first signal you start your clock. You then measure time until you receive the second signal and then the third signal. It should be fairly obvious that you by this method only end up with TWO values from THREE satellites.
IF you did carry around your own atomic clock you could in theory be your own time fix. You would know _exactly_ when the satellites are going to broadcast their signal so you could start your timing clock before receiving any signal.
Atomic clocks are however big as a fridge, so nobody actually does this, not even the military.
If we're talking about US vs europeans, pls explain to me why someone should trust those that in the last century had still colonies all over the world and started two global wars, the last one with a genocide. Sigh, I'm from Europe, but it makes me sick when someone suggests that Europe might have a moral superiority over the US.
I really suspected it wasn't a sphere, but my brain power wasn't able to imagine what the correct shape would be, so I'm happy to finally know.
Still, absent that mistake, the explanation is essentially correct. Second satellite makes the set of possible locations a 2D surface, third satellite reduces it to a line of some sort, fourth cuts that down to two possible points, etc. So three satellites still isn't sufficient for a 3D fix.
Right, in practice it doesn't matter. In practice, there are all lots of sources of errors, and if you try to naively solve the system of equations I wrote, you'll find no exact answer, because of these errors. And that's not even considering that, depending on the relative positions of the satellites, the equations might not even be independent (e.g. if all satellites are in the same plane, which is very unlikely, but can happen). The best you can do is to find the best approximation (i.e., the point that most closely satisfies the equations). A good way to do that is discussed in the paper I linked to.
I think you are making the mistake of thinking you know how long the signal took to get to you from each sat?
afaik, what you get is
sat1:I'm at x,y,z and the time is t
sat2:I'm at x,y,z and the time is t
sat3:I'm at x,y,z and the time is t
where the difference between the t in the message and the "real" t when you receive it is how long the message took to get there.
So two sats gets you the "real" t
and the 3rd allows you to derive your x,y,z
again, could be wrong - but afaik until you get the real t you know nothing about your position 2D or 3D.
My point is the above poster doesn't understand why 3 points is not perfect.
still pretty sure you know enough to get a fairly good estimate of t from 2 sats.
Showing working would require ThinkingAboutShit(TM), which I'll leave up to people who are SureAboutShit(TM)(you).
Conjecture:
either you know t by three sats or you need 4 sats unless you have t
I'll give it a quick go though
sat 1 is x1,y1,z1, t=0
sat 2 is x2,y2,z2, t=1000ns
sat3 is x3,y3,z3, t=1000ns
you are therefore 300m further away from sat2 and sat3 than sat1
you know how far away sat1 is from sat2 and sat3 -
form a bounded tri - you now calc how far you are away from sat1 and can hence calc "real t".
Why do I have the feeling you would complain if the US cured cancer and AIDS? "But they're still evil bastards who HATE folks with malaria!"
They provided a free useful service for everyone in the entire world, with no licensing fees that I'm aware of. It's a friggin clock and radio in the sky, that has been running very well since 1994 and not mucked with. "Monopoly"? No one is stopping you from putting your own clocks in the sky. You're basically upset that they built it for their own purposes, but opened it to everyone when it became obvious it was globally useful? You're complaining that a FREE system doesn't do everything YOU want, so it's evil and bad and probably kicks puppies.
Some folks would complain if you hung them with a golden rope, geesh.
That said, sure, always room for improvement. It irks the heck out of me when folks let blind prejudice block out all of the good things and focus solely on the bad. More systems are good for improved accuracy and redundancy. Sharing the cost for satellite navigation between countries is also good. As long as they all play nice with each other, I don't see any downside.
esa have no real failproof record. i'm paranoid again i know but if they can't deliver a payload into orbit without external help where did the tek for a global tracking system come from ????
Free speech was meant to be free for all... how can anyone grow up in a nanny state ?
As opposed to those that committed genocide within their own country and instituted slavery for another ethnic population, you mean ?
I'm not one to visit the sins of the father unto the Nth generation, I think actions are the responsibility of the individual/entity that does them. I don't think any other approach makes sense, so I don't blame the current US citizens for what happened in historical times. I also don't blame current Europeans for actions that happened donkey's years ago...
IMHO, if you do, you either have a chip on your shoulder, or you're nuts.
Simon.
Physicists get Hadrons!
Unfortunately the US chose to have no ground based back up to GPS and I assume the EU will go the same way. One major Coronal Mass Ejection (CME), severe meteor storm, or even EMP and we'll all be without navigation signals. We (in the US) had an ideal back up in the new Enhanced, or E-Loran, but that was scrapped and the equipment (including antennas) immediately destroyed. Non Directional Beacons (NDBs) which are very simple, but require a little skill and practice to use are already being phased out and the VORs are also scheduled to be decomissioned. Many airports, at least through class C require GPS for instrument approaches. If we are going to get hit by a major CME I hope it's before they get all the ground based backups decommissioned. One other point: Beyond a certain point additional satellites gain you little in accuracy. My question is why do people with consumer devices want more accuracy? With the current number of US satellites it can tell you where you are on a taxiway within 15 to 20 feet and that is without the additional, high accuracy ground based augmentation transmitters. GPS is not infallible. It has failed for a few hours a couple of times. It is also not immune to interference, or even strong signals a few channels off to the side, or even farther. Fly or drive in the SW US and you'll see what I mean. It is not a good system for putting all your eggs in one basket.
You already know the location of the satellites without receiving anything at all from the satellites. The orbits are well known and downloaded into your GPS device. The satellites themselves have no way of knowing their own position, they only know the same data as was downloaded into your GPS. The only principal information from the satellite is the timing of the signal. The signal also tells you the time of the day with a precision of 1 second, but you hardly need an atomic clock to know that already.
Your basic misunderstanding of the system is that you believe you that you have 3 points. But the only thing you actually got is the timing of the relative delay of reception of three signals which gives you two values to work with. From these two values you have to calculate your position and no magical tricks can somehow infer three points from 2 values.
"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.
"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.
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.
Did you see the paper I linked? It uses exactly this idea (the relative positions of the satellites) to do the calculations, completely eliminating the need to worry about time. Still, this reduces the number of equations from 4 (one for each satellite, involving position and time) to 3 (involving only position). But if you begin with only 3 satellites, you end up with 2 equations involving only position, which consists of 3 variables (x,y,z). So, I still don't understand how you can calculate the position of the receiver with only 3 satellites.
About differential GPS: from what I understand, you still need 4 satellites in addition to the ground station. The ground station just broadcasts the difference between the signals received from the satellites and the signals you'd get if there were absolutely no errors (it can do that because it knows its exact location and also the trajectories of the satellites). This information can then be used by GPS receivers to correct their readings and improve accuracy. That's still not perfect, because the corrections are exact only at the exact position of the ground station; so the farther you are from the station, the worse the correction gets (still, Wikipedia suggests that the corrections are still useful hundreds of miles away from the ground station).
It's interesting to note that initially, differential GPS was used to completely bypass the signal degradation that was built in the GPS system (the satellites used to intentionally introduce random errors in their time signals, a "feature" called "selective availability"). The differential GPS correction was so successful that "selective availability" became pointless, and in 2000 the US decided to stop degrading the GPS signal.
I posted this yesterday, but somehow posted it in reply to my own message by mistake.
Fair enough, I wasn't considering the ideal theoretical situation (with the twist of throwing out the second point) but instead actual practical ones.
That's probably not so much of an issue this decade, but I've still not replaced the "proper" GPS, because I frankly don't see the need ; my navigation is perfectly adequate without one. The wife did get us a SatNav (which uses GPS for it's position finding) for the car, and it's base maps are over 20 years out of date, illustrating the point that the important thing about a SatNav system is not one of the position-finding technology, or the route-finding algorithm, or the base map, or the "wireless updates for the safety camera database", but it is all of the components and their interactions.
(Incidentally, I object to being required to subscribe to a "safety camera database" which is a euphemism for "speed where ever you dare database" ; if we ever replace this "Road Angel" heap of shit, I'll be looking for a system without this unnecessary capability.)
Birds are not dinosaur descendants;birds are dinosaurs, for all useful meanings of "birds", "are" and "dinosaurs"
Comments like these suggest that you're not really interested in studying physics. On the other hand, John Cramer's Alternate View columns inspired me to study physics in high school. In 1998, FTL Photons introduced me to the Casimir effect. In 2001, I made an offhand remark about these faster-than-light (FTL) implications to my experimental physics professor, and he asked me to give a presentation to the class.
The next comment I wrote summarized the first part of my presentation. The second part showed that virtual particles actually slow down light in the standard vacuum, because photons spend some of their time as electron-positron pairs that travel slower than "true" lightspeed. Because the Casimir effect suppresses some of these virtual particles, light actually travels faster between the plates (perpendicular to the plates) than in the standard vacuum. This is called the Scharnhorst effect.
Why are you talking about Hawking? I already pointed you to "Wormholes, Time Machines, and the Weak Energy Condition":
"The following model explores the use of the 'Casimir vacuum'[12] (a quantum state of the electromagnetic field that violates the unaveraged weak energy condition[11]) to support a wormhole..." [Morris, Thorne, and Yurtsever, 1988]
Again, why are you talking about Hawking? You might want [1] to read "FTL Photons":
"Since the energy density of normal vacuum is defined to be zero, the vacuum between the metal plates actually becomes a region of negativ
Good grief, you're arguing with the definition of potential energy. I was referring to the fact that all conservative forces can be described as the negative vector gradient of a potential energy function. Many of your statements on this topic are confusing:
Yeah, forces are vectors...
The force vector points from a region with high potential energy to a region with lower potential energy. That's why an attractive force implies that the Casimir vacuum has less energy than the standard vacuum. No energy is "directed" anywhere because we're talking about potential energy, not calculating Poynting vectors.
The Casimir force between two parallel conducting plates is negative/attractive. Period. More complicated geometries can have repulsive Casimir forces, but that doesn't affect the attractive force between parallel plates any more than your meaningless caveat does. Perhaps you meant to say "According to the article, the energy is negative..."
In my
If you really did "understand that logic" then you wouldn't have written all that nonsense about vectors. Instead, you'd have skipped immediately to this point, which now implicitly acknowledges that the Casimir vacuum has lower energy than the standard vacuum.
Remember that spacetime is curved near large masses, but ~flat far away from masses where only vacuum energy is present. This implies that vacuum energy exerts ~zero gravitational force, so its stress-energy tensor must be ~zero, so the standard vacuum has ~zero energy.
If you're interested in the details, John Baez summarizes several vacuum energy density calculations. A naive quantum field theory calculation yields a vacuum energy with a mass density of +10^96 kg/m^3, which would've ripped the universe apart [1] before galaxies could form. On the other hand, general relativity and observations of our nearly-flat universe place a more rigorous upper bound at +10^(-26) kg/m^3. It seems like [2] gravity renormalizes vacuum energy to zero, within about one part in 10^122. Even though renormalization was harshly criticized at first, it's necessary to explain why galaxies (and thus humans!) exist.
Here's another, purely quantum-based, argument [3] for renormalization:
"As there is no lower energy state than the ground state, there is no energy level transition available to release the ZPE. Therefore, it can be argued that hf/2 should be dropped before integration of the quantum expression. This procedure is an example of renormalization, which basically redefines the zero of energy." [Abbott et al. 1996]
Footnotes
[1] One might assume that a large positive vacuum energy would collapse the universe just like a large amount of positive mass-energy would. This doesn't happen because in general relativity gravity depends on energy and pressure. In natural units, vacuum energy has pressure equal and opposite to its energy density. Because the stress-energy tensor has three pressure terms (for x,y,z) and only one energy density term, the negative pressure of positive vacuum energy dominates, causing the expansion of the universe to accelerate. back
[2] It's also vaguely possible that zero point energy doesn't gravitate at all
ok
simplification (drop y,z which require a 3rd point of reference)
receive from
sat1 0m, t=150,000ns
1000ns later receive
sat2 900m, t=150,000ns
gives
you are 300m further away from sat2 than sat1
therefore you are 300m from sat1
and 600m from sat2
your x = 300m
and
t when you received the first message = 151,000ns
While talking with my first research advisor around 2003, I mused that it's unfortunate how the Casimir effect only supresses vacuum fluctuations with wavelengths larger than twice the spacing between the plates. Since fluctuations with shorter wavelengths have more energy, the Casimir effect only depletes a vanishingly small fraction of the vacuum energy between the plates. So I agree that a naive quantum calculation leads to a huge vacuum energy. But as I've just explained, the same theory of general relativity [1] that implies stable wormholes and the Alcubierre drive also seems to renormalize the vacuum energy to zero. So this just means that depleting vacuum energy could potentially lead to very negative energy densities.
I asked which team and you replied:
Agreed:
Not having done the math often does lead to quantum Goretex and ironic references to Maxwell's (broken) Demon.
Maclay and Forward 2004 [2] imagined accelerating a mirror fast enough that the dynamic Casimir effect creates real photons. A more recent example was in 2009, which imagined spinning magneto-electric nanoparticles fast enough that the centripetal acceleration created real photons. At the time, I called this device a photon drive. On page 2 of their 2004 paper, Maclay and Forward point out that more conventional photon drives would arguably be better than their propulsion system.
Good grief. Electric fields are zero in perfect conductors. I explain this fact to freshman physics students by asking: what would happen if we tried to place an electric field across a conductor? Electrons would move opposite the field, and positive electron holes would move with the electric field, exactly enough to cancel out the original field inside the conductor. Better conductors cancel out faster, so electric fields are zero in perfect conductors.
Mentioning that this fact can be derived from Maxwell's equations is meant to be helpful, because all physics students should be familiar with the first theory that emerged in a Lorentz-invariant form. In other words, Maxwell's equations were consistent with special relativity before relativity even existed. They're the basis of all radio equipment, and the correspondence principle checks that quantum electrodynamics (one of the most accurate theories in history) is identical to Maxwell's equations for large systems. If your reaction to hearing "Maxwell's equations" is to spray chaff about quaternions, you'll be disappointed to find that core classes based on junior-level Griffiths and graduate-level Jackson are almost exclusively about Maxwell's equations.
Quaternion notation is useful when desribing 3D rotations, but it's not used in electrodynamics because vector notation is more intuitive. That doesn't stop crackpots from insisting that Maxwell's equations are wishful thinking.
Physicists use Maxwell's vector equations despite the fact that we're well aware of quaternion notation. John Baez even wrote a paper on octonians. As Baez quips, if the noncommutative quaternions are like a shunned eccentric cousin, then the nonassociative octonians are like the crazy old uncle nobody lets out of the attic.
In fact, look at p542 of Griffiths 3rd edition: "Equation 12.136 combines our previous results into a single 4-vector equation-- it represents the most elegant (and the simplest) formulation of Maxwell's equations."
Page 555 of
That is ONE of the reasons I have called you rude and obtuse.
But the one argument I will make is this: you ALSO insist on taking my comments out of context, and insisting that I meant something other than I did. Take the one about vectors, for example. I mentioned that it had direction (with which you apparently agreed), then objected to me mentioning the direction in which it was "directed".
This is a completely ridiculous splitting of hairs. By "directed" I simply meant it had direction. I was not proposing that it was being "directed" by anything.
" Instead, energy is removed from the vacuum itself."
And just what is it that makes you think I was arguing with anybody about that point?
Nevertheless, as I pointed out, depending on what theory you choose to follow, the positive energy density of the vacuum is anywhere from 10^-9 joules/m^3, to 10^119 joules/m^3. Anything in that range is still significantly positive.
My point was that depending on the way you do the math, sure you CAN show negative energy... but it is far from necessary. There are just as valid methods of caculation that show it as merely an absence of the positive energy elsewhere. That was all I was trying to say.
Anything else is hair-splitting on your part. YOU may not think so, but you have continually insisted on taking me too literally and picking my comments apart, then stalking me in other forums (and I suspect that you have tried to do it elsewhere, as well). And launch into this great diatribe about how wrong I am, in a situation in which you know damned well I am not interested in taking the time and effort to defend myself.
Go the fuck away, and leave me alone. Do you understand THAT? Or do I need to explain THOSE words to you, too?
I emailed the Casimir motor idea to a few scientists, saying: My gut tells me that vacuum energy can't be made to do work. But I don't see an obvious, fatal problem with the following scheme. Do you?
In response, Geoffrey Landis pointed out that there will be a latent heat at the phase transition, even for type II superconductors. He uses the same reasoning that explains why magnetic fields cause latent heat. In other words, Casimir-induced latent heat will exactly cancel the net work done by the plates, which seems to forbid this free lunch...