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PhotobucketOver the course of the past two weeks you probably did some serious driving, hiking, or flying. You may have traveled 'over the river and through the woods to grandmother's house' and back home without getting lost. Some voice might have been telling you when and where to turn just when you needed it. Your phone might have been smart enough to locate you and direct you to your destination.

PhotobucketGPS devices are ubiquitous. We take them for granted and don't think much about them. They are a remarkable piece of technology with applications in many areas. Our son-in-law uses it while farming. During harvest, GPS records his field position and associates it with the yield. This information is overlaid onto his field maps with GIS (Geographic Information System). Soil testing uses GPS mapping to see which field areas need chemicals. Insect infestations can be mapped with GPS. The following truck spreaders or airplane sprayers can follow the GPS maps for precisely located applications.

GPS is being used for fire, ambulance, police, search and rescue, trucking, delivery vehicles, and public transportation. Recreational uses of GPS include navigation while hiking, hunting, skiing, and on golf courses to track golf carts, and to let players know how far it is to the center of the greens. GPS is being used for recreational sailing and fishing and for commercial shipping fleet management. In the air, GPS is being used for en-route navigation, aircraft landing, and air-collision avoidance systems.



Do you have any idea how GPS locates you? It is actually quite simple in concept, but complex in practice. This diary focuses on the simple concept. If you are curious, join me below.



The Constellation of Satellites
The Global Positioning System (GPS) primarily consists of 24 active satellites with several more in reserve and in orbit. There are 31 in orbit as of 2011. They are made by Rockwell, now Boeing, and Lockheed Martin. Older satellites are replaced with newer ones when needed. Some satellites are over 20 years old. The reserve satellites are in positions to be readily available.
The GPS constellation delivers consistently high performance due to the dedicated efforts of its operators -- the men and women of the U.S. Air Force. The 2nd Space Operations Squadron at Schriever Air Force Base in Colorado Springs, Colorado, is responsible for the daily command and control of the GPS constellation. The squadron ensures continuous GPS availability and high accuracy to millions of users, both military and civilian, on a 24/7 basis.

Characteristics of the constellation..
  1. Orbits are circular
  2. Period of orbit is 12 hours
  3. Altitude of orbit is 12,500 miles
  4. Six orbital planes inclined 55〫to the equator
  5. Four satellites in each orbit with reserves in some

Standard Positioning Service (SPS) provides the data for the general consumer. With 4 or more satellites acquired, the delivered signal can provide accuracy of within 7.8 meters 95% of the time. The actual accuracy end users can expect depends on factors outside the government's control, including atmospheric effects and receiver quality. Some high-quality GPS SPS receivers can at times attain better than 3 meter horizontal position accuracy.

For nominal performance, GPS satellites need to be higher than about 25〫above the horizon in order for the ground based mobile unit to 'see' and securely lock onto the signal. The mobile unit needs to access 4 or more satellites. This is usually not a problem. Sometimes as many as 9 satellites are accessed depending on conditions on the ground. The following 5 minute video has some good animations illustrating GPS access by a ground mobile unit in Los Angeles. You will see how the number and directions of satellite signals acquired is constantly changing.





The GPS system can calculate speed, direction, and estimated time of arrival. All of this is done by a constellation of satellites moving several thousand miles/hour and involving users who might also be moving at high rates of speed.

We still have not answered the question of how the system locates the user on the ground and defines a position horizontally and vertically. The key to plotting position lies in combining the simple relationship of distance = rate x time with the procedure of Trilateration in 3-D. First, let's consider the simpler case of Trilateration in 2-D. Then, we can extend that to 3-D.

Trilateration in 2-D
Imagine the following situation. You are in a profoundly long sleep after some intense New Year's celebrations. Your three friends decide to play a practical joke on you, knowing you will be sleeping like a log for a very long time. They deposit you in a motel room in some small town with no identifying information in view about your location. They hide all of your clothes except for your underwear. They leave you a cell phone and a big U.S. map, ruler, and drawing compass.

When you wake up, you want to find out where you are located. But, it is -25〫outside and you can't leave the room. So, you call friend #1. He answers and you start yelling at him in anger. He says to cheer up. This is a puzzle to solve. He tells you that he is in Casper, WY and you are 720 miles from Casper. You draw a circle on the map that big.

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Well, that doesn't help much. You could be anywhere on that circle. So, you call friend #2. You yell at her. She also says to cheer up and tells you she is in Fargo, ND and you are 555 miles from Fargo. You draw another circle on the map that big.

Photobucket
That helps somewhat. You could be either in Canada or Iowa. How is that supposed to cheer you up? Now, you call friend #3 and read him the riot act. You are getting cold and more angry. He also says to cheer up. He says his clue should help you solve the puzzle and know your location. Once you do, they will tell you where to find your clothes and how to get home. He tells you he is in Wausau, WI and you are 280 miles from Wausau. Hurriedly you draw the circle on the map centered on Wausau. Bingo! Where the three known distances intersect is your location.

Photobucket
You peer in closer and check the name of the town in Iowa. "Very funny, guys!"

Photobucket


Trilateration in 3-D
That silly example is designed to show one thing. Once you know three accurate distances from three specific locations, it is an easy matter to plot their intersection on a two dimensional map. For satellites in space, orbiting a three dimensional Earth, the task is more challenging. GPS uses the intersection of four spheres instead of circles to define your location. In addition, there are sources of error which make the distances of the radii of the spheres to be inexact. Let's examine what information is transmitted by each satellite?

Satellite Transmissions
For this part of the discussion, I am borrowing and modifying some graphics from an online article by Diana Cooksey, MSU GPS Laboratory, Department of Land Resources and Environmental Sciences, Montana State University-Bozeman.

Each satellite has an atomic clock on board. All of the clocks are kept synchronized by the 2nd Space Operations Squadron. They constantly transmit two kinds of signals to the ground. One radio signal is called an ephemeris. It contains a unique code that identifies the satellite. The signal also tells the location of the satellite.  Clock behavior and any clock corrections, and GPS system time are included. The time is coded so the receiver knows when it was transmitted. The receiver clock is synchronized with the satellite clock. Signal transmission takes about 0.06 seconds to reach the receiver.

When the time of the received signals are compared to the code telling when the signal was sent, there is a time difference between them. By multiplying the time difference by the speed of light, the receiver calculates the distance to the satellite at that time.

Photobucket

An almanac is also transmitted telling the ground unit the approximate location data for each of the 24 active satellites. The almanac is automatically downloaded and takes several minutes to be received.

Signal From Satellite 1
As each moment passes, your GPS unit should be receiving at least 4 signals. Let's consider the information obtained from the first satellite of the four. The ground unit is located in this example where the yellow dot shows on the Earth, but it doesn't know that for sure. The unit receives the time signal and computes the time difference from the time code method described above. For example, it might calculate a distance of 12,000 miles. Distance = speed of light x time diff. The GPS unit 'thinks' its location could be anywhere on the surface of that large sphere based on only knowing it is 12,000 miles from the satellite.

Photobucket

Signal From Satellite 2
The GPS unit also receives a signal from a second satellite. The time delay is used to calculate a radius of the second sphere. It might get a value this time of 11,000 miles. Now the GPS unit 'thinks' it could be on any of the points that are both 12,000 miles from #1 and 11,000 miles from #2. That intersection of spheres defines a circle. In the figure, the circle is viewed obliquely. We can see the yellow dot on the surface of the Earth is part of the circle. But, the GPS unit still doesn't know for sure where it is located. It only 'thinks' its location could be at any point on the circle. But, that is an improvement.

Photobucket

Signal From Satellite 3
The signal from the third satellite might give a radius of 11,500 miles. This time the intersection of the circle and the surface of the third sphere includes only 2 points, marked as yellow dots. One of those is out in space and is discarded. The GPS unit 'concludes' it is on the surface of the Earth.

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Why Do We Need Satellite 4?
Various factors introduce errors into the time difference calculation. The signal could reflect off of another nearby object. It refracts as it goes through the atmosphere. The speed of light is altered by air and water vapor. And, the clocks on the satellite and GPS unit are not perfectly in sync. There is a small timing offset. These factors cause a range of uncertainties in the time differences and in the resulting radial distance calculations. The speed of light is exceedingly fast. A time error of 1 billionth of a second results in a distance error of about a foot. The intersection of the surfaces of the three spheres is not sharp and exact. The intersection is a 'fuzzy' volume of space several tens of meters across.

The fourth satellite signal sphere intersects with the first three. The GPS unit uses this additional radius to rapidly calculate an adjustment factor for all 4 of the radii. This adjustment lets the intersection of all four spheres pass as near as possible through one point. Doing so more accurately defines the position within a few meters both horizontally and vertically.

Since this is an ongoing process in time, changes to that position with respect to time are used to calculate speed and direction of travel. These values are used in concert with the database of maps and highways to compute travel times and arrival times.

FAA data collected in early 2011 shows that the horizontal accuracy of GPS SPS is often within 1 meter.
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Accuracy of GPS
GPS satellites broadcast position and timing data on two radio frequencies, L1 and L2. Two kinds of code are broadcast on the L1 frequency, C/A code and P code. Coarse Acquisition C/A code is available to civilian GPS users and provides Standard Positioning Service (SPS). Precise P code is broadcast on both the L1 and L2 frequencies. P code, used for the Precise Positioning Service (PPS), is available only to users with an authorized decoding key, such as the military.

From the GPS.gov site...

The accuracy of the GPS signal in space is actually the same for both the civilian GPS service (SPS) and the military GPS service (PPS). However, SPS uses only one frequency, while PPS uses two. This means military users can perform ionospheric correction, a technique that reduces radio degradation caused by the Earth's atmosphere. With less degradation, PPS provides better accuracy than the basic SPS.

From the Purdue University School of Technology, they discuss GPS accuracy in terms of surveying.
The GPS equipment will potentially maintain an accuracy of 5 millimeters, even when performing measurements over several miles. GPS equipment’s level of accuracy at great ranges is especially useful on extremely large construction projects, such as an airport project including runways, or on highway construction projects covering hundreds of miles.
Comments and More Technical Information
My goal for this diary was to give the typical Kos reader who is interested in science and technology a better understanding of how GPS is able to determine their location. In doing so, I have learned a lot. I hope I have come close to reaching that goal for most of you.

In doing the research for this diary, I realized how I have barely touched the surface of the technologies that are in effect making it all happen. For those of you who are more capable and curious, here are a few sources with more technical information that I chose not to put into the diary.

http://www.gps.gov/
http://www.nstb.tc.faa.gov/
http://what-when-how.com/...
http://hubtechinsider.wordpress.com/...
http://www.tomtom.com/...

Video of GPS use for aircraft navigation from the FAA



The next time you drive, fly, hike, and use a GPS unit, give some thought to how these units constantly monitor your position. Consider the technology that enables them to locate you within a few meters anywhere on the Earth. I hope you have safe and accurate travels during 2012.


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Comment Preferences

  •  Update your maps! (10+ / 0-)

    An out of date GPS map is sometimes a terrible inconvenience.

    Our TomTom has a 2 year old map and he has no idea that the road we live on even exists.  We were waiting until the new year rolled over to pay for an update, but it was sorely needed.

    Keep your religion out of my government.

    by catwho on Mon Jan 02, 2012 at 08:34:05 AM PST

  •  Very nice post! (8+ / 0-)

    I would think Community Spotlight material, for sure.

    One question on a minor point.  I thought stable orbits of all orbiting bodies had to be elliptical, so the satellites' orbits could not be circular?

    We reach for the stars with shaking hands in bare-knuckle times.

    by TheOrchid on Mon Jan 02, 2012 at 08:34:15 AM PST

    •  Thank you. Let me know if this helps about... (5+ / 0-)

      orbits. All orbits are elliptical. Ellipses have a property called eccentricity. If the eccentricity = 0, the orbit is a circle. If eccentricity is closer to 1, the orbit is more elongated. All of those orbits can be stable and ongoing. Here is a link to more information about the date of January 4 and Earth's orbit.

      Let me know if I can answer your question better.
      Thanks for stopping by.


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 09:00:35 AM PST

      [ Parent ]

    •  Yes. (0+ / 0-)

      Strictly speaking, the GPS constellation satellites' orbits are elliptical. They are quite close to circular in fact (a circle is a degenerate ellipse), and have "semi-synchronous" orbits (they orbit the earth twice per day). The ephemeris that each satellite transmits contains all of its orbital elements -- it is sufficient to describe any basic (elliptical) orbit. (The ephemerides used to be publicly available and free, but a quick search of google isn't revealing a set to me. IIRC, each is a set of six numbers, and is also known as a "Keplerian" set of orbital elements. Also IIRC, one of those components is the eccentricity, and for the GPS satellites is very close to 1.)

      These ephemerides are updated at least daily (and typically much more often), as they are required to be extremely precise.

  •  Thanks for posting this (8+ / 0-)

    I'm half way thru it.
    I'll come back & finish reading this later.
    It's amazing what one can learn at the GOS !

    Hope your day goes well.

  •  One time I chatted up a couple of county employees (7+ / 0-)

    who were re surveying a bunch of old markers. They had a GPS stick which was obviously of the p type. It read out location and altitude down to a hundredth of a foot. The stick was carbon fiber and I was impressed. You would have trouble getting it within an eighth of an inch of vertical and even then it wouldn't change the accuracy. That's within the thermal expansion limits of the underlying concrete.

  •  Recalculating route, recalculating {CRASH} (6+ / 0-)

    love those commercials ("I'm the smartest raccoon in the whole neighborhood").

    But it is truly amazing technology.  Though not perfect when integrated onto existing maps, it's hard to imagine being without a GPS unit in the car when in an unfamiliar place to find a location or business.

    Also useful for checking your speed against your speedometer (mine is about 5 mph off).

    Profoundly humbled by DKos generosity of spirit and selflessness of nature. Forever grateful beyond measure.

    by wretchedhive on Mon Jan 02, 2012 at 08:44:21 AM PST

    •  Be careful of speed traps if you are off by 5. (6+ / 0-)

      Here is a question for you. If GPS reads +5 over your car speedometer, are your tires too small or too large? And, by how much?

      Please see ⬇ the sentence just below the blue line.


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 09:09:56 AM PST

      [ Parent ]

      •  speedo too low, tires too big (3+ / 0-)

        but I have the same size tires that the car was equipped with out of the factory.

        Impossible to answer the question given the amount of information available, as the car could be sliding sideways with the brakes locked up, or you could be going in reverse or airborne.

        Profoundly humbled by DKos generosity of spirit and selflessness of nature. Forever grateful beyond measure.

        by wretchedhive on Mon Jan 02, 2012 at 10:22:39 AM PST

        [ Parent ]

      •  Note that some cars, especially German ones, (1+ / 0-)
        Recommended by:
        wretchedhive

        tend to calibrate their speedos a couple mph high -- I've seen this with BMW, Audi, & VW. I'm not exactly sure why they do this, but I've read several discussions on enthusiast forums presenting plausible theories.

        •  bragging rights or that correct speed is more (0+ / 0-)

          important when you have something other than the factory summer tires (smaller profile = smaller circumference) meaning you'd be driving in less than ideal weather...?

          Profoundly humbled by DKos generosity of spirit and selflessness of nature. Forever grateful beyond measure.

          by wretchedhive on Mon Jan 02, 2012 at 02:25:01 PM PST

          [ Parent ]

        •  Matches my experience. (0+ / 0-)

          My VW Jetta is 2-3 MPH off at all reasonable speeds.

          My previous car was a Geo Prizm (a U.S. built Corolla), and it was dead-on at everything I could reasonably test. Certainly it was accurate to better than 1/2 MPH at 60 and 75 MPH. I've also tested a Mazda truck, and it is closer to exact than the VW, although I didn't test it thoroughly.

          It seems to me that having the speedometer read high (as mine does) would tend to minimize speeding tickets. But I really can't say I know their motivation.

      •  Traffic Ticket (1+ / 0-)
        Recommended by:
        jim in IA

        about 15 years ago when I was writing GPS/AVL software I frequently drove with GPS and laptop in the car (homebrew, before they were available for ordinary  cars), I got a ticket from a state patrolman, and beat it in court using GPS data to prove that what I said was true, and it wasn't about speed....

        http://www.witsends.com/...

        and of course I was using software (that I wrote) that kept a log of everywhere the car went, the exact time and speed, etc. Modern Navigational units mostly don't do that.

        btw, AVL means Automatic Vehicle Locator, a GPS coupled to a radio system.... that eventually evolved into smartphone technology, but in those days we were using business radio channels

        Without geometry, life is pointless. And blues harmonica players suck.

        by blindcynic on Mon Jan 02, 2012 at 04:07:57 PM PST

        [ Parent ]

    •  heh. wish I'd had one in '98-'99 working census (5+ / 0-)

      surveys off hand-drawn maps made by the 1980 enumerators. Geesh.

      LBJ & Lady Bird, Sully Sullenberger, Molly Ivins, Barbara Jordan, Ann Richards, Drew Brees: Texas is No Bush League! -7.50,-5.59

      by BlackSheep1 on Mon Jan 02, 2012 at 09:17:31 AM PST

      [ Parent ]

  •  Now to get the inner world sorted (9+ / 0-)

    Ya have to click on it to see the punch line... Sorry.

    Photobucket

    Great diary - got it bookmarked.

  •  Can I put one on a sponge? ;-) n/t (4+ / 0-)

    Listen, strange women lyin' in ponds distributin' swords is no basis for a system of government. Supreme executive power derives from a mandate from the masses, not from some farcical aquatic ceremony.

    by EdMass on Mon Jan 02, 2012 at 09:09:30 AM PST

  •  Very nifty - thanks! (2+ / 0-)
    Recommended by:
    palantir, belinda ridgewood

    Is it true? Is it kind? Is it necessary? . . . and respect the dignity of every human being.

    by Wee Mama on Mon Jan 02, 2012 at 09:25:08 AM PST

  •  We still use paper maps, sometimes turning on (5+ / 0-)

    the onboard compass.

    That, in its essence, is fascism--ownership of government by an individual, by a group, or by any other controlling private power. -- Franklin D. Roosevelt --

    by enhydra lutris on Mon Jan 02, 2012 at 09:33:17 AM PST

    •  It worries me that people travel without real maps (7+ / 0-)

      these days. I've rescued a few lost souls up this way who didn't realize that GPS and a cell phone won't keep you from being lost everywhere.

      Fry, don't be a hero! It's not covered by our health plan!

      by elfling on Mon Jan 02, 2012 at 09:37:30 AM PST

      [ Parent ]

      •  I agree with you both. The only time I used... (5+ / 0-)

        it in the car was on a trip to the Outer Banks. We borrowed a unit for that. My lovely wife is a good navigator. On that trip, we drove south on the O Banks strip to cross back west at Manteo for the return. It kept yelling at us to make a U turn. Finally, it shut up as though it was mad. Once we were into the state a ways, it returned all cheery and such as tho nothing had happened.


        Yes...this will be on the test.

        by jim in IA on Mon Jan 02, 2012 at 09:48:22 AM PST

        [ Parent ]

      •  Many years ago I flew (2+ / 0-)
        Recommended by:
        eyesoars, elfling

        my Wife, her brother and his girlfriend to Utah in a light plane from Boulder Colorado, for skiing. As we departed SLC international afterward to the south, my wife acting as copilot had the maps out about where we could get some altitude to clear the mountains. I kept looking over to see altitudes and what was in front of us but couldn't figure out the map. Turns out most pilots hold the map so that North is up and make any adjustments mentally. She, however, being outward-bound trained in "Orienteering", placed the map so that the terrain view matched what she saw, so she had "south" up....

        But yes, at least we had maps. and no GPS, hadn't been invented yet....

        and the same brother and his daughter had to spend the night in the winter snowmobiling on Vail Pass because he had a GPS but no maps, and didn't know in the dark that a gully was in the way of where the GPS said to go...

        GPS = handy, but not a cure-all.

        A pilot friend once reported that he had to call Air Traffic Control once to get oriented again, and they said "Are you lost?" and he said, "No, I can see where I am, but I'm surrounded by lostness...."

        Without geometry, life is pointless. And blues harmonica players suck.

        by blindcynic on Mon Jan 02, 2012 at 04:36:22 PM PST

        [ Parent ]

        •  glider pilot here... (0+ / 0-)

          We use logging GPS units for contests -- they prove the ground track that the pilot flew.

          Much better than the old technology, which was using a film strip from a camera mounted in the cockpit, where the pilot would fly over/around designated turnpoints, and take a photo of the turnpoint while turning over it. So easy to blow a photo, or choose the wrong turnpoint. And you might not know until the film strip had been developed.

          With GPS, it's not even a snap. You finish the race, download your track to the contest director, and the computer figures your score (plus the GPS tells you when you've gone through the turn arc, so you don't get a bad/wrong turnpoint). Plus you can run "worm races", where everyone is synchronized from their start (or finish) times and the computer displays the competitors' progress in virtual time.

  •  Fascinating technology... (5+ / 0-)

    Thanks for the insight! I'm a little in awe of the people who've conceived of and developed all these technologies.

    But I have to say I have a GPS app on my phone that I've never used -- in my somewhat convoluted mind, it's in a class with cruise control, which paradoxically makes me feel terribly out of control!  

    There's something about having my own physical relationship with my surroundings that keeps me...grounded, for want of a better word. If I take my foot off the gas and let the car manage that part of driving, I get terribly anxious -- I just can't reconcile the sensation of moving/going somewhere with not doing it myself.

    And letting a handful of satellites and a suite of really cool software tell me where I should be going...it just makes me feel like I'm not really there! Is that weird?

    But I did use GPS the first few times I worked in Las Vegas a couple of years ago...and then I stopped, because I realized I had no idea where we actually were on the map. We were staying in one part of the city and the office was across town...and I didn't know whether we were going north or west to get there. Once I started looking at maps, and seeing how all the freeways interacted, I hardly even needed the maps, let alone the GPS.

    I'm just a weird combination of techie & luddite, I guess...

    What we have are markets. Culture rewards both action and restraint, in many ways; markets can only reward action, which makes them sociopathic when used to operate culture. h/t Gooserock 6/7/2011

    by SingerInTheChoir on Mon Jan 02, 2012 at 09:58:47 AM PST

    •  I really appreciate your comments. Not weird. (3+ / 0-)

      I agree with needing to feel a sense of place, of knowing where I am located with respect to my surroundings. Being able to read maps and navigate is an important skill.

      For those of us who live in orthogonal communities where the streets are mostly N-E-S-W and straight, map reading and such works fine. There is no need for GPS. Getting into unfamiliar and winding roads with lots of possible turns, GPS can really be helpful. But, I still want to see a paper map. I am old school.

      Thank you for your thoughtful remarks.


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 10:08:59 AM PST

      [ Parent ]

  •  Sorry you lost me (1+ / 0-)
    Recommended by:
    belinda ridgewood

    Thanks jim! Happy New Year

  •  How many other countries have their own GPS? (2+ / 0-)
    Recommended by:
    belinda ridgewood, jim in IA

    China?  Russia? France?

    I understand the Russian system is very very accurate.

    Also, my iPhone Google Maps (very useful) works with cell phone towers as many other systems work.  Do the cell phone towers triangulate like satellites?

    Daily Kos an oasis of truth. Truth that leads to action.

    by Shockwave on Mon Jan 02, 2012 at 10:17:23 AM PST

  •  I just got back from a trip to Long Beach, CA (2+ / 0-)
    Recommended by:
    jim in IA, belinda ridgewood

    and my TomTom did a fantastic job of getting me in and out of there. My niece lives in a spot where one wrong turn will quickly get you lost and the TomTom got me there and the Live Traffic Update feature somehow predicted accurately that I would arrive at 4:19pm in spite of varying traffic along the route.

    I told my niece that if I had to choose between my cell phone and GPS I'd probably keep the GPS and dump the cell phone.

    Excellent diary!

    Honesty pays, but it doesn't seem to pay enough to suit some people. Kin Hubbard

    by Mr Robert on Mon Jan 02, 2012 at 10:22:45 AM PST

  •  Drives me buggy every time... (1+ / 0-)
    Recommended by:
    TheMeansAreTheEnd

    The trilateration scheme only works if you know exactly what time it is. You don't.

    Trilateration can't work without precise knowledge of the local time.

    What can work is hyperbolation.

    Each satellite broadcasts exactly what its time is. (They do this simultaneously, and all on the same frequency, which makes receiving all the signals its own neat little trick.) You receive all of their times, and by noting the differences, you can tell how much farther you are from one satellite to another.

    If you plot these differences (the satellites also broadcast their own precise positions (an ephemeris, or ephemerides) and the approximate positions of their brethren (almanacs)), you get a set of hyperbolas. If they're reasonably positioned around the sky, four of them will give you a unique solution for your local time, and an exact position. [The almanacs and any crude approximation of your location will tell your unit which satellites should be in the sky, and the ephemerides of four or more satellites will allow you to compute a position.]

    Once this is done, your GPS unit contains a fairly good clock, and it's easier to compute your position using trilateration and updating its clock for drift as necessary. (And in fact, most units do exactly that.) But until you have a reasonably good value for your local time, you can't determine distances to the satellites or your local position.

    •  I was unable to find much about hyperbolation... (0+ / 0-)

      in a quick search. Do you have some references for me to see?

      Thanks for your comments.


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 10:59:16 AM PST

      [ Parent ]

      •  Not for GPS (0+ / 0-)

        Although the major predecessor to GPS (Loran) used hyperbolation (on near-100kHz signals). That was naval and surface navigation only; there's no vertical guidance from Loran.

        In Loran navigation, the time difference between a master and a slave position yields a hyperbolic line-of-position. (See the Wikipedia Loran entry.) In three dimensions, it yields one half of a hyperboloid of revolution; two of these yields one or two lines of position; three yield a unique intersection on the surface of the earth, and four or more yields a unique and/or overdetermined solution in time and space.

        In GPS practice, it seems likely that an iterative, converging scheme is used to arrive at simultaneous solutions for time and position, and subsequently maintain the solution as the receiver moves and the receiver's clock attempts to drift.

        Once a solution is found, there is additional information available to help keep the receiver synchronized -- pseudo-doppler information from the satellites can suggest the direction of motion and direction and magnitude of accelerations (some of the particulars of this is still classified IIUC). It's likely these could also be used to help establish approximate initial positions and clocks.

    •  That's because the local time (0+ / 0-)

      tells the GPS how to use the last ephemerides to figure out what satellites should be in view and look for them. otherwise, it has to search the sky for random Satellites, download a lot of info for the calculations. Try taking the batteries out of a handheld unit for a day or so, replacing them and see what it does....

      And actually, three satellites are sufficient for a horizontal position, the fourth is needed, and noted, for improved accuracy and especially for altitude computations - so Aviation GPS units really need the 4th Satellite for approaches, but ground based hiking, not so much...

      also, the time issue is significant because in the pursuit of the mysterious "nutrinos faster than light" issue of a few months ago it appears that the atomic clocks on GPS satellites  and their synchronization became the issue, since when measuring huge speeds like the speed of light, very small errors, of azimuth or synchronization could bias the speed computations. If the computation showed the nutrinos were slower than the speed of light no one noticed, but a computation showing them above the speed of light was instantly (so to speak) worrisome - and noteworthy.

      Without geometry, life is pointless. And blues harmonica players suck.

      by blindcynic on Mon Jan 02, 2012 at 04:52:34 PM PST

      [ Parent ]

      •  not quite... (1+ / 0-)
        Recommended by:
        Ender

        What you are saying is right -- the local (approximate) time + location allows a GPS unit to use a current almanac (not! ephemeris) to immediately know which GPS satellites (SVs) should be above the horizon and perhaps usable.

        As soon as the GPS unit locks on to any SV, it knows the current time to within several milliseconds. That's not nearly good enough to determine an exact position, however. For that, it needs a local time accurate to a few nanoseconds (billionths of a second). Determining that requires a signal from several SVs (which provide timing), their ephemerides, and some computation.

        The actual data that the SVs send comes very slowly -- the data rate is 50 bits/second (yes, bits), and each SV sends frames of 1500 bits, divided into five sub-frames of 300 bits. Each frame contains an up-to-date ephemeris (i.e., the precise orbital track of the sending satellite), a GPS time, and part of the current almanac (which contains approximate orbital information for all the satellites).
        (Wikipedia has a good page on gps signals. There's also a very good description of the signal modulation and demodulation techniques, which allows all the SVs to transmit simultaneously on the same frequency.)

        The entire almanac is sent every 25 frames (i.e., downloading the entire almanac from one satellite takes 12m30s). Almanac data can be valid for as long as six months; ephemeris data is never valid for more than four hours.

        In older units, which could only attempt lock-on to a few satellites at a time, substantial time would be lost attempting to obtain a current almanac during cold-start. And that could only start once it had achieved lock on to at least one satellite. New units can lock on to multiple satellites simultaneously, and obtain multiple parts of the almanac simultaneously from different satellites to assemble a current almanac quite quickly.

        Having a current almanac allows a GPS receiver to avoid trying to decode satellite signals it has no chance of receiving. For earlier units, which could only attempt lock-on to one or two signals at a time, this was a big deal -- starting from a cold start could take several minutes, even in good conditions. For newer units, not so much.

        An ephemeris is useful only for establishing an exact fix, and never for searching for other satellites. An almanac is useful for determining what satellites should be in the sky given an approximate time and location, but is not otherwise useful in establishing an exact time/location "fix".

  •  Thanks for this great diary. (0+ / 0-)

    You obviously put a lot of effort into it, and I learned much that I did not know.

  •  I love geocaching, a game you play with a GPS. (1+ / 0-)
    Recommended by:
    jim in IA

    Now, it's not the Tom-Tom type you mount on your dashboard, but a handheld. My SO just got a Garmin Nuvi for Christmas, and he wanted to know if it showed coordinates, like my handheld does.

    Real Democrats don't abandon the middle class. --John Kerry

    by Lucy Montrose on Mon Jan 02, 2012 at 10:47:25 AM PST

    •  That activity is something I forgot to include. (1+ / 0-)
      Recommended by:
      Lucy Montrose

      Thanks for bringing it up. If anyone doesn't know about it. Here is a link to a popular Geocaching we site.

      I have two caches hidden in my neighborhood. They get visited regularly. Out of town folks in for a visit will often make a point of looking up geocaches to find when they visit different places.

      Thanks for the reminder of that.


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 11:04:09 AM PST

      [ Parent ]

  •  Been using GPS since 1994 (6+ / 0-)

    in forestry.  Oddly enough (or it seems odd to today's GPS users), I began using GPS to make maps, not to find where I was on a map.

    Being a forester used to require finding a patch of woods that you've never seen before in your life, using only paper maps and aerial photographs.  Estimating the total acreage in that patch of woods (very important if the trees were for sale) was something of a crapshoot.  You could hire a surveyor (time consuming and expensive).  You could do your own traverse (also time consuming, and any error that you made carried over to all subsequent points).  Or you could make a tracing off the aerial photo and hope that the scale was halfway accurate.

    Acreage estimate was often a challenge, because timber sale boundaries were sometimes meandering creek buffers, or a randomly painted line in the woods, which could not even be guessed at on the aerial photo.

    Along comes GPS.  Now you can take points along the boundaries of that piece of woods, in any order, unlike a traverse where each point had to be taken in sequence.  Any error in a single point does not carry over to the other points.  GPS was an incredible tool.  If all went well, I could estimate the size of a piece of land down to the tenth of an acre.

    In the early days, we had to deal with "Selective Availablilty," a deliberate signal distortion introduced by the military.  SA, as it was called, caused your location to be off by tens or hundreds of feet.  You had to record your GPS file onto a handheld data recorder, and then run that file against a second file from a base station.  Generally you'd download the correction file from that newfangled Internet, and often you had to wait until the next day for it to be posted.

    At first, those base stations were few and far between.  Sometimes I'd get home only to discover that that the nearest base station was out of service when I was taking my data!  Without correction, the data was nearly useless.  The Clinton administration eventually ended SA, opening up GPS to real-time civilian use.

    Oh, and in those days the satellite constellation was pretty thin.  Acquiring 4 satellites under the forest canopy was tricky, especially if it was cloudy or rainy.  All that water vapor was not good for signal acquisition.

    We have come a long way since then.  Never, ever take GPS for granted.  Think how amazing it is, that your tiny receiver can read signals from satellites whizzing 12,000 miles overhead, and tell you exactly where you are on the face of the earth.

    •  Those are great comments, foresterbob. (1+ / 0-)
      Recommended by:
      foresterbob

      I really appreciate them. First hand experience accounts like that are interesting.

      Again, distance = rate x time is very cool stuff. Physics...

      Thank you... jim


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 11:08:58 AM PST

      [ Parent ]

      •  By the way, I saved copies (1+ / 0-)
        Recommended by:
        jim in IA

        of two of those correction files.  They were generally produced in one-hour packets.  I made it a point to archive the final hour's file from 1999, and the first hour's file from 2000.  Happy new millenium!  

        Some historian might ask me for them in 2999, if I'm still around.  Gee, how did you live to be more than a thousand years old?  And what's this strange device that you call a floppy disc?

        •  Was it a 5.25" floppy? Or, the smaller one? (1+ / 0-)
          Recommended by:
          foresterbob

          You are lucky you didn't have to use a cassette tape for storage. I did some of that on a TRS-80 (trash80).


          Yes...this will be on the test.

          by jim in IA on Mon Jan 02, 2012 at 12:03:33 PM PST

          [ Parent ]

          •  The smaller floppies. (1+ / 0-)
            Recommended by:
            jim in IA

            I do have one or two of those 5.25" floppies in a box somewhere, just for fun.

            When I first began doing GIS mapping, which was about the time I began using GPS in the field, the company-owned computer had a tape backup system.  The tapes were about the size of cassettes.  They worked poorly, and became obsolete so fast that it became difficult to find any for sale.  That technology came and went really fast.

  •  It turns out that General Relativity (4+ / 0-)

    gives big enough corrections that it needs to be accounted for. The satellites are high enough for their clock rates to be increased significantly. (They're also slowed by smaller Special relativistic effects.) The rate difference between the satellite clocks and the earth-surface clock would give position errors of kilometers per day, if there were no corrections, and one were to use trilateration. I think the hyperbolation method described above by eyesoars is less sensitive to this effect. At any rate, all GPS systems have the relativistic corrections. This bugs the hell out of Conservapedia.

    Michael Weissman UID 197542

    by docmidwest on Mon Jan 02, 2012 at 10:55:51 AM PST

  •  Quibble about title (0+ / 0-)

    Instead of how GPS finds you, I think it should be how you find yourself using your GPS unit.

    For example, unless a signal is transmitted from you to another location, no one can find you.  There are some applications that appear to be GPS but which do more.  Onstar by General Motors sends a signal to a cell phone tower, and in so doing also sends your position.  Also, at sea or in a remote forest, there are emergency beacons which include a GPS position that goes to satellites so as to aid in search and rescue.

    But for the paranoid among us, GPS by itself will not report our location to others.

  •  I did some serious driving. (1+ / 0-)
    Recommended by:
    jim in IA

    6000+ miles. I-10, I-20, I-30, I-35, I-40, I-55, I-57, I-69, I-80, and I-90. Plus a passel of loops, U.S. highways, state highways, and more.

    I ran over something on I-30 outside of Little Rock which will cost us an insurance deductible for a rebuild engine. That meant most of the driving was done in two rental cars.

    We lost our main credit card in CA. and one of the rentals caused our backup card to go over it's limit. We discovered that just as we were ready to get a hotel.

    We had enough cash to drive to our next destination at 3:30 AM with only a quarter tank of gas. (We don't have a cell phone ad use the phone in the car, which was in the shop, when traveling.)

    My partner wanted to head home on Saturday but I told her  that December had been the best and worst month we have had in a long time and spending Saturday playing 42 with family would add to the best month while driving home had a chance to add to the worst month we have had in years.

    We stayed and enjoyed the greatest achievement of sentient life, 42, until the new year dawned.

    •  That is a serious driving trip. Was GPS with you? (1+ / 0-)
      Recommended by:
      Tomtech

      If you crossed IA on I-80, you went within a mile of me.

      I will check out the game 42. We like to play dominoes. But, cards and dominoes? And the state domino game of Texas? Does Rick Perry like it?

      Thanks for stopping. I hope your car and year are ok.


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 11:26:40 AM PST

      [ Parent ]

      •  I turned South to St. Louis. (1+ / 0-)
        Recommended by:
        jim in IA

        No GPS.

        I have a better internal navigation system than most hummingbirds. I just look at the big picture map before leaving on a trip and create a heavily zoomed in map in case I am going somewhere I have never been too before.

        I had two young men on their cell phones with me when we hit heavy Friday P.M. traffic in Ft. Worth and they couldn't find traffic info on their cell phones.

        We barely made it in time to my daughter's graduation even though we had hoped to get there early for dinner.

        My son and nephew are in their mid 20's and have been raised with gadgets but they weren't any help as navigators.

        I will look for a system that can provide traffic info and put that on top of my wish list this year.

  •  Wonder if GPS's Cover Arizona 99? (0+ / 0-)

    The sign pointing out that Arizona 99 was to the left betrayed no hint of what lay ahead: that the smooth asphalt of the state highway would switch to a dirt road that would lead to a locked gate.

    This little-used highway was the route taken by a college student who, authorities said, ended up snowbound and stuck in her car for 10 days, surviving on two candy bars and snow she placed in a water bottle to melt.

    Read more: http://www.azcentral.com/...

    •  That story could have had a tragic ending. (0+ / 0-)

      I viewed the highway with Google Maps. You can get onto it and follow along it with Streetview up to a point. Then it stops. I did see where the paved road turns into gravel.


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 11:55:13 AM PST

      [ Parent ]

  •  How accurate is the GPS altitude measurement? (0+ / 0-)

    I've read (somewhere) that it's less accurate than lat/lon measurements.

    •  You are correct. It is a little less accurate... (0+ / 0-)

      in the vertical. Not by a lot, though. In walking with my handheld around our streets, it does a good job if there are no obstructions. It it within about 15' vertical most of the time compared to the paper maps I have seen.


      Yes...this will be on the test.

      by jim in IA on Mon Jan 02, 2012 at 11:59:24 AM PST

      [ Parent ]

      •  I think +/- 15 meters is what is generally (0+ / 0-)

        quoted.  15 feet is exceptionally good, and is pretty much what you'd expect for the horizontal accuracy.  I don't think that's typical.

        To believe that markets determine value is to believe that milk comes from plastic bottles. Bromley (1985)

        by sneakers563 on Mon Jan 02, 2012 at 12:11:48 PM PST

        [ Parent ]

      •  ... (0+ / 0-)

        and if you have WAAS (wide-area augmentation system), the vertical navigation is to within a meter.

        This system takes the satellite signals recorded by a fixed ground station, determines the errors in the signal, and broadcasts them. Suitably equipped receiver + GPS systems can compensate using the extracted errors and generate very accurate positions over a substantial area (a few hundred miles).

        This type of system is used for precision aircraft approaches.

  •  Thank you, American taxpayers. You paid to develop (2+ / 0-)
    Recommended by:
    LeoQ, SingerInTheChoir

    this wonderful technology.

    The whole GPS industry should be grateful!

  •  Nice Article. (2+ / 0-)
    Recommended by:
    jim in IA, eyesoars

    In practice, the solution of one's position is not done by drawing circles and looking for intersecting points. Rather, the approach is a set of partial differential equations (one equation per satellite) used to generate a covariance matrix and solve for x,y,z and time. In this way, you can use how ever many satellites are in view, which is often more than 4.

  •  For the true technology geek in you (2+ / 0-)
    Recommended by:
    jim in IA, eyesoars

    you can monitor the locations of selected GPS satellites in real time here.

    What can be asserted without proof can be dismissed without proof. - C. Hitchens

    by sizzzzlerz on Mon Jan 02, 2012 at 12:30:15 PM PST

  •  Another thing we can thank Bill Clinton for... (2+ / 0-)
    Recommended by:
    Theoleman, jim in IA

    Is the removal of "Selective Availability", which was the semi-permanent fudging of accuracy for use by the unwashed masses.

    Before "SA" was removed, civilian access and accuracy was downgraded compared to what the military was getting.

    The government can still shut the public off almost instantly for whatever reason they deem necessary, but today's accuracy is much better than it was at first...

    "SEMPER UBI SUB UBI...."

    by Hoosierdaddio on Mon Jan 02, 2012 at 01:04:05 PM PST

  •  Absolutely right on.....but (1+ / 0-)
    Recommended by:
    jim in IA

    When I read the title GPS - How Does It Locate You? I thought it was about GPS locating you, which of course it doesn't in the sense that someone (GPS) knows where you are.

    There is rather common belief that big brother (whoever that may be) can track your location by GPS. Of course that is not true, nor is it suggested by the author. But a slightly different title might have made that more clear.

    Anyway, this is an excellent piece, well done.  Thanks.

  •  Thanks, one of the most useful posts I've seen (0+ / 0-)

    "Slip now and you'll fall the rest of your life" Derek Hersey 1957-1993

    by ban nock on Mon Jan 02, 2012 at 01:39:16 PM PST

  •  GPS and Plate Tectonics (1+ / 0-)
    Recommended by:
    jim in IA

    GPS is amazing. Geophysicists have used GPS measurements to check the motion of the Earth's plates. Turns out they get the same answer as geologists do by using the standard techniques (paleomagnetism, radiometric dating, etc.) Just one more datum to bug the creationists! : - )

  •  I can explain the need for an extra satellite (2+ / 0-)
    Recommended by:
    eyesoars, jim in IA

    When I was studying GPS, I was confused by the need for four satellites to determine X, Y and Z coordinates.  It takes three equations to solve for three unknowns, right? What I failed to take into account is that you don't know what time it is.  You don't have an atomic clock.  Here are the four equations that you have to solve.  X, Y and Z coordinates with numeric subscripts are the known values transmitted by the satellites.  The ones with u subscripts are your unknown values.


    From the book: Fundamentals of Global Positioning System Receivers A Software Approach by JAMES BAO-YEN TSUI.

    I assume that an ordinary GPS receiver for terrestrial use does not bother to calculate the Z coordinate, so you only need three satellites.

  •  thanks! (0+ / 0-)

    US universities contradict their mission statements and endorse climate denial, racism, sexism, and partisan lying by broadcasting sports on Limbaugh radio stations.

    by certainot on Tue Jan 03, 2012 at 05:41:07 AM PST

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