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Noble Donor
location:
Minneapolis
Gender: Male
 |  | GPS & Triangulation
< on 5/28/2004 2:22 AM >
|  | | | Anyone know of a GPS unit that would allow you to enter two angles measured at two locations, and produce a new waypoint/give coordinates via triangulation?
In further detail/clarity: Say I'm along a road, and see a structure I want to get to. So I take a GPS reading at my current location, and with a seperate compass, take a bearing and enter it into the GPS unit. Then I go to another spot and do the same. The GPS unit now produces the coordinates of where the triangulation points. Basically this would be easier than bringing along a topo map of everywhere I could possibly go.
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Heartless
location:
Dakota Territory
Gender: Male
nowhere is a state of mind
| |  |  | Re: GPS & Triangulation
<Reply # 1 on 5/28/2004 3:34 AM >
| | | | Interesting question, and one I cannot answer. I'd say write down the coords and the headings and map them out later. That way you wouldn't have to actually carry the maps. Or, one "minute" is equal to one nautical mile, and one degree is equal to 60 nautical miles on the maps, so if you could actually see the place you wanted to mark and had a good guess as to the range you could just kind of adjust your current coordinates accordingly.
[last edit 5/28/2004 3:36 AM by Heartless - edited 1 times]
"I hope that I find you in heaven, because I'm so lost without you down here..."
Lost Highway Photography |
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Arrow
Noble Donor
location:
Minneapolis
Gender: Male
| | Re: GPS & Triangulation
<Reply # 2 on 5/28/2004 3:39 AM >
| | | | Perhaps if I brought my TI-82 along, I could have a program on it that would do the triangulation calculations for me. I'd have to write that of course, and just happen to have it with me when I'm driving home from the Milwaukee area after a trip to Ireland.
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Heartless
location:
Dakota Territory
Gender: Male
nowhere is a state of mind
| | | | Re: GPS & Triangulation
<Reply # 3 on 5/28/2004 3:43 AM >
| | | | Or you could just remember what direction it was from whatever nearest exit/intersection/town you happened to be at and come back to find it later, and get the coordinates as you're standing next to/in/on top of it.
"I hope that I find you in heaven, because I'm so lost without you down here..."
Lost Highway Photography |
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Mark
   
Very Noble Donor
location:
South Carolina
Gender: Male
What is a lion, king of the savannah, when hes at the south pole?
| | Re: GPS & Triangulation
<Reply # 4 on 5/28/2004 4:38 AM >
| | | | Well there are some exspesnive but nifty aircraft devices that do that. They take the radio freqancy from towers and do basicly the same thing. They run around 500-1000 bucks I believe.
"If the threat level goes up its probably because of me." "I am looking for a girl who enjoys headbutting beltbuckles" |
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MacGyver
location:
St Paul, Minnesota
Gender: Male
"Someone go find me a paperclip, a D-cell battery, and a cheese grater"
| | Re: GPS & Triangulation
<Reply # 5 on 5/28/2004 4:53 AM >
| | | | I do not know of any GPS units that have that capability natively, but like you say, it wouldn't be hard at all to write a pretty slick program to crunch the numbers for you and provide coordinates of the triangulated point. I used to be a TI programming wizard back in high school (83/83+ mainly, but some halfhearted attempts were made on my new 89 in early college)
Like a fiend with his dope / a drunkard his wine / a man will have lust for the lure of the mine
"If you are not part of the solution, you are not dissolved in the solvent." |
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scourge
location:
United States
Gender: Male
strive
| | Re: GPS & Triangulation
<Reply # 6 on 5/28/2004 5:40 AM >
| | | | Some GPSs will do half of that. I have a Garmin Etrex Vista, and you can point it at something (it has an internal compass) and then tell it to guide you in that direction. As I understand it will keep you along the line that is drawn by the sighting as you walk.
But as others say to do it the way you mention, would be very easy with a programmable calculator.
sierra hotel |
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phae-girl
location:
Ottawa Canada
| | Re: GPS & Triangulation
<Reply # 7 on 5/30/2004 2:21 PM >
| | | | Triangulation of a remote point can be done reasonably accurately using most handheld GPS units in the field using the following method:
- Establish your two known waypoints as WPT001 and WPT002.
- Project from WPT001 a secondary waypoint a distance beyond where you figure your triangulated wpt will be. For example, project WPT011 at 45 degrees bearing and 10 km distance. Do the same for WPT002.
- Create a route going from WPT001 to WPT011 to WPT022 to WPT002.
- Where the routes intersect will be your new triangulated waypoint. Use the map screen to navigate to the intersection. Keep increasing your zoom level as you approach. Some units may allow you to GOTO a cursor position, which is a little simpler.
Depending on your particular unit, you *may* be able to trick the coordinates out of the map. I'm pretty sure my Meridian will, and I'm pretty sure my GPS 12 won't.
-d
edit: I just took the Meridian outside and tried this. You can pull coordinates off the map screen by marking the cursor position. I would imagine the mapping Garmin units will do this as well.
[last edit 5/30/2004 2:33 PM by phae-girl - edited 1 times]
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Arrow
Noble Donor
location:
Minneapolis
Gender: Male
| | Re: GPS & Triangulation
<Reply # 8 on 5/30/2004 3:17 PM >
| | | | Awesome, very good to know. Thanks.
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sidvicious
location:
Cowedge, Kansas
Gender: Male
We subsist to learn, because through learning, we grow.
| | Re: GPS & Triangulation
<Reply # 9 on 5/30/2004 11:39 PM >
|  | | | correct me if i'm wrong, but doesn't triangulation need THREE points to computate?
same reason why a GPS receiver needs the signals from at least three satellites to be able to calculate your position.
Commiting crimes with no remorse
As good as gold now an evil force |
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phae-girl
location:
Ottawa Canada
| | Re: GPS & Triangulation
<Reply # 10 on 5/31/2004 3:04 AM >
| | | | Triangulation is traditionally a graphical method of determining position using bearing lines to two or more points of known position.
GPSrs work on the principle of intersection of spheres. When two spheres intersect the solution curve is that of a circle http://mathworld.wolfram.com/Sphere-SphereIntersection.html">http://mathworld.wolfram.com/Sphere-SphereIntersection.html. If you add a third sphere to the model, this sphere will give zero, one, or two solutions points.
In the trivial case of zero solution points, the third sphere will encompass one of the other spheres entirely and not intersect the first intersection circle, or similarly will have a radius too small to reach the intersection circle.
In the case of one intersection, the third sphere will have a radius such that it is exactly tangent to the first intersection circle at some point. This case occurs at the radii Rmin and Rmax which establish the boundary values of the trivial case.
For two intersections to occur, the radius of the third sphere must be Rmin < R < Rmax. This is the case used by GPSrs to determine position. Because the spheres are so large, one point of intersection occurs in space. This solution is discarded even though it is valid, it is not very useful for terrestrial navigation.
For both techniques, adding more points of known position gives an overdetermined system of equations that does nothing to enhance the solution in exact mathematics. From a practial standpoint however, especially using graphical methods, adding more points and bearing lines gives an average position and an estimate of positional error.
-d
edit: spelling
[last edit 5/31/2004 3:06 AM by phae-girl - edited 1 times]
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sidvicious
location:
Cowedge, Kansas
Gender: Male
We subsist to learn, because through learning, we grow.
| | Re: GPS & Triangulation
<Reply # 11 on 5/31/2004 5:17 AM >
| | | | Posted by digging-it
<snip>...some technical stuff that's way over my head
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ooook. i'll take you're word on that. thanks for the info.
so, what you're saying is, two lines of intersect is just as good as three?
Commiting crimes with no remorse
As good as gold now an evil force |
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scourge
location:
United States
Gender: Male
strive
| | Re: GPS & Triangulation
<Reply # 12 on 5/31/2004 6:42 AM >
| | | | Posted by sidvicious
ooook. i'll take you're word on that. thanks for the info.
so, what you're saying is, two lines of intersect is just as good as three?
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Well, if you got three, or four, or fifty, you can make a better average. But on a flat 2-d map, two are enough in theory, assuming good precision. Think about it this way: you're trying to figure out your position, based on the positions of 2 landmarks you can see and can find on the map. If you can use a compass to measure the azimuth angle to each point, from your location, you have enough information to generate the equations of two lines in 2-d space. As you know on a flat surface (euclidean geometry) two lines can intersect in at most one place. This place is your position.
In addition, GPS trangulation is different from terrestrial triangulation. In terrestrial triangulation, you figure out where you are based on angles from known reference points. Each measurement you take gives you a line on the map. You might be at any point on this line. Get at least 2 lines and where they intersect is where you are. The GPS figures it out based on distances from known reference points. Given a distance, there is an imaginary sphere and you might be anywhere on it. You need 3 sphere intersections to get a position and a fourth to get an altitude.
If you were to try the latter method on the earth (triangulating based on distances from known reference points) you would find that you need 3 points. Around each point you'd draw a circle, its radius being that known distance. You are located somewhere on this circle. If only 2 are drawn there are at most 2 solutions, where the circles intersect. You are at one of these two points. You need a third circle to narrow it down to one of those points. This is how one of the old school aircraft navigation systems works (VOR I believe but could be mistaken).
These 2 different methods of triangulation lead to the widespread misconception that you need 3 reference points to triangulate a position. This is true only if you are triangulating based on distance from known points. If you are doing it based on angles, you need only 2 points.
sierra hotel |
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phae-girl
location:
Ottawa Canada
| | Re: GPS & Triangulation
<Reply # 13 on 5/31/2004 1:17 PM >
| | | |
If only 2 are drawn there are at most 2 solutions, where the circles intersect. You are at one of these two points. You need a third circle to narrow it down to one of those points. This is how one of the old school aircraft navigation systems works (VOR I believe but could be mistaken).
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I was thinking about VOR and LORAN when I was posting the bit about spheres intersecting. It seems entirely reasonable that it would use the 3 circle intersection technique. Unfortunately, I can't remember either if this is the case or not.
[wild guess theory]
One thing I didn't consider was the effect of assuming the earth to be a sphere itself. Since the GPS birds are at a known altitude, the equation of the intersecting circle would be known and you could theoretically pick your position using only two birds. If you were to assume the shape of the earth as a geoid (a squashed sphere), I'm guessing that the intersection would take the shape of an ellipse. Again, knowing the equation of the ellipse would only require a second bird for solution to a point.
[/wild guess theory]
WRT triangulating on the surface of the earth, it's a function of distance when straight line methods stop working. As soon as the assumtion that you are no longer on a flat plane is invalid, you have to resort to circular techniques.
Anyone good with celestial navigation?
-d
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sidvicious
location:
Cowedge, Kansas
Gender: Male
We subsist to learn, because through learning, we grow.
| | Re: GPS & Triangulation
<Reply # 14 on 5/31/2004 6:26 PM >
| | | | Posted by scourge
If you were to try the latter method on the earth (triangulating based on distances from known reference points) you would find that you need 3 points. Around each point you'd draw a circle, its radius being that known distance. You are located somewhere on this circle. If only 2 are drawn there are at most 2 solutions, where the circles intersect. You are at one of these two points. You need a third circle to narrow it down to one of those points.
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ahh, okay. i understand now; makes perfect sense. thanks for the clarification.
now don't go confusing me again... ;)
Commiting crimes with no remorse
As good as gold now an evil force |
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Heartless
location:
Dakota Territory
Gender: Male
nowhere is a state of mind
| | | | Re: GPS & Triangulation
<Reply # 15 on 5/31/2004 6:40 PM >
| | | | Posted by Mark
Well there are some exspesnive but nifty aircraft devices that do that. They take the radio freqancy from towers and do basicly the same thing. They run around 500-1000 bucks I believe.
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Try upwards to $25,000 for a nice dual Garmin system. 
Wow, there's some really interesting info being thrown around this thread. But VOR and LORAN don't need three "circles" to pinpoint a location. How it works is that the reciever in the aircraft picks up the signal from the VOR transmitter on the ground, which tells you the pilot what direction you are from the station in terms of magnetic north - magnetic north and true north are different because of earth's tilt, so one must excersize caution when plotting courses on charts. But the "grids" on av and topo maps account for the curvature of the earth, and point up to true north (the top of the globe, not mag north). Once you account for the difference in heading between mag and tru north, you can establish yoursefl a simple compass heading.
If you have one VOR telling you that you are centered on radial "a" going away from the station, and a second VOR telling you that you are centered on radial "b" going TO the station, you can just draw a line going out from the two VOR's on the chart on the radials you are centered on, and where they intersect is roughly your position.
Some stations are VOR-DME, which stands for distance measuring equipment. These will not only give you the radial to or from the station, but they will also provide the pilot with his slant range distance from the station as well. With this, a pilot can fairly accurately determine his or her position using only one station instead of two or more.
I wouldn't exactly call VOR and LORAN "old-school," as it's still used heavily by commercial, military, and private flight operations around the world. GPS at this point can't do everything a radio navigation system can. If you want to talk about straight up OLD school radio nav systems, try NDB's. They're the same as flying by AM radio; in fact one can actually use most AM radio stations across the country to get around just the same as one can use an NDB station. It can also be used to listen to some oldies when flights between St. Paul and International Falls become long...
VOR "triangulation" is actually very precise, though obviously not as much so as a nice GPS system. For all practical purposes though, it's enough. Then a pilot can always buzz a town and read the water tower (I've had to do this  ), look for terrain features depicted on the charts, and follow major highways.
But like I was saying before, if you see a place and have a GPS unit that does not do triangulations, but can roughly determine its distance from you, you can simply adjust your coordinates accordingly. For example, let's say I'm at N 46;10 W 97;05. One "minute" (D;M;S) on any chart is equal to one nautical mile (1.151 statute, or US miles or 1,852 meters), so if you see a location you wish to visit later off to the West of your location at a distance of roughly one mile, then the rough coordinates for the new location would be N 46;10 W 97:06. One "degree" is equal to 60 nautical miles, and so on.
With this you can plot the rough coordinates on a chart later, then work it in between any terrain features you may remember to better plot it, and record the new coordinates. Then, once you visit the place, you can see how right you were, I guess.
"I hope that I find you in heaven, because I'm so lost without you down here..."
Lost Highway Photography |
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scourge
location:
United States
Gender: Male
strive
| | Re: GPS & Triangulation
<Reply # 16 on 6/1/2004 6:07 AM >
| | | | Posted by digging-it
[wild guess theory]
One thing I didn't consider was the effect of assuming the earth to be a sphere itself. Since the GPS birds are at a known altitude, the equation of the intersecting circle would be known and you could theoretically pick your position using only two birds. If you were to assume the shape of the earth as a geoid (a squashed sphere), I'm guessing that the intersection would take the shape of an ellipse. Again, knowing the equation of the ellipse would only require a second bird for solution to a point.
[/wild guess theory]
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Yes, you sort-of can do that, because you have a third geoid, the earth itself, which can be included in the equations, if you assume that your position is somewhere on this geoid. I believe that is how my GPS manages to keep a lock even when it loses all but 2 satellites. Especially if it already had my position before the signal was lost. However you can only approximate position data this way, and cannot get elevation data at all, as you have to make an assumption on the shape of the earth.
[Edit] Just thought about it: yes, this works but only if the GPS already knew where I was. With two satellites, the solution circle intersects the earth geoid at two points. If that is all you have the GPS does not know which one to pick. But if it had 3 satellites for a moment, briefly, it can narrow it down to one. Since it's unlikely you'll move to the other hemisphere of the earth in a single instant, the GPS can discard the other solution now even if it loses one of the satellites, and navigate with just 2. But precision suffers greatly, because of the assumption I mentioned above.[/Edit]
As for me messing up the way VOR works - looks like it is an angle-based nagivation system so you only need two. But if you were to use a method that measures distances, you need one more reference. Anyway I'm a glider pilot so everything I do is VFR, thus I got an excuse . But regardless, looks like we got a good insightful discussion going here.
As for celestial nav. I know orbit mechanics and basic astrodynamics real well, but only in a general sense - i.e. I can figure out how to get a spacecraft from shuttle orbit to geosynch, or to the moon or mars or escape the solar system, but I can't design a means for the spacecraft to figure out exactly where it is. That's a class I'll be taking next semester.
Fun stuff huh?
[last edit 6/1/2004 6:12 AM by scourge - edited 1 times]
sierra hotel |
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phae-girl
location:
Ottawa Canada
| | Re: GPS & Triangulation
<Reply # 17 on 6/1/2004 1:29 PM >
| | | | It's fun in a really geeky kind of way. I suspect this is how the l33t haX0rs discuss code, but with much better spelling.
I was also wrong about VOR. I really should have remembered that. As for Celestial Nav, we were supposed to learn it in survey school but ran out of time. I have a couple of friends who are ex-navy types that know how to work a sextant, so maybe I'll hook up with them and learn it [rant](Learning something for the sake of learning? Independently? What will the education system think?)[/rant]
Perhaps cartography is a sub-genre of UE that needs to be more fully developed.
-d
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MaximusNT
Gender: Male
| | Re: GPS & Triangulation
<Reply # 18 on 6/2/2004 3:30 PM >
| | | | Just to correct this, a GPSR needs 4 satellites to get a proper fix. 3 satellites gets you an unreliable 2D fix, and 4 gets you a proper 3D fix. Remember that to get Lat and Long properly you need to know your elevation. However even with four satellites, you're not getting much accuracy.
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