# Calculating position from observation of landmarks or beacons

I am attempting to educate myself about the process of navigating by the observation of landmarks or beacons. This is not new technology,
since seamen have used this method for centuries. But, for some reason I have been unable to find a good web site to teach me the method. Perhaps I am using the wrong search terms.
The papers I am finding are generally over my head mathmatically, though I have good algebra and some trig. Perhaps someone can recommend a site which will start the explanation at a lower level, or even explain some of it here on the newsgroup.
I can visually picture how observation (from the robot's camera) of the angle between two landmarks will restrict the possible position of the robot to an arc. Then, adding a 3rd landmark will allow another arc to be drawn, and the intersection of the two arcs is the position of the robot.
But, mathmatically, how are these arcs calculated?
Joe Dunfee
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Search for triangulation and radio direction finder.
It is my understanding that nautical triangulation is done by having two sights on the ship a know distance appart. You point each site at a common object and measure the angles of each site to the beam of the ship. You now have the length of one side of a triangle, and the angles between two sides. Using trigonometry you can calculate everything else.
Radio direction finders are more like you example. You have two known landmarks at a known distance, and you measure the angle to each form one 'sensor'.
TC
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On 4 Feb 2005 22:05:05 -0800, snipped-for-privacy@yahoo.com wrote:

Check out the articles here:
Specifically, "A Circular Navigation System" by Jim Ubersetzig. The issues are:
Sept 1999 Oct 1999 Nov 1999
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TD, the navigation system I am concerned about does not require two observers. Rather, it is done measuring the angle between two targets with known positions.
Ed, thank you for the link to the articles. They filled in my missing knowledge exactly.
Joe Dunfee
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Jim U. is a smart cookie. He used to be in my club here in Thousand Oaks as well. Trust whatever he puts out as accurate.
Mike

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Apparently the word "Jim Ubersetzig" was the search term I should have been using all along! I was so impressed by his article, that decided to search on his name and find what else he's been up to.
Here is another article he wrote, which makes more effort to describe the math and geometry involved in the process.
http://www.seattlerobotics.org/encoder/200109/lasernav.htm
Joe Dunfee
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It is all trig. Lots of trig.
Get a book like (no offense) Trig for dummies. Worth every penny. Once you ubderstand how to use the trig, the navigation will fall into place...
Mike

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