Triangulation scalene known angles and two positions

[414184]

Hello i am trying to make a localization system. Therefore i would try Triangulation to calculate the position of my unknown node.
For example see image:



I would like to calculate the x, y coordinate of the system knowing the angles of node A and B to the system and the x, y locations of node A and B.
Actually i though there were a lot of default formula's for this case, like there is for trilateration.

Do you guys have any clue how i can solve this ? Or is it even possible because i can barely find anything about it..

 

[Dr.Peterson]

It looks as if you don't know the relation of your angle [MATH]\alpha=0[/MATH] to the coordinate axes. If that's true, then in effect you only know the angle between the two fixed nodes at the "system", and there is insufficient information. (The unknown point could lie anywhere on a circular arc.)

But if you do know what direction [MATH]\alpha=0[/MATH] means, then you can just construct the lines from the two nodes to the system and find their intersection.

I don't know what you mean by "a lot of default formulas". But certainly triangulation is a well-known concept.

 

[414184]

It looks as if you don't know the relation of your angle [MATH]\alpha=0[/MATH] to the coordinate axes. If that's true, then in effect you only know the angle between the two fixed nodes at the "system", and there is insufficient information. (The unknown point could lie anywhere on a circular arc.)

But if you do know what direction [MATH]\alpha=0[/MATH] means, then you can just construct the lines from the two nodes to the system and find their intersection.

I don't know what you mean by "a lot of default formulas". But certainly triangulation is a well-known concept.

My system knows hes direction ([MATH]\alpha=0[/MATH]). It turns around to see which direction the signal is the most strong and saves it as the angle. It also know the x, y axis from node A and B. So i think it should be able to calculated its intersection. But i have no clue how.. Some links or help would be very appreciated.

 

[Dr.Peterson]

So you're saying it can figure out that \alpha=0 corresponds to 45 degrees below the positive x-axis, in my example? Or are you just saying how it finds relative angles? If it finds absolute angles (relative to the fixed axes, rather than to its own unknown orientation), then you could triangulate, and wouldn't need the distances.

Did you do the search I suggested? That should surely give you a clue!

 

[414184]

So you're saying it can figure out that \alpha=0 corresponds to 45 degrees below the positive x-axis, in my example? Or are you just saying how it finds relative angles? If it finds absolute angles (relative to the fixed axes, rather than to its own unknown orientation), then you could triangulate, and wouldn't need the distances.

Did you do the search I suggested? That should surely give you a clue!

I know i wont need the distances, thats the im trying to achieve: Determining the position of the system based on angles instead of distance.

My system knows which direction is 0 degrees. It will turn around and measure at each degrees the signal strength. After turning 360 degrees it knows which direction the signal strength was the strongest so thats defined as the angle of arrival from the node to my system. My system can also communicate with the nodes and request the x, y axis of the node. So at that point i know the angle of arrival and the coordinates of the nodes.

Now it all comes to math, I need the formula to give the angles and fixed x, y coordinates as parameter so it gives me the x, y coordinate of my system. I have searched all over the internet, but cant find a basic formula for this case.

 

[Dr.Peterson]

I was confusing you with another recent thread about trilateration in a game. Sorry about that.

But can you tell me why alpha isn't measured from the direction of an axis? (By the way, you seem to be confusing the terms "axis" and "coordinate", so be careful.)

If you do know absolute angles, then you can construct lines from nodes A and B at those angles, and find their intersection. That is, find equations for those two lines and solve.