Well, I think your problem is slightly different from mine. Mine is the resection problem, where you calculate your position based on the angles you measure from your unknown location to known points.
I think your problem might be more accurately described as the triangulation problem, where...
I believe a book called 'Algebraic Geodesy and Geoinformatics' describes a few analytic approaches. However I have to say I don't think there are any benefits in going with an analytic approach. The iterative approach I used can be accurate to like 10 decimal places and it takes less than a...
I'm glad to help. For the insane amount of time I spent on this, it's nice to at least get some use of it it. That sounds like a cool project.
I did encounter a method that wasn't quite suited for my application, but sounds like it could be exactly what you need. It's called the POSIT...
Sort of. It is helpful to know that the problem is called the 'three dimensional resection problem.' You'll find much more information with that term.
I've read that analytical solutions do exist, but they take just as long or longer than iterative techniques. Applying the Newton-Raphson...
I was just looking at the spindle torus and I agree, that appears right. It would be preferable if I could have the math only describe the outer shell, but maybe that's not practical.
Good point about the other shape not being an ellipsoid. I don't think I would have noticed that. I guess...
A 180 degree circular arc (i.e. a half sphere) is obvious:
When you rotate this about its two end points, you get a sphere.
What about for something less than 180 degrees (e.g. 90)?:
I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to...
vrmuth, the position needs to be calculated in reference to the position of anyone of the beacons, each of which will have a 3D coordinate in reference to a global coordinate system. See the link below for a diagram.
chiro, thanks for the welcome. I actually found that while 3 beacons is...
There is indeed a practical end to this; I'm working on some triangulation-based positioning. This will be a calculation that is constantly repeated on a microcontroller, perhaps every second, so an analytic solution would have been nice, but it is not required.
Haruspex, I do appreciate...
I actually was using the sine rule instead of the cosine rule, but the cosine rule seems like it might be a more direct way to go about this. I can get an equation with a single unknown pretty easily, however it seems very difficult to actually write this equation in terms of the unknown, as...
Here's a picture of an irregular tetrahedron, for reference:
The base triangle (ABC) is completely known (lengths AB, AC, BC, and the angles between them are all known). The 3 angles at vertex P are also known (APB, APC, and BPC).
I believe that is enough information to completely solve the...
I'm trying to work out the mathematics of this for a school project.
Say you have 4 beacons arranged in a square (I think you only need 3, actually) at known positions relative to one another. Now say you are in a random position within this square, at a random height, and at a random...
I encountered that website myself while trying to find suitable GPS units. It appears that it's a bit old and the models are no longer available, but there might be similar, next generation, versions of some of them.
I'm working on a robotics project that I believe could greatly benefit from the use of differential GPS. The robot will be navigating within a known 100m by 100m area and will need to have a positional accuracy of about 25cm. These two things lead me to believe that DGPS is a good fit.
I...