?
Solved

please help to understand the concept behind 3d multilateration (screenshot attached)

Posted on 2009-04-12
7
Medium Priority
?
729 Views
Last Modified: 2012-08-13
please find attached the tutorial if the screenshot does not make sense

ok... this is from Matlab and shows the intersection of the hyperbolas at the point (4,8) to show the location of TX while f1, f2, f3, f4 are RX's.

This gives a location ok for x,y or x,y,0

but what about if I wish to locate a point at x,y,z.

this is done with hyperboloids intersecting?

Can someone please explain what would be required and the concept behind it?

thanks in advance.


screenshot.jpg
0
Comment
Question by:jtiernan2008
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 4
  • 2
7 Comments
 
LVL 1

Author Comment

by:jtiernan2008
ID: 24126197
tutorial attached below;
toa.pdf
0
 
LVL 27

Expert Comment

by:aburr
ID: 24127862
"this is done with hyperboloids intersecting?"
yes
The concepts are the same as in the 2D case. There is a relation between distance and time. The details are in the tutorial. I know, it takes som,e study and practice. But the tutorial is 12 pages long. One cannot expand on everything in it without typing 24 pages.
Now if you have a specific question perhaps it can be answered in fewer pages.
0
 
LVL 1

Author Comment

by:jtiernan2008
ID: 24129659
I dont see anything about it in the tutorial? I just refers to it at the start.

"The manner in which the arrival time mea-
surements locate the source can be determined
graphically from the fact that the differences inhe arrival times at a pair of stations i,j con-
strain the source to lie on a hyperboloid of rev-
olution about the baseline between the two sta-
tions."

"to lie on a hyperboloid of revolution" - what does this mean?

Do you know any reading material on this like the pdf that shows how to plot and find the intersection of these hyperboloids?
0
Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 
LVL 1

Author Comment

by:jtiernan2008
ID: 24129792
I understand the 2D version (x,y) fine as explained in the tutorial not the 3D version (x,y,z)
0
 
LVL 15

Accepted Solution

by:
yuk99 earned 2000 total points
ID: 24130391
Hyperboloid with baseline along z can be described by equation:
z^2/a^2 - x^2/b^2-y^2/c^2=1
Hyperboloid of rotation is hyperboloid with b=c. So at z>a its intersection with xy plane will be a circle.
Remember when you derived hyperbola playing with circles of different radii with the same difference? With 3D you have one more degree of freedom. So you have to do the same, but now with spheres with centers located on z axis.
Also note that rotation of hyperboloid in 3D is more complex then what you did in 2D.
0
 
LVL 1

Author Comment

by:jtiernan2008
ID: 24130403
Thanks for the great explanation... I appreciate it and understand what you are saying...
Do you know any reading material on this?
0
 
LVL 15

Expert Comment

by:yuk99
ID: 24130548
For TOA in 3D I don't know.
For mathematical concepts of hyperboloid, just google it. You will find a lot of material, including wikipedia, mathworld, etc.
Rotation in 3D and rotation matrices are also easy to find there.
Good luck!
0

Featured Post

On Demand Webinar: Networking for the Cloud Era

Did you know SD-WANs can improve network connectivity? Check out this webinar to learn how an SD-WAN simplified, one-click tool can help you migrate and manage data in the cloud.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

743 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question