reverse 3D euclidean distance

4 次查看(过去 30 天)
Hi there,
I am standing at an unknown point U(x,y,z) in the room. I can measure 3 (euclidean) distances D to 3 known points P in the room. I try to find the point, where I am at. My equation system looks like this:
(x-3)²+(y-1)²+(z-4)²=D1²=81
(x-12)²+(y-1)²+(z-4)²=D2²=36
(x-34)²+(y-2)²+(z-4)²=D3²=601
I can put the known points into a matrix P, the measured distance in a vector D:
P=[3 1 4;12 1 4; 34 2 4]
P =
3 1 4
12 1 4
34 2 4
D=[81 36 601]
Do you know how I can find U(x,y,z) ?
I am not sure if I can use
D = pdist(X,'euclidean');

采纳的回答

Star Strider
Star Strider 2019-7-25
Try this:
P=[3 1 4;12 1 4; 34 2 4];
D=[81 36 601];
fcn = @(b,x) (b(1)-x(:,1)).^2 + (b(2)-x(:,2)).^2 + (b(3)-x(:,3)).^2;
B = fminsearch(@(b) norm(D(:) - fcn(b,P)), [1; 1; 1])
producing:
B =
10.0000
5.0000
-0.0000
that are the (x,y,z) coordinates, as best fminsearch can calculate them.
  2 个评论
Ferdinand Grosse-Dunker
Works perfekt, thank you. Can you comment on the function you use?
Star Strider
Star Strider 2019-7-25
As always, my pleasure.
The documentation for the fminsearch function is at the link. It is an unconstrained optimiser that uses a derivative-free method to find the minimum.
The code I use for my objective function ‘fcn’ and as an argument to fminsearch are Anonymous Functions. They are quite useful for coding short functions, although they have their limitations.
I use the norm function so that the fminsearch function finds the minimum value that satisfies the sum-of-squares criterion (since this is essentially a curve-fiting problem).

请先登录,再进行评论。

更多回答(1 个)

Akira Agata
Akira Agata 2019-7-25
There should be 2 answers.
Here is my try.
P = [3 1 4;12 1 4; 34 2 4];
D = [81 36 601];
func = @(x) (vecnorm(x - P(1,:))-sqrt(D(1)))^2+...
(vecnorm(x - P(2,:))-sqrt(D(2)))^2+...
(vecnorm(x - P(3,:))-sqrt(D(3)))^2;
x1 = fminsearch(func,[1 1 1]);
x2 = fminsearch(func,[10 10 10]);
>> x0
x0 =
10.0000 5.0000 -0.0000
>> x1
x1 =
10.0000 5.0000 8.0000

类别

Help CenterFile Exchange 中查找有关 Mathematics 的更多信息

产品


版本

R2018b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by