I have 4 equations and 3 unknowns for trilateration problem. I wanna solve these 3 unknowns from these equation accurately.

 x1=475060; y1=1096300; z1=4670;
 x2=481500; y2=1094900;z2=4694;
 x3=482230;y3=1088430; z3=4831;
 x4=478050; y4= 1087810; z4=4775      
 %coordinates

% ((x-x1)^2)+((y-y1)^2)+((z-z1)^2)=5942.607^2

% ((x-x2)^2)+((y-y2)^2)+((z-z2)^2)=2426.635^2

% ((x-x3)^2)+((y-y3)^2)+((z-z3)^2)=5094.254^2

% ((x-x4)^2)+((y-y4)^2)+((z-z4)^2)=5549.874^2

%these are equations.

Answer 1

[Matt J]

You can try FSOLVE. However, it seems unlikely for there to be a 4-way intersection between 4 spheres.

[Nuno]

How?

[Matt J]

The answer to "how" to use a command is always going to be "go look at the documentation",

http://www.mathworks.com/help/optim/ug/fsolve.html

Answer 2

[Roger Stafford]

Like Matt J, I suspect you ask too much of your four spheres. In general three spheres will intersect in just two discrete points if they intersect at all. There is an explicit solution for such a problem which has appeared in "Answers" and "Newgroup" a number of times in the past. However, what do you think the chances are of your fourth sphere passing through either of these two particular points?