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

solve

 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.

Best Answer

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

Related Solutions

MATLAB: Using fsolve over a range of equations.

Solve the equations once and then plug in the values.

for z = 100:105
  x1=velprof(z,y1);
  x2=velprof(z,y2);
  x3=velprof(z,y3);
  x4=velprof(z,y4);
  c = [ (((x3*y4-x4*y3)*x2^2+(-x3^2*y4+x4^2*y3)*x2+x3*x4*y2*(-x4+x3))*x1^3+((-x3*y4+x4*y3)*x2^3+(-x4^3*y3+x3^3*y4)*x2+y2*x3*x4^3-x3^3*x4*y2)*x1^2+((x3^2*y4-x4^2*y3)*x2^3+(x4^3*y3-x3^3*y4)*x2^2+x3^2*x4^2*y2*(-x4+x3))*x1-x3*x2*x4*y1*(-x4+x3)*(x2-x4)*(x2-x3))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((-y2+y1)*x4^2+(y2-y4)*x1^2-x2^2*(y1-y4))*x3^3+((-y1+y2)*x4^3+(y4-y2)*x1^3+x2^3*(y1-y4))*x3^2+((y3-y2)*x1^2+x2^2*(y1-y3))*x4^3+((y2-y3)*x1^3-x2^3*(y1-y3))*x4^2+x1^2*x2^2*(y3-y4)*(x1-x2))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((y4-y3)*x2+(y2-y4)*x3-x4*(y2-y3))*x1^3+((y3-y4)*x2^3+(y4-y2)*x3^3+x4^3*(y2-y3))*x1+((-y1+y4)*x3+x4*(y1-y3))*x2^3+((y1-y4)*x3^3-x4^3*(y1-y3))*x2-x3*x4*(-x4+x3)*(x3+x4)*(-y2+y1))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((y3-y4)*x2+(y4-y2)*x3+x4*(y2-y3))*x1^2+((y4-y3)*x2^2+(y2-y4)*x3^2-x4^2*(y2-y3))*x1+((y1-y4)*x3-x4*(y1-y3))*x2^2+((-y1+y4)*x3^2+x4^2*(y1-y3))*x2+x3*x4*(-y2+y1)*(-x4+x3))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)) ];
  disp(z)
  disp(c)
end

MATLAB: I have more non-linear equations than unknowns. How to solve it in matlab? One method I know is non-linear least squares, how can I implement it in Matlab or you just suggest me anything you deem more proper.

Aside from FSOLVE, you can try LSQNONLIN which is another least squares solver. However, I obtain nearly the same results (x,y,z) for your problem with both FSOLVE and LSQNONLIN.

    F=@(x,y,z)[((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
    ]
    fun=@(u) F(u(1),u(2),u(3));
    x0=mean([x1 y1 z1;x2 y2 z2; x3 y3 z3; x4 y4 z4])
    [u1,fval1]=fsolve(fun,x0),
    [u2,~,fval2]=lsqnonlin(fun,x0)
>> norm(u1-u2)
ans =
     9.7868e-04

Best Answer

Related Solutions

MATLAB: Using fsolve over a range of equations.

MATLAB: I have more non-linear equations than unknowns. How to solve it in matlab? One method I know is non-linear least squares, how can I implement it in Matlab or you just suggest me anything you deem more proper.

Related Question