Solving 3 unkowns with 3 knowns

I have three equations in the following form:

c*TDOA(1) = sqrt((x(1)-xe)^2 + (y(1)-ye)^2 + (z(1)-ze)^2) + sqrt((x(2)-xe)^2 + (y(2)-ye)^2 + (z(2)-ze)^2)

c*TDOA(2) = sqrt((x(1)-xe)^2 + (y(1)-ye)^2 + (z(1)-ze)^2) + sqrt((x(3)-xe)^2 + (y(3)-ye)^2 + (z(3)-ze)^2)

c*TDOA(3) = sqrt((x(1)-xe)^2 + (y(1)-ye)^2 + (z(1)-ze)^2) + sqrt((x(4)-xe)^2 + (y(4)-ye)^2 + (z(4)-ze)^2)

Everything is known EXCEPT xe,ye, and ze.

I don't know how to easily isolate them into an Ax=b form.

Thanks,

K

Answer 1

[Honglei Chen]

What you have are not linear equations so they cannot be solved in Ax=b form. You need to use a solver for nonlinear equations. The following page should be helpful

http://www.mathworks.com/support/solutions/en/data/1-15NRJ/index.html?product=OP&solution=1-15NRJ