In the following article, section 3.1 authors use SVD to solve overdetermined system of linear equations:
http://www.matematik.lu.se/matematiklth/personal/solem/publications/Solem-Heyden-ICPR2004.pdf
The idea behind using SVD is clear, but the confusing part is that the system has been made homogeneous by embedding right hand side vector into the system matrix $M$. This means that the unknown vector $v$ has a known constant as an element.
$$ \underbrace{ \begin{bmatrix} -1 & {} & {} & \mathbf{p}_{1x} & \mathbf{L}_{1x} & {} & \cdots \\ {} & -1 & {} & \mathbf{p}_{1y} & \mathbf{L}_{1y} & {} & \cdots \\ {} & {} & -1 & \mathbf{p}_{1z} & \mathbf{L}_{1z} & {} & \cdots \\ -1 & {} & {} & \mathbf{p}_{2x} & {} & \mathbf{L}_{2x} & \cdots \\ {} & -1 & {} & \mathbf{p}_{2y} & {} & \mathbf{L}_{2y} & \cdots \\ {} & {} & -1 & \mathbf{p}_{2z} & {} & \mathbf{L}_{2z} & \cdots \\ \vdots & \vdots & \vdots & \vdots & {} & {} & \ddots \end{bmatrix} }_{M} \underbrace{ \begin{bmatrix} \mathbf{X}^l_x \\ \mathbf{X}^l_y \\ \mathbf{X}^l_z \\ 1 \\ \mu_1 \\ \mu_2 \\ \vdots \end{bmatrix} }_{\mathbf{v}} = 0 $$
How does it make sense to do SVD of such Matrix?