【原创】VIO/VISLAM中的BA问题详解2
（转载请注明出处）
这一篇打算分析一下一般情况下，针对多源传感器融合的的非线性最小二乘优化，其增量方程的结构。
假设描述利用M个传感器信息进行融合的优化问题如下：$$
\tag{1} \label{1}
\begin{array}{l}
\min \mathop {\arg }\limits_{\bf{x}} \left( {\left| {{{\bf{f}}1}\left( {\bf{x}} \right)} \right|{{{\pmb{\Omega }}_1}}^2 + \left| {{{\bf{f}}2}\left( {\bf{x}} \right)} \right|{{{\pmb{\Omega }}2}}^2 + \cdots \left| {{{\bf{f}}M}\left( {\bf{x}} \right)} \right|{{{\pmb{\Omega }}M}}^2} \right)\
= \min \mathop {\arg }\limits{\bf{x}} \sum\limits^M {\left| {{{\bf{f}}k}\left( {\bf{x}} \right)} \right|{{{\pmb{\Omega }}_k}}^2}
\end{array}
\tag{2} \label{2}
{\pmb{\Omega }} = \left[ {\begin{array}{*{20}{c}}
{{{\pmb{\Omega }}_1}}&{}&{}\
{}& \ddots &{}\
{}&{}&{{{\pmb{\Omega }}_M}}
\end{array}} \right]
\tag{3} \label{3}
\min \mathop {\arg }\limits_{\bf{x}} \left| {{\bf{f}}\left( {\bf{x}} \right)} \right|_{\pmb{\Omega }}^2
\tag{4} \label{4}
{\bf{f}}\left( {\bf{x}} \right) = {\left[ {\begin{array}{*{20}{c}}
{{\bf{f}}_1^T\left( {\bf{x}} \right)}& \cdots &{{\bf{f}}_1^T\left( {\bf{x}} \right)}
\end{array}} \right]^T}
\tag{5} \label{5}
{\bf{H}} = \left[ {\begin{array}{*{20}{c}}
{{{\bf{H}}{11}}}& \cdots &{{{\bf{H}}{1l}}}& \cdots &{{{\bf{H}}{1L}}}\
\vdots & \ddots &{}&{}& \vdots \
{{\bf{H}}^T}&{}&{{{\bf{H}}{ll}}}&{}&{{{\bf{H}}{lL}}}\
\vdots &{}&{}& \ddots & \vdots \
{{\bf{H}}{1L}^T}& \cdots &{{\bf{H}}^T}& \cdots &{{{\bf{H}}_{LL}}}
\end{array}} \right]
