标签：mathbf 积分 boldsymbol IMU bmatrix end VINS omega dt
连续时间IMU积分
\[\begin{aligned}
&\mathbf{p}_{b_{k+1}}^w=\mathbf{p}_{b_k}^w+\mathbf{v}_{b_k}^w\Delta t_k+\iint_{t\in[t_k,t_{k+1}]}\left(\mathbf{R}_t^w(\hat{\mathbf{a}}_t-\mathbf{b}_{a_t}-\mathbf{n}_a)-\mathbf{g}^w\right)dt^2\ \\
&\mathbf{v}_{b_{k+1}}^w=\mathbf{v}_{b_k}^w+\int_{t\in[t_k,t_{k+1}]}(\mathbf{R}_t^w(\hat{\mathbf{a}}_t-\mathbf{b}_{a_t}-\mathbf{n}_a)-\mathbf{g}^w)dt\\
&\mathbf{q}_{b_{k+1}}^w=\mathbf{q}_{b_k}^w\otimes\int_{t\in[t_k,t_{k+1}]}\frac{1}{2}\boldsymbol{\Omega}(\hat{\boldsymbol{\omega}}_t-\mathbf{b}_{w_t}-\mathbf{n}_w)\mathbf{q}_t^{b_k}dt\\
&其中\\
&\boldsymbol{\Omega}(\boldsymbol{\omega})=\begin{bmatrix}-\lfloor\boldsymbol{\omega}\rfloor_\times&\boldsymbol{\omega}\\-\boldsymbol{\omega}^T&0\end{bmatrix},
\lfloor\boldsymbol{\omega}\rfloor_\times=\begin{bmatrix}0&-\omega_z&\omega_y\\\omega_z&0&-\omega_x\\-\omega_y&\omega_x&0\end{bmatrix}
\end{aligned}
\]
标签：mathbf,
积分,
boldsymbol,
IMU,
bmatrix,
end,
VINS,
omega,
dt
From： https://www.cnblogs.com/narjaja/p/18185716