VINS中的加速度-位移公式
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VINS中的加速度-位移公式
\[p(t_2)=p(t_1)+\int^{t_2}_{t_1}v(\tau)d\tau\] \[v(\tau)=v(t_1)+\int^{\tau}_{t_1}a(\zeta)d\zeta\] \[\begin{aligned} p(t_2)&=p(t_1)+\int^{t_2}_{t_1}v(\tau)d\tau \\ &=p(t_1)+\int^{t_2}_{t_1}\left(v(t_1)+\int^{\tau}_{t_1}a(\zeta)d\zeta\right)d\tau \\ &=p(t_1)+v(t_1)\Delta t+\int^{t_2}_{t_1}\int^{\tau}_{t_1}a(\zeta)d\zeta d\tau \end{aligned}\]