Understanding FAST-LIO: Supplementary Derivations and Explanations
In this document, we provide detailed derivations complementing those presented in [2]. Details of the Derivation Discrete Model Based on the $\boxplus$ operation defined above, we can discretize the continuous model in (1) at the IMU sampling period $\Delta t$ using a zero-order holder. The resultant discrete model is $$ \mathbf{x}_{i+1} = \mathbf{x}_i \boxplus (\Delta t f(\mathbf{x}_i, \mathbf{u}_i, \mathbf{w}_i))$$where $i$ is the index of IMU measurements, and the function $f$, state $\mathbf{x}$, input $\mathbf{u}$, and noise $\mathbf{w}$ are defined below: ...