Camera Filtering

Camera Error Models

The error model used for a FeatureTracker is

\begin{align} \begin{bmatrix} \pose{f_x}{C} \\ \pose{f_y}{C} \\ \pose{f_z}{C} \end{bmatrix} = R(\quat{L}{C})(p^L_F - p^L_C) \end{align}

\begin{align} \begin{bmatrix} x_n \\ y_n \end{bmatrix} = \begin{bmatrix} \pose{f_x}{C} / \pose{f_z}{C} \\ \pose{f_y}{C} / \pose{f_z}{C} \end{bmatrix} \end{align}

\begin{align} \begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} f_x\left[x_n \left(1 + k_1 r^2 +k_2 r^4\right) + 2p_1 x_n y_n + p_2 \left(4^2 + 2 x_n^2\right) \right] + c_x \\ f_y\left[y_n \left(1 + k_1 r^2 +k_2 r^4\right) + p_1 \left(4^2 + 2 y_n^2\right) + 2 p_2 x_n y_n \right] + c_y \end{bmatrix} + \begin{bmatrix} n_u \\ n_v \end{bmatrix} \end{align}

where

\begin{align} r^2 = x_n^2 + y_n^2 \end{align}

and \(n_u\) and \(n_v\) are Gaussian white noise processes

@inproceedings{2022_Multi_Cal,
  title     = {Online Multi Camera-IMU Calibration},
  booktitle = {2022 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR)},
  author    = {Jacob Hartzer and Srikanth Saripalli},
  year      = {2022},
  pages     = {360-365},
  doi       = {10.1109/SSRR56537.2022.10018692},
  preview   = {multi_cam_imu/setup_thumb.png},
  arxiv     = {2209.13821},
}