Calibration graph

Main Graph Formulation

This page will explain the main cost functions for the calibration.

The MVIS factor graph jointly optimises camera intrinsics, IMU intrinsics, all extrinsics, time offsets, and rolling-shutter readout times in a single maximum-a-posteriori estimate. Schematically:

$$\arg\min_{\boldsymbol{x}} \; \sum_{i,k} \rho\!\left(\| \mathbf{r}_{\text{cam}}^{i,k} \|_{\Sigma_c}^2\right) + \sum_{j,k} \rho\!\left(\| \mathbf{r}_{\text{imu}}^{j,k} \|_{\Sigma_i}^2\right) + \sum_{j,k} \rho\!\left(\| \mathbf{r}_{\text{imu-imu}}^{j,k} \|_{\Sigma_{ij}}^2\right) + \Pi(\boldsymbol{x}, \boldsymbol{\mu}_0)$$

where $\boldsymbol{x}$ is the full calibration state vector, $\rho(\cdot)$ is a robust loss (Huber), and $\Pi$ encodes Gaussian priors on each calibration parameter.

Detailed derivations of each residual block are documented in:

• Base IMU Calib
• Aux IMU Calib
• Camera Calib
• Observability
• Degeneracy