RIGHT MSCKF

This implements the Right MSCKF called so cause it is the right way to implement it with proper Hamiltonian Quaternions. Also a nice play on words as Hamiltonian Quaternions are also in the right handed coordinate system hence the name.

Main purpose is to serve as a reference for people that want to implement a MSCKF with Hamiltonian style quaternions, and not have to resort to using JPL style.

Most of the derivations are taken from [2] a fantastic resource for ESKF derivation with hamiltonian style quaternions.

Rant

The original MSCKF was first published in [1]. It is a fantastic piece of work, the only downside being that Stergios and his collaborators(Mostly University of Minnesota students/alumni) use JPL style quaternions, in contrast to much of the robotics, math, and physics literature. Sadly everyone that decides to implement a MSCKF directly pulls their equations from the original source, or one of its derivatives written by someone associated with Stergios. This has resulted in a large number of JPL style quaternions, which I am not a fan of. I very much dislike this existence of two styles/coordinate systems. I believe it brings confusion, and harms collaboration efforts, especially when there isn't really a benefit. For more about the existence of these two styles and their history I recommend [4].

Other comments

• Note that there is some evidence in [3] that the JPL style aka Global error performs better.

TODO

• [ ] Finish all parts of MSCKF
• [ ] Create pdf with derivations
• [ ] Create Visual Inertial Simulator

References

1)
@article{Mourikis2007a,
  author = {Mourikis, Anastasios I. and Roumeliotis, Stergios I.},
  title = {{A multi-state constraint Kalman filter for vision-aided inertial navigation}},
  year = {2007}
  }

2)
@techreport{JoanSola2012,
author = {{Joan Sol{\'{a}}}},
title = {{Quaternion Kinematics for Error-State KF}},
year = {2012}
}

3)
@article{Li2012,
author = {Li, Mingyang and Mourikis, Anastasios I.},
title = {{Improving the accuracy of EKF-based visual-inertial odometry}},
year = {2012}
}

4)
@article{Sommer2018,
author = {Sommer, Hannes and Gilitschenski, Igor and Bloesch, Michael and Weiss, Stephan and Siegwart, Roland and Nieto, Juan},
title = {{Why and how to avoid the flipped quaternion multiplication}},
year = {2018}
}