README.md

IEKF

This repository contains the code for state estimation for a unicycle system. The states are estimated using Unscented Kalman Filter (UKF), Extended Kalman Filter (EKF) and Invariant Extended Kalman Filter (IEKF). The code was developed in an effort to regenerate the results of [1].

System equations

The system considered in this problem is a unicycle system with the following equations

$$\dot{x} = v\cos(\theta) + C_xd,$$ $$\dot{y} = v\sin(\theta) + C_yd,$$ $$\dot{\theta} = \omega,$$

where $(x,y)$ are the position of the robot, $\theta$ is the heading, $v$ is the linear velocity, and $\omega$ is the turning rate. $d$ is the disturbance acting on the system through the matrices $C_x$ and $C_y$. The disturbance dynamics is given by

$$\dot{d} = Ad.$$

For more information see section 3 in [1].

Undisturbed system

In the first example, there is no disturbance acting on the system, i.e., $d=0$. Try running runMe.m in the undisturbed folder to get the following results.

As it could be seen from these plots, the IEKF outperforms the EKF and UKF in terms of RMSE of estimation.

Disturbed system

In the second example, a disturbance $d \in \mathbb{R}^4$ acts on the system. There are two different IEKF designs provided in [1]. Run runMe.m in the disturbed folder to get the results. Some results are shown here.

To do

The result from the second example does not exactly match the result from the paper.

References

1- Coleman, K., Bai, H. and Taylor, C.N., 2021. Extended invariant-EKF designs for state and additive disturbance estimation. Automatica, 125, p.109464.