Larisa Loke

Larisa Loke

Ph.D. Student at Northwestern University, interested in assistive and rehabilitation robotics

Unscented Kalman Filter

Overview

This project was done as a homework assignment for CS/ME 469 ML and AI for Robotics at Northwestern. The task was to implement the Unscented Kalman Filter (UKF) from scratch for a mobile robot to localize itself. The UKF was tested on a real robot dataset, and results from filtering were compared to ground truth robot positions measured using a system fo cameras. The datasets used for the project can be found here. Code is not provided since this is a regular homework assignment.

Models

The motion model for the robot was designed based on differential drive kinematics [1] and used as the state transition model for the UKF.

The sensor model for the robot was designed based on the range-bearing sensor model and used as the measurement model for the UKF.

UKF Algorithm

The UKF algorithm is a Bayes filter using a moments parametrization (mean and covari­ance). It assumes that the belief state can be represented by a gaussian (i.e. the initial belief is normally distributed). Like the Extended Kalman Filter (EKF), it can be used for systems with non­linear dynamics (g) and measurement models (h). It differs from the EKF in how it linearizes the transformation of the gaussian through non­linear functions. The UKF employs the unscented transform,­ explicitly sampling sigma points from the gaussian and passing each of them through g and h. These sigma points are sampled at the mean and symmetrically about the mean for each of the state variables, resulting in 2n + 1 sigma points, where n is the dimensionality of the state. Sampled sigma points are then passed through the non­linear state­-transition function g along with the control command at that each timestep the set of transformed sigma points.

More on the UKF can be found at [1] and [2].

Results

Using only the motion model, robot motion was forward simulated and compared against the ground truth:

When filtering is applied using the UKF, the simulated robot motion was much closer to the ground truth:

References

[1] Thrun, S., Burgard, W., Fox, D. & Arkin, R. (2005). Probabilistic robotics. MIT Press.

[2] Terejanu, G. A. (2011). Unscented kalman filter tutorial. University at Buffalo, Buffalo.