Unscented Kalman Filter#

The fundamental issue of state estimation impacts widespread robotics applications. Sensors give us an imperfect view of the world, as they tend to contain noise in their readings. Similarly, when a robot moves in the physical world, its motion has some amount of uncertainty, deviating randomly from the ideal model that we predict it might follow. Rather than ignoring these uncertainties and forming a naive state estimate, we will be harnessing the power of probability to yield mathematically optimal estimates using the Unscented Kalman Filter (UKF) algorithm. The Kalman Filter (KF) algorithm and its variants such as the UKF comprise part of the field of probabilistic robotics, which aims to account for uncertainties that the robot will inherently face as it interacts with the world with imperfect information. An entire course could be taught only on the topics of filtering and state estimation.

In this project, we give a high-level overview of the necessary foundations to understand the UKF algorithm. Then, you will implement a UKF with a simple one-dimensional model of the drone’s motion to estimate its position and velocity along the vertical axis. Later on in the project, we will expand the model to three spatial dimensions.