Programme Content
The course will begin with a gentle introduction to state-space models in engineering, and then move on to the idea of observer design based on a state-space model. A simple problem of predicting the position and velocity of a translating object like a car through a sensor (like a lidar or a tachometer) would be considered. The pros and cons of performing this prediction using simple tools like differentiating the signal or integrating the signal would be explored. This would be followed by a brief non-rigorous (in a mathematical sense) exposure to an object called the Kalman filter. Hands-on experience will be provided with an Inertial Measurement Unit (IMU) fitted with a gyroscope, an accelerometer and a magnetometer. Then we would move on to estimating the orientation of a rigid body - a requirement in drones, autonomous vehicles, and spacecraft - by understanding the basic requirement, then exploring two algorithms for constructing and orientation matrix from measurements - the TRIAD and the QUEST. This would be followed by employing the Kalman filter for dynamically estimating orientation, bringing in ideas such as the Extended Kalman Filter (EKF) and the Multiplicative Extended Kalman Filter (MEKF.) Moving further, the ideas of Complementary Filter (introduced by R. Mahony and coworkers) will be presented. All these algorithms would be implemented on the hardware described later in this write up. The last module of the course will introduce the Simultaneous Localization and Mapping (SLAM) problem and discuss algorithms for implementing this objective.
