Data and Observer Design

Sensors generate vast amounts of data. In autonomous robots, drones, and spacecraft, data is used to predict the position, velocity, and orientation of a vehicle: a procedure known as observer design. As sensor technology has grown, so have the sources: cameras, lidars, sonars, doppler, and lasers.

The course begins with a concrete problem: predicting the position and velocity of a translating object such as a car, using a sensor such as a lidar or tachometer. Simple approaches like signal differentiation and integration are examined, along with their limitations. This leads to a mathematically non-rigorous introduction to the concept of an observer/filter, which is then designed to perform the same task, with its advantages and disadvantages assessed. The course then generalizes this exercise to problems of larger dimension, working in n-dimensional Euclidean state-space.

This progression leads to the Kalman Filter, one of the most powerful algorithms in signal processing, data prediction, and control. Proposed by R. E. Kalman in 1960, it extracts true information from noisy sources. Its applications span cellphones, drones, aircraft, GPS, orbiting spacecraft and satellites, and the 1969 moon landing.

 This course introduces the principles of observer design for extracting meaningful information from sensor data. Beginning with state-space modelling and estimation for simple dynamic systems, students explore observer-based approaches for predicting position and velocity before progressing to the Kalman Filter for data fusion and state estimation. The course also introduces orientation estimation, observers on Lie groups, and Simultaneous Localization and Mapping (SLAM), supported by hands-on experience using sensors such as lidar and inertial measurement units (IMUs).

 By the end of this course, students will be able to:

• Understand state-space modelling for simple dynamic systems.
• Explain the principles of observer design for estimating system states from sensor measurements.
• Understand the Kalman Filter and its application to state estimation from noisy sensor data.
• Explore orientation estimation using complementary filters, Mahony observers, and observers on Lie groups.
• Gain practical experience implementing estimation algorithms using lidar and inertial measurement unit (IMU) sensors.

Upon successful completion of this course, students will be able to:

• Develop state-space models for simple dynamic systems.
• Analyse the advantages and limitations of different state estimation approaches.
• Apply the Kalman Filter for estimating system states from noisy sensor measurements.
• Implement sensor fusion techniques using data from inertial measurement units.
• Explain the role of observer design and SLAM in robotics, autonomous systems, and computer vision.

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