Autonomous Robots: Kalman Filter

Design and implement a one-dimensional Kalman filter using linear algebra, building the state, uncertainty, state transition and measurement matrices, then apply the predict–update cycle to refine position estimates.

Review the assignment 2 starter code for Kalman filters, with prebuilt matrices, and implement state prediction and update using identity, transpose, and inverse in any language.

The solution to assignment 2 initializes the Kalman filter with large uncertainty, tests constant speed, and adds post-update uncertainty to balance responsiveness and accuracy in autonomous robot tracking.

Implement a full two-dimensional Kalman filter in the 2D simulator, adjusting matrix sizes and adopting a five-state model (x, y, speed, heading, steering) to estimate car position.

Expand the assignment 3 code to two dimensions by enlarging x and y matrices and implementing predict, measure, and update, and explore the five-state bonus and raw measurements.

Review the assignment three solution for autonomous Kalman filter, using a four-by-one state vector and four-by-four uncertainty, expanded from assignment two to four dimensions.

Explore Kalman filter prediction in autonomous robots by forecasting a self-driving car's state three seconds ahead to clear intersections, using state transitions, delta t, and input u.

Use a Kalman filter to rapidly localize and decide at a traffic light by predicting three seconds ahead, stopping if the forecasted position is before the light.

Explore assignment 4 solutions for Kalman filters in autonomous robots, showing how to set the p matrix diagonals and modify the state transition with light duration to predict red-light behavior.

Explore how Kalman filters update and predict states with a transition matrix, manage uncertainty, and scale from one dimension to two dimensions in robotics, with real self-driving car applications.