This report delves into the application of Kalman and Extended Kalman Filters (EKF) in state estimation, crucial for various engineering applications. It begins with an introduction to the Kalman filter as a recursive Bayesian estimator, highlighting its advantages in linear systems and real-time processing. The report then presents practical examples, including the estimation of a bridge crane's state using Kalman filters, and a ship's state using EKF. The bridge crane example involves developing prediction and correction models, incorporating sensor data, and implementing state prediction using Matlab functions. The ship example focuses on developing Jacobians for the motion model and implementing prediction and correction stages within the EKF framework. The discussion section addresses the limitations of Kalman filters with non-linear systems and the advantages of EKF in such scenarios. Finally, the report concludes by summarizing the practical applications of both filters, emphasizing their role in state space estimation for both linear and non-linear systems. Matlab code snippets are provided in the appendices to illustrate implementation details.
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