Kalman Filter Course

This repository contains MATLAB scripts for learning and applying Kalman Filtering techniques, including classical Kalman Filters, Extended Kalman Filters (EKF), and Unscented Kalman Filters (UKF), with applications to mechanical systems and stochastic processes.

📁 Repository Structure and Contents

| Folder | Script | Description | |:------|:------|:-------------| | MHE/ | protomhe.m | Prototype for Moving Horizon Estimation (MHE). | | Section1/ | Gaussian_plot.m | Visualizes Gaussian distributions. | | | KramersSS.m | Computes steady-state of Kramers equation. | | | Kramers_euler_maruyama.m | Simulation of Kramers dynamics with Euler-Maruyama method. | | | Mult_Gaussian_animation.m | Animation of multivariate Gaussian evolution. | | | brownian_motion.m | Simulation of basic Brownian motion. | | | chol_LDL.m | Cholesky decomposition via LDL factorization. | | Session_2/ | MSD_Euler.m | Simulates a mass-spring-damper system using Euler method. | | | MSD_RK4vsRK1.m | Compares Runge-Kutta 4th order with Euler integration. | | | discrete4order_example.m | Example of discrete-time 4th order system simulation. | | session_3/ | CL_Cart_KF.m | Closed-loop cart simulation with Kalman filter. | | | Cart_Kalman_Filter.m | Classical Kalman Filter applied to a cart system. | | | Cart_generative_model.m | Generative model for cart dynamics simulation. | | Session_4/ | CA_KAlmanFilter_Q.m | Kalman filter with process noise tuning. | | | CA_model.m | Constant-acceleration model setup. | | | nonliearMSD_Kalman.m | Kalman filtering on a nonlinear MSD system. | | | nonlinearMSD.m | Nonlinear MSD system dynamics. | | session_5/ | EKF_example.m | Example of Extended Kalman Filter (EKF) application. | | | MSD_dualSPE.m | Dual-state estimation using EKF. | | session_6/ | Example_UKF.m | Unscented Kalman Filter (UKF) example simulation. | | | adaptivecontrol_EKF_cart.m | Adaptive control using EKF on a cart model. | | session_7/ | MSD_SRUKF.m | Square Root UKF applied to a mass-spring-damper system. | | | MSD_UKF.m | Regular UKF applied to mass-spring-damper system. | | session_8/ | nonlinearMSD_SRUKF.m | Square Root UKF applied to a nonlinear MSD model. |

📚 Topics Covered

• Basics of Gaussian processes and Brownian motion
• Euler-Maruyama simulations for stochastic differential equations
• Kalman Filter (KF) for linear systems
• Extended Kalman Filter (EKF) for nonlinear systems
• Unscented Kalman Filter (UKF) and Square Root UKF (SRUKF)
• Applications to mechanical systems like mass-spring-damper models and cart dynamics
• Introduction to Moving Horizon Estimation (MHE)

🛠 Requirements

• MATLAB R2020b or newer
• Recommended Toolboxes:
  • Control System Toolbox
  • Statistics and Machine Learning Toolbox (for advanced filtering tasks)

🚀 How to Use

1. Clone the repository: bash git clone https://github.com/YOUR_USERNAME/KalmanFilter_course.git
2. Add to MATLAB path: matlab addpath(genpath('path_to_cloned_folder'))
3. Run examples, for instance: matlab cd Section1 run('Gaussian_plot.m')

✨ Highlights

• Full pipeline from basic stochastic simulation to advanced Kalman filtering.
• Practical examples on mechanical system state estimation.
• Includes Moving Horizon Estimation (prototype).

📜 License

This project is licensed under the MIT License — see the LICENSE file for details (if available).

👨‍💻 Author

Developed by Adrian Guel.