A comprehensive course on nonlinear and data-driven estimation techniques taught by Floris van Breugel. This repository contains Jupyter notebooks, Python implementations, and practical examples covering fundamental concepts from batch estimation to advanced data-driven techniques using neural networks and dimensionality reduction.
The course is designed to follow a single example, a planar drone, throughout the sequence of lessons to help build intuition and see how the tools stack together. This example is intended to serve as a template for how other projects can be applied to the sequence of lessons. The course material is designed to build progressively:
Foundation (Lessons 1-6): Classical estimation theory, from batch least squares to the Kalman filter
Observability Analysis (Lessons 7-8): Understanding what can be estimated from available measurements
Nonlinear Filtering (Lessons 9-10): Extended and Unscented Kalman Filters for nonlinear systems
Data-Driven Methods (Lessons 11-16): Machine learning approaches including ANNs and SINDy
Dimensionality Reduction (Lessons 17-18): Dimensionality reduction and reduced-order estimation for ANNs
New to the course? Check out our Tips on Getting Started with GitHub, Google Colab, and Docker to set up your development environment.
Topics:
- Introduction to google colab notebook environment
- Introduction to installing and important python packages and custom utilities
Topics:
- Planar drone dynamics modeling and simulation
- Control affine system representation
- Animation and visualization of dynamical systems
- Introduction to PyBounds for using Model Predictive Control
Topics:
- Parameter estimation fundamentals
- Linear least squares (batch processing)
- Statistical foundations of least squares estimation
- Error analysis and uncertainty quantification
Topics:
- Linear sequential estimation algorithms
- Random variables and covariance analysis
Topics:
- Minimum variance estimation theory
- Cramér-Rao Lower Bound (CRLB)
Topics:
- Linearizing continuous-time nonlinear models
- Discretization techniques for dynamic systems
- Discrete-time Kalman filter derivation and implementation
- Understanding Kalman filter limitations
Topics:
- Observability fundamentals for linear systems
- Observability matrix and Gramian
Topics:
- Nonlinear observability analysis using symbolic computation
- Monocular camera example case study
Topics:
- Empirical observability matrix computation
- PyBounds framework for empirical analysis
- Custom simulator integration with PyBounds
Topics:
- Extended Kalman Filter (EKF) theory
- EKF implementation for planar drone
- Comparison with linear Kalman filter
Topics:
- Unscented Kalman Filter (UKF) algorithm
- Sigma point generation and propagation
- Comparison of EKF vs. UKF performance
Topics:
- Training dataset creation from simulations
- Data visualization and validation
Topics:
- Neural network-based state estimation
- ANN architecture design for estimation problems
- Training and evaluating ANN estimators
- Application to planar drone altitude estimation
Topics:
- Hybrid AI-Kalman filtering approaches
- Integrating neural networks with UKF
Topics:
- Numerical differentiation from noisy data
- PyNumDiff library and methods
- Smoothing and filtering techniques
Topics:
- Discovering governing equations from data
- PySINDy library for sparse regression
- Learning dynamics and measurement models from data
- Integration with UKF for state estimation
Topics:
- Neural network-based dynamics and measurement models
- Data-driven UKF with learned models
Topics:
- Singular Value Decomposition (SVD) theory for compression
- Terrain and optic flow data analysis
- Reduced-order representations of high-dimensional data
Topics:
- ANN training on compressed representations
- Performance evaluation of ROM-ANN estimators
By completing this course, you will:
- Master classical estimation theory from batch to sequential methods
- Understand and implement Kalman filtering for linear and nonlinear systems
- Analyze observability for both linear and nonlinear systems
- Apply modern data-driven techniques including neural networks and SINDy
- Combine classical filtering with machine learning for hybrid estimators
- Perform dimensionality reduction for high-dimensional estimation problems
- Develop practical skills in state estimation for autonomous systems
- Python 3.x
- Jupyter Notebooks
- NumPy / SciPy - Numerical computing
- Matplotlib - Visualization
- SymPy - Symbolic mathematics
- TensorFlow / Keras - Neural networks
- PySINDy - Sparse identification of nonlinear dynamics
- PyNumDiff - Numerical differentiation
- PyBounds - Empirical observability analysis
Each lesson directory contains:
- Jupyter notebooks with theory, examples, and exercises
- Solution notebooks (marked with
_SOLUTIONor_SOLUTIONS) - PDF lecture notes and derivations
- README files with additional context
- Links to text and video references
git clone https://github.com/florisvb/Nonlinear_and_Data_Driven_Estimation.git
cd Nonlinear_and_Data_Driven_Estimation
# Install dependencies -- see `requirements_minimal.txt` and `Utility/Requirements`
jupyter notebookAll notebooks can be run directly in Google Colab. See github_colab_tips.md for instructions.
This course material is developed and maintained by Floris van Breugel, Associate Professor in Mechanical Engineering at the University of Nevada, Reno.
This work is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0).
In brief: You are free to use and adapt these materials for non-commercial educational purposes with attribution. Commercial use requires permission. See LICENSE for full details.
Contributions, issues, and feature requests are welcome! Feel free to check the issues page or submit pull requests.
This course bridges classical control and estimation theory with modern data-driven machine learning approaches, providing students with both theoretical foundations and practical implementation skills.