Introduction to System Identification and Parameter Estimation

How do we build accurate mathematical models of complex systems when we only have access to noisy, real-world data? This course introduces the fundamental principles of system identification, parameter estimation, and data-driven learning. Through this text-based guide, you will transition from understanding basic data observations to constructing, validating, and optimizing robust mathematical representations of dynamic systems. You will learn how to extract meaningful patterns from noise and apply statistical learning tools to real-world engineering problems. What you'll learn: - Understand foundational terminology of system representation, noise dynamics, and mathematical modeling. - Apply least squares estimation techniques and analyze their convergence behavior. - Configure Kalman filters to estimate hidden states in noisy dynamic environments. - Evaluate model performance using criteria like Maximum Likelihood and Akaike's Information Criterion. - Design informative experiments to collect high-quality data for system identification. - Explore modern machine learning approaches, including neural networks and function approximation, for complex system learning. The course begins with essential definitions of signals, systems, and noise before guiding you step-by-step through classical estimation, state filtering, and modern statistical learning techniques. You will practice these concepts through written explanations and step-by-step mathematical derivations. This course is designed for beginners in engineering, data science, and applied mathematics who want to master the basics of modeling systems from data, with no advanced prerequisites required. Start reading today to master the core principles of data-driven system modeling.