Nonlinear Kalman Filters and Parameter Estimation

Real-world physical systems are rarely linear. To track moving objects, navigate autonomous vehicles, or estimate battery states, you must master nonlinear estimation techniques. This course provides a clear, text-based pathway to understanding and implementing advanced estimation algorithms. You will transition from basic linear estimation concepts into the powerful world of nonlinear Kalman filtering. By exploring the mathematical foundations and logical steps of these algorithms, you will gain the confidence to model, predict, and update states and parameters when systems exhibit complex, non-linear behaviors. What you'll learn: - Understand the fundamental limitations of linear Kalman filters in real-world scenarios - Derive and apply the Extended Kalman Filter (EKF) using Taylor series linearization - Implement the Unscented Kalman Filter (UKF) using the unscented transform for highly nonlinear systems - Configure joint and dual estimation techniques for simultaneous state and parameter tracking - Analyze filter performance and tune covariance matrices for optimal estimation accuracy The course begins with key terminology, basic probability concepts, and foundational state-space definitions. From there, you will progress through detailed written explanations of EKF and UKF derivations, ending with practical pseudocode examples designed for modern applications like robotics and sensor fusion. This course is designed for engineers, programmers, and technical enthusiasts who want a clear, conceptual, and mathematical grounding in nonlinear estimation. A basic understanding of linear algebra and general programming concepts is recommended. Start reading today to unlock the power of advanced state estimation in your projects.