Stochastic Estimation and Control: Foundations of State Estimation

In real-world engineering, systems are constantly subjected to unpredictable noise and environmental disturbances. Understanding how to accurately estimate states and control these dynamic systems is crucial for aerospace, robotics, and autonomous systems. This text-based course guides you through the core mathematical concepts and practical frameworks needed to design robust estimation and control algorithms, transitioning from basic probability theory to implementing the iconic Kalman filter. What you'll learn: - Understand the foundational concepts of probability, random variables, and stochastic processes. - Model how random noise propagates through linear dynamic systems using state-space representations. - Design classical frequency-domain filters and compensators to mitigate noise. - Apply the Kalman filter algorithm to estimate the hidden states of noisy dynamic systems. - Analyze the stability and convergence conditions of filter equations. - Explore modern applications of sensor fusion and discrete-time state estimation. You will begin with essential terminology and probability theory before progressing step-by-step through state-space modeling, filter design, and stability analysis. Every concept is reinforced with detailed written explanations, clear mathematical derivations, and structured exercises. This course is designed for beginners in engineering, robotics, or data science who want to build a solid theoretical foundation in stochastic systems without needing advanced prior background. Start reading today to master the math behind modern state estimation and control.