This is a short course covering advanced topics in state estimation and Kalman filtering. It focuses on the Orbit Determination problem. This course is structured to present the basic concepts without the in-depth theoretical background and mathematical derivations that commonly accompany an academic presentation of the subject. My intention is to introduce state estimation in a simplified manner to those with no previous background in the field, or to provide a review to those who have studied the subject previously. Readers should have a familiarity with differential and integral calculus and differential equations to help understand some equations presented. The form of this short course is like the many short courses I've taught at government agencies and private corporations during my thirty-five-year career as an aerospace engineering professor at Auburn University. It presents the material in a simplified outline / bullet format using many understandable figures, rather than using lengthy, detailed explanations with complex mathematical derivations and proofs. It provides the practical equations that are useful to the practicing engineer. The objectives of this short course are to: - Introduce the concepts and fundamentals of state estimation, with applications to the orbit determination problem. - Present the concepts of batch estimation using least squares, weighted least squares, minimum variance, and ridge-type estimation methods. - Introduce the fundamentals of sequential estimation using the Kalman filter, the Extended Kalman filter, and the Unscented Kalman filter. - Discuss the sources of error in orbit determination and present methods of improving accuracy in the solution process- - Present practical considerations of orbit determination involving observational data, update intervals and fit spans, the results of differential correction, and the use of smoothers and GPS. The material presented is usually covered in graduate level course in estimation theory except that there's no required homework, quizzes, projects, computer programs to write, or examinations. I believe that even a novice reading through this material will gain an in-depth understanding of state estimation. My former students should recognize everything in this presentation, and if they didn't learn it the first time, they can learn it now through this simplified short course with much less work. State estimation and Kalman filtering is not easy, but it's my goal to make it enjoyably simple once the fundamentals are understood. To do so, I've attempted to present the difficult concepts as clearly as possible to facilitate that understanding. Completion of this short course should enhance the knowledge base of all those who read through its content. This short course is part of a series I've developed as a Professor at Auburn University. Others in this series include: Orbital Mechanics, Part I: The Two-Body Problem Orbital Mechanics, Part II: Satellite Perturbations Fundamentals of Inertial Navigation and Missile Guidance David A. Cicci, Auburn, Alabama, [email protected]