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With Applications to Orbits/Target Tracking/GPS and Navigation

ATI's Applications-Oriented Kalman Filtering course

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    Technical Training Short On Site Course Quote

      This applications-oriented course provides a comprehensive overview of the Kalman filter. The course begins with a brief review of probability, stochastic processes, dynamics and modeling of systems. This is followed with an in-depth discussion of estimation theory and methods, concluding with the derivation of the Kalman filter algorithm.

      The remainder of the course focuses on the practical use of the Kalman filter. Methods of implementing the Kalman filter algorithms are discussed, including initialization and convergence. Applications of the Kalman filter are presented in several areas including: target tracking, orbit determination, navigation and the Global Positioning System (GPS). Participants will receive a complete set of notes.



      Dr. C. Allen Butler is a recognized expert in the field of Multi-Sensor Correlation, Kalman Filtering and Multi-Target Tracking, with over 15 years experience in both theoretical and engineering development of correlation and tracking systems. As a senior associate with D. H. Wagner Associates, he has worked on the development of several Navy, Air Force, and Army tracking and fusion systems. He recently developed and implemented new algorithms for the Composite Combat Identification (CCID) program under the Navy's Missile Defense FNC.

      Dr. Donald A. Kelly received his Ph.D. in Electrical Engineering from Colorado State University and MSEE from the University of Colorado. Dr. Kelly has more than 17 years experience in engineering, specializing in estimation and navigation. He is an expert in estimation and Kalman filtering with applications to orbit determination, multi-target tracking and real-time systems, and navigation/GPS. Dr. Kelly is principal of AdvanTech, which specializes in navigation/GPS, systems engineering, and software engineering. Most recently, he has supported the Navy in developing real-time Kalman trackers, and supported the Air Force in systems engineering and analysis for air-to-air and air-to-surface weapon systems. Previously he was involved in spacecraft attitude and orbit determination.

      Contact these instructors (please mention course name in the subject line)

    What you will learn:

    • Batch and recursive estimation; when to use which method.
    • Kalman filter implementation and diagnostics.
    • Applications to orbit determination and target tracking.
    • Current literature sources and software packages.

    Course Outline:

    1. Fundamentals. A review of probability, statistics, stochastic and random processes. The basics of matrix manipulation and linear system theory. Discussions of covariances, correlation, and Gaussian distribution.

    2. Dynamics and Modeling. Formulation of process and measurement models. Forming the state-space representation from differential dynamic equations. Structure of linear and nonlinear models, including time variant and time invariant cases.

    3. Estimation Theory. Definition of filtering, prediction and smoothing. Derivation of a linear, unbiased, minimum variance, optimal estimator. Least-squares, weighted-least-squares, maximum likelihood, and Bayesian estimation algorithms. Handling of a priori information, development of recursive estimation approaches.

    4. Derivation of the Kalman Filter. Step-by-step derivation of the Kalman filter algorithm. Discrete and continuous versions. Various alternate forms of the Kalman filter and suggestions for when to use which Kalman filter form.

    5. Implementation Issues Using the Kalman Filter Algorithms. Initialization and convergence criteria. Modeling errors and concerns, process and measurement noise issues. Various integration algorithms and techniques. Square-root filter algorithm and fading memory method. Linearization of nonlinear systems.

    6. Advanced Topics Current Literature and Software Packages. Adaptive Kalman filtering, identification methods. Using Kalman filtering for process control. Recent developments in Kalman filtering and applications.

    7. Target Tracking. An overview of the basics of target tracking are presented, followed by the formulation of two kinematic tracking process models. Applications of target tracking for missile guidance and radar target tracking are discussed. The Hyperbolic In-Air Tracking System (HITS) is discussed, emphasizing the tracking algorithms, real-time code, and accuracy.

    8. Orbit Determination. A discussion of the dynamics involved for spacecraft orbit is followed by the development of a process model for orbit determination. A range/range-rate measurement model is derived, and examples using both batch and recursive methods are presented. The dynamic model for spacecraft orbit is developed, and a lab exercise conducted.

    9. GPS and Inertial Navigation. An overview of the Global Positioning System (GPS) is presented, followed by a discussion on inertial navigation systems. Integrated INS/GPS models for aircraft and smart munitions are developed, including the design of a reduced-order flight filter.


      Tuition for this three-day course is $1790 per person at one of our scheduled public courses. Onsite pricing is available. Please call us at 410-956-8805 or send an email to