Kalman, H-Infinity, and Nonlinear Estimation Approaches

Course length:

3 Days



Course dates

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This three-day course will introduce Kalman filtering and other state estimation algorithms in a practical way so that the student can design and apply state estimation algorithms for real problems. The course will also present enough theoretical background to justify the techniques and provide a foundation for advanced research and implementation. After taking this course the student will be able to design Kalman filters, H-infinity filters, and particle filters for both linear and nonlinear systems. The student will be able to evaluate the tradeoffs between different types of estimators. The algorithms will be demonstrated with freely available MATLAB programs.

A pdf copy of Dan Simon’s text, Optimal State Estimation, is provided to students along with course slides.  It is beneficial –but not required- to bring a laptop loaded with MATLAB to this class. 

What You Will Learn:

  • How can I create a system model in a form that is amenable to state estimation?
  • What are some different ways to simulate a system?
  • How can I design a Kalman filter?
  • What if the Kalman filter assumptions are not satisfied?
  • How can I design a Kalman filter for a nonlinear system?
  • How can I design a filter that is robust to model uncertainty?
  • What are some other types of estimators that may do better than a Kalman filter?
  • What are the latest research directions in state estimation theory and practice?
  • What are the tradeoffs between Kalman, H-infinity, and particle filters?

Course Outline:

  1. Dynamic Systems Review. Linear systems. Nonlinear systems. Discretization. System simulation.
  2. Random Processes Review. Probability. Random variables. Stochastic processes. White noise and colored noise.
  3. Least Squares Estimation. Weighted least squares. Recursive least squares.
  4. Time Propagation of States and Covariances.
  5. The Discrete Time Kalman Filter. Derivation. Kalman filter properties.
  6. Alternate Kalman filter forms. Sequential filtering. Information filtering. Square root filtering.
  7. Kalman Filter Generalizations. Correlated noise. Colored noise. Steady-state filtering. Stability. Alpha-beta-gamma filtering. Fading memory filtering. Constrained filtering.
  8. Optimal Smoothing. Fixed point smoothing. Fixed lag smoothing. Fixed interval smoothing.
  9. Advanced Topics in Kalman Filtering. Verification of performance. Multiple-model estimation. Reduced-order estimation. Robust Kalman filtering. Synchronization errors.
  10. H-infinity Filtering. Derivation. Examples. Tradeoffs with Kalman filtering.
  11. Nonlinear Kalman Filtering. The linearized Kalman filter. The extended Kalman filter. Higher order approaches. Parameter estimation.
  12. The Unscented Kalman Filter. Advantages. Derivation. Examples.


Stan Silberman is a member of the Senior Technical Staff of the Applied Physics Laboratory. He has over 30 years of experience in tracking, sensor fusion, and radar systems analysis and design for the Navy, Marine Corps, Air Force, and FAA. Recent work has included the integration of a new radar into an existing multisensor system and in the integration, using a multiple hypothesis approach, of shipboard radar and ESM sensors. Previous experience has included analysis and design of multiradar fusion systems, integration of shipboard sensors including radar, IR and ESM, integration of radar, IFF, and time-difference-of-arrival sensors with GPS data sources, and integration of multiple sonar systems on underwater platforms.

Dr. Dan Simon, creator of this course, was a professor at Cleveland State University from 1999-2021 and is currently a research engineer at Rebellion Defense. He has applied Kalman filtering and other state estimation techniques to a variety of areas, including motor control, neural network and fuzzy system optimization, missile guidance, communication networks, fault diagnosis, vehicle navigation, robotics, prosthetics, and financial forecasting. He has over 200 publications in refereed journals and conference proceedings, including many on the topic of Kalman filtering. He has written three graduate-level textbooks.


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SCHEDULING: If this course is not on the current schedule of open enrollment courses and you are interested in attending this or another course as an open enrollment, please contact us at (410)956-8805 or ati@aticourses.com. Please indicate the course name, number of students who wish to participate. and a preferred time frame. ATI typically schedules open enrollment courses with a 3-5 month lead-time. To express your interest in an open enrollment course not on our current schedule, please email us at ati@aticourses.com.

For on-site pricing, you can use the request an on-site quote form, call us at (410)956-8805, or email us at ati@aticourses.com.