The Kalman filter has become arguably the most
widely applied technique in modern control
systems. This course will cover the theory of
Kalman filters and their application to problems in
guidance control and navigation. Given a linear
system model and any measurements of its
behavior, plus statistical models that characterize
system and measurement errors, plus initial
condition information, the Kalman filter describes
how to process the measurement data.
Instructor
Donald L. Mackison is an Adjunct Professor of
Aerospace Engineering at the University of
Colorado. He has a PhD from CU in Controls and
Systems, and has worked at Johns Hopkins
University Applied Physics Laboratory, Ball
Aerospace, and the National Oceanic and
Atmospheric Administration. His 40 years of
professional experience have included
development work on submarine inertial and
satellite navigation systems, satellite attitude
control and attitude determination (gravity
gradient and spin stabilized system, Orbiting Solar
Observatory, Hubble Space Telescope, Upper
Atmospheric Research Satellite- UARS)
and several lightsats at CU. His
research has included application of
Linear Quadratic and Kalman Filter
methods to satellite atitude control
systems, including the development
of "modal weighting" methods
for both controllers and filters.
Contact this instructor (please mention course name in the subject line)
What You Will Learn
- Theory of the Kalman filter.
- Application to typical dynamic systems
- Matlab modeling of Kalman filters applied to
typical linear and nonlinear systems.
- Extended Kalman filters.
- How to develop measurement and state noise model
for the Kalman filters.
- Comparison of discrete and continuous filter
models.
- What are extended Kalman filters, and how to apply
them to problems with nonlinear dynamics and
nonlinear measurement.
- Advantages and disadvantages of time dependent
and constant gain filters.
- Two points of view- Noise models representing
physical reality and noise models as tuning knobs
for both constant gain and time dependent filters.
- The relation between the Kalman gain, the noise
models, and time response of the filter.
- The Kalman filter as a AR filter.
Course Outline
- Review of linear algebra and random processes. Review of the mathematics of linear algebra and random processes necessary to
understand the engineering application of Kalman filters.
- Development of the discrete Kalman Filter. Mathematical development of the discrete filter- based on a linear dynamic system driven by white noise, and linear measurements of the state corrupted by white noise. The addition of shaping filters to the model to account for non-white noise sources.
- Development of the continuous Kalman Filter. The continuous filter is shown to be a limiting case of the discrete filter. For the constant gain (steady state) filter, the filter gains and the steady-state state error covariance matrix are derived from an eigenvector decomposition of the control Hamiltonian (Potter-MacFarlane) implemented in Matlab codes.
- Development of the Extended Kalman Filter. The linear Kalman filter is exact, based on the linear dynamics model and the linear measurement model. For most systems, orbit determination, for example, both the dynamics and measurements are nonlinear functions of the state. In the Extended Kalman Filter (EKF) the state estimate is propagated with the full nonlinear model, and the predicted measurtement is computed with the full nonlinear model. Linearized models are used to propagate the covariance, and to compute the filter gains using the state and measurement Jacobian matrices. The EKF solved much of the early problems of filter divergence.
- Estimators for linear dynamic systems. A series of simple dynamic models will be used to focus all these ideas in a tractable problem.
- Application to navigation systems. Modern navigation system (inertial, celestial, GPS) computations are driven by Kalman filter estimators. We will look at several of these systems in light of what we have learned about Kalman filters.
- Application to orbit determination and attitude determination
systems. Several examples will be examined including both discrete and continuous linear Kalman filters, and the Extended Kalman Filter, for various orbit measurements, and for a variety of attitude sensors.
- Covariance analysis methods. One of the most important applications of Kalman filter methods is covariance analysis, used to predict the performance of a system using assumed system dynamics and assumed covariance models for system disturbances, measurement noise, and uncertain internal parameters of the system. This analysis allows one to specify parameters for hardware and software and schedule measurement updates.
- Feedback control systems.
Tuition
Tuition for this three-day course is $1290 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 ati@aticourses.com.
Register Online
Return to ATI's Schedule
Return to ATI Homepage
ATI Courses - Applied Technology Institute Training Seminars ·
349 Berkshire Drive Riva, Maryland 21140-1433
Phone: 410-956-8805 or toll free 1-888-501-2100; Fax 410-531-1013
E-mail: ati@aticourses.com
Copyright 1999-2007 ATI - Applied Technology Institute Training Seminars - All Rights reserved
