Applied Kalman Filtering
525.745

Course Description
Theory, analysis, and practical design and implementation of Kalman filters are covered, along with example applications to real-world problems. Topics include a review of random processes and linear system theory; Kalman filter derivations; divergence analysis; numerically robust forms; suboptimal filters and error budget analysis; prediction and smoothing; cascaded, decentralized, and federated filters; linearized, extended, second order, and adaptive filters; and case studies in GPS, inertial navigation, and ballistic missile tracking.

Syllabus

1. Review of random processes
2. Review of linear system theory (state space modeling)
3. Linear system response to random process
4. Kalman filter derivation(minimum mean square error linear filter) and examples
5. Conditional mean derivation and alternate forms
6. Nonlinear filtering via linearization, complimentary filtering, extended Kalman filter
7. Application to Global Positioning System (GPS) navigation and orbit determination
8. Divergence analysis, suboptimal and error budget analysis, aided inertial navigation example
9. Prediction and smoothing, square root filtering and smoothing
10. Radar tracking of a ballistic body, higher order nonlinear filtering
11. Cascaded filters, decentralized filters, federated filters
12. Adaptive filters, application to farm tractor control with GPS
13. System identification with Kalman filters, application to missile guidance modeling
14. Advanced topics in Kalman filtering

Prerequisites
525.414 Probability and Stochastic Processes for Engineers and 525.466 Linear Systems Theory or equivalent.

Instructor
Larry Levy joined APL in 1971, working on performance analysis of Kalman-filter-integrated transit/inertial navigation systems in the space department. He was appointed to the Principal Professional Staff in 1978. Dr. Levy has had a series of increasingly important responsibilities in the areas of navigation system development and system test and evaluation. He is recognized as an expert in Kalman filtering and system identification and is the author of numerous papers and presentations on these subjects. He was the co-developer of the GPS translator concept in SATRACK and was instrumental in developing the end-to-end methodology for Trident II accuracy evaluation.

Dr. Levy is also a graduate lecturer in Kalman filtering and system identification courses in the Johns Hopkins University Whiting School of Engineering and a short course lecturer on these subjects for Navtech Seminars.

E-mail the instructor.

Textbook
Introduction to Random Signals and Applied Kalman Filtering by R.G. Brown & P.Y.C. Hwang

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updated September 1997