Course 447: Applied Kalman Filtering

All course materials this year will be provided in a more portable,
secure electronic PDF format. We've heard your requests to lighten the
weight of travel home by eliminating heavy, spiral bound paper notebooks.
We want to provide a more dynamic & beneficial experience for all tutorial/course attendees. On-the-fly notations can be typed during your class using
the "Sticky Note" feature of Acrobat Reader 9 (provided for your convenience).
A laptop is required.

Take your notes To-Go and have them wherever you go.

Thank you to all attendees for your continued support and feedback over the past 25 years!

Instructors	Dr. Patrick Hwang, Rockwell Collins Mr. Michael Vaujin, Raytheon
About This Course	This course is a highly intensive short course on Kalman filtering and Kalman filtering applications. Emphasis in the course is on practical applications, but sufficient supporting theory is provided to give attendees the necessary tools for meaningful research and development work in the field. Considerable time is devoted to modeling, the most difficult aspect of Kalman filtering, in an application setting. There will be a high level of instructor/attendee interaction, designed to provide hands-on problem solving and solution discussions. The learning experience will also be supplemented by homework assignments to assist attendees in improving their understanding of course concepts.
Prerequisites	• A basic understanding of linear systems and random signal theory. • A thorough familiarity with matrix algebra principles.
Equipment Recommendation	• A laptop (PC or Mac) with full version of MATLAB™ 5.0 or later installed. This will allow you to work the problems in class and do the practice "homework" problems each evening. All of the problems will also be worked in class by the instructor, so this equipment is not required, but is recommended.
Course Schedule	DAY 1 Dr. Patrick Hwang, Rockwell Collins
	8:30 - Random Process Review Random variables, probability densities, Gaussian & multivariate Expectation, covariance matrix Random process, autocorrelation, Power Spectral Density (PSD), stationary & non-stationary Linear response, shaping filters 9:45 - State-Space Modeling From differential equations, power spectral densities & block diagrams Discrete time solution Mean and covariance response Markov and integrated Markov examples Transition and process covariance 11:00 - Random Process Simulation Vector random process simulation Autocorrelation & PSD from data Computer demonstration *12:00 - Lunch on your own* 1:30 - Kalman Filter System Integration Integration with complementary filtering GPS/inertial, GPS only, radar tracking, orbit & attitude determination integration examples State-space modeling Simplified KF derivation 2:45 - The Kalman Filter Simplified algorithm description Bias, random walk, and Markov examples Off-line error (covariance) analysis 4:00 - Alternate Kalman Algorithms State augmentation Sequential processing Known control inputs Other Kalman forms (including smoothing and “information” filter) Generalized Kalman Filters for correlated noises 5:00 - Day 1 ends
	DAY 2 Dr. Hwang
	8:30 - Kalman Theoretical Review Review of simplified “best linear” derivation vs. alternate conditional mean derivation Gaussian vs. non-Gaussian Equivalence to Wiener filter Relation to least squares 9:45 - Linearization and Nonlinearity in Kalman Filters Taylor series vs. perturbation Linearized and extended KF Linearization examples in GPS and orbit determination Nonlinear Kalman filters 11:00 - Application to GPS Navigation GPS measurement and error models Relative navigation Carrier phase differential (or real-time kinematic) GPS Global differential GPS (e.g. Starfire) *12:00 - Lunch on your own* 1:30 - Practical Kalman Filter Implementation Issues Divergence detection & causes Residual analysis Numerically robust KF Suboptimal filter analysis due to mismodeling 2:45 - More Kalman Filter Examples Computer demonstration, modeling and design Markov random process modeling Random walk characterization using Allan variances 4:00 - More Application Examples Range/bearing (rho-theta) example Simultaneous Localization And Mapping (SLAM) 2D example Relative navigation for network of users High stability clock modeling and time-transfer augmentation Carrier phase ambiguity resolution 5:00 - Day 2 ends
	DAY 3 Mr. Michael Vaujin, Raytheon
	8:30 - GPS Aided Inertial Design Basis for inertial navigation Inertial System error models Observability analysis 9:45 - Building Extended Kalman Filters Radar tracking of vertical body motion (nonlinear dynamics) Sled test tracking of horizontal motion (nonlinear measurements) 11:00 - Linearization & Practical Implementation Small angle error equations Gravity error modeling Integrated velocity error State Transition matrix computation Process noises & sensor random walks *12:00 - Lunch on your own* 1:30 - Multi-Sensor Fusion Derivation of measurement sensitivity for aiding devices: GPS, Odometer, Doppler radar Sensor error models 2:45 - Multi-Sensor Fusion (cont.) Derivation of measurement sensitivity for aiding devices: EM-log, Baroaltimeter Ground alignment (zero velocity updates) 4:00 - Suboptimal Analysis Two pass covariance analysis Error budget design analysis 5:00 - Day 3 ends
	DAY 4 Mr. Vaujin
	8:30 - Measurement Processing Sequential vs. batch Correlated measurements Differencing methods Delta-range measurements & Feedback considerations 9:45 - Integrity Monitoring CHI square editing Adaptive limits Receiver Autonomous Integrity Monitoring Filter Bank Integrity Monitoring 11:00 - Partitioning & Schmidt Filtering Motivation Covariance & Transition matrix partitioning Range Bias Error States Schmidt Consider State filtering *12:00 - Lunch on your own* 1:30 - Smoothing Classifications Fixed-point derivation Fixed-interval derivation Simple Examples 2:45 - Square Root Filtering Motivation Joseph’s Form Square root covariance filtering UD filtering 4:00 - Adaptive Estimation Residual tuning Magill adaptive filter Multiple Model filtering 5:00 - Day 4 ends
	DAY 4 Mr. Vaujin
	8:30 - Aided Inertial Navigation Example Discrete Strapdown mechanization Quaternion vs. DCM update Gravity models Altitude control 9:45 - Aided Inertial Navigation Example (cont.) Simple Kalman Filter mechanization Loosely vs. tightly coupled GPS aiding Delta-range vs. carrier phase 11:00 - Aided Inertial Navigation Example (cont.) Advanced Kalman Filter mechanization Ground alignment Coarse vs fine alignment Baroaltimeter Doppler radar 12:00 - Course ends
Materials You Will Keep	• A USB Drive with PDF electronic course notes used during the course. Bringing a laptop is highly recommended; power access will be provided. • A voucher for the following text or a substitute of your choice: Introduction to Random Signals and Applied Kalman Filtering, 3rd edition, John Wiley & Sons, Inc., 1996.
Continuing Education Units	2.7 (27 hours) Return to top of page