Course 447: Applied Kalman Filtering

INSTRUCTOR CHANGE	Dr. Larry Levy established our intensive course on Kalman Filtering in November of 1989. Some of you may have been there! We are extremely sorry to report that Larry died on April 21, 2008 after a long illness. We will miss his excellent, vigorous and always exciting teaching style. Larry was a teacher in the truest sense, always caring that his class was “with him” and doing his best to get across the obtuse technical concepts he was portraying in the clearest manner possible. Larry was the finest of men and his joyful spirit remains with us.
New 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 either the student version or regular version of MATLAB™ 4.0 installed. If you do not have MATLAB™ 4.0, we will provide CDs with the student version of the software for the use in class ONLY. 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, PSDs & 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 analysis 4:00 - Alternate Kalman Algorithms State augmentation Sequential processing Known control inputs Other Kalman forms Suggested homework 5:00 - Day 1 ends
	DAY 2 Dr. Hwang
	8:30 - Linearization in Kalman Filters Taylor series vs. perturbation Linearized and extended KF Linearization in GPS/inertial navigation 9:45 - Application to GPS Navigation Integration levels GPS measurement and error models GPS/inertial navigation Stand-alone GPS navigation 11:00 - Practical Kalman Filter Implementation Issues Divergence detection & causes Residual analysis Numerically robust KF Suboptimal filter analysis due to mismodeling Aided inertial design & analysis *12:00 - Lunch on your own* 1:30 - 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 2:45 - More Kalman Filter Examples Computer demonstration, modeling and design Orbit determination linearization Range/bearing (rho-theta) 2D example 4:00 - More Application Examples Relative navigation for network of users High stability clock modeling and time-transfer augmentation Rigorous modeling of carrier phase continuity 5:00 - Day 2 ends
	DAY 3 Mr. Michael Vaujin, Raytheon
	8:30 - GPS Orbit Determination Inverse GPS navigation perspective Orbit & measurement models Single vs. multi-satellite estimate Paradigm example analysis 9:45 - GPS Aided Inertial Design Basis for inertial navigation Inertial system error models Computer demonstration of off-line Kalman design Observability analysis 11:00 - Computer Demo On Building Extended Kalman Filters Radar tracking of vertical body motion (nonlinear dynamics) Sled test tracking of horizontal motion (nonlinear measurements) *12:00 - Lunch on your own* 1:30 - Linearization & Practical Implementation Small angle inertial error equations Gravity error states Integrated velocity error states High rate State Transition Matrix calculation Process noises & sensor random walks 2:45 - Multi-Sensor Fusion Derivation of measurement sensitivity equations for aiding devices: VMS, GPS, Doppler radar, EM-log Use and limitations Sensor error models 4:00 - Advanced suboptimal Analysis & KF design Error budget design analysis Computer demo: suboptimal & error budget analysis for aided inertial navigation design 5:00 - Day 3 ends
	DAY 4 Mr. Vaujin
	8:30 - Measurement Processing Sequential processing vs, batch De-correlating correlated measurements Methods of single differencing Forming Delta Range residuals Feedback considerations 9:45 - Integrity Modeling Two pass CHI square editing Dynamic limits Receiver Autonomous Integrity Monitoring Filter Bank Integrity Monitoring Fault detection and exclusion 11:00 - Partitioning & Schmidt Filtering Covariance and state transition matrix partitioning Range bias error states Schmidt “Consider State” filtering *12:00 - Lunch on your own* 1:30 - Smoothing and Prediction Prediction recursive equations Smoothing classifications Fixed-point & fixed-interval derivations Simple examples 2:45 - Square root filtering and Smoothing Motivation Square root covariance filtering and smoothing UD filtering 4:00 - Adaptive Filtering Residual tuning filter for Q and R Magill adaptive filter (differential ambiguity fixing) Multiple Model filtering (MMF) 5:00 - Day 4 ends
	DAY 4 Mr. Vaujin
	8:30 - Off-Line Aided Inertial Navigation Examples I MatlabTM implementation of discrete strapdown equations Navigation using tactical grade IMU High rate state dynamics matrix 9:45 - Off-Line Aided Inertial Navigation Examples II GPS clock error models Use of pseudorange bias error states for measurement editing 11:00 - Off-Line Aided Inertial Navigation Examples III Differential measurements RTK example Course review; Q & A session 12:00 - Course ends
Materials You Will Keep	• A set of notes containing copies of all transparencies used during the course. • 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