CS461D

ADVANCED MATLAB®
KALMAN FILTERING APPLICATIONS

The "Advanced MATLAB® with Kalman Filtering Applications" isahands-on course providing a comprehensive understanding of the applicationofMATLAB® to Kalman filtering applications for estimating or predictingquantitieswhich cannot be observed with perfect accuracy. Unlike many othercourseson this subject, this course provides a pragmatic understandingof the Kalman-Bucyfiltering process without obscuring the student's understandingby dwellingon elegant mathematical formalism. With MATLAB® , Kalman-Bucyfilters and highspeed personal computers make solvable a large number ofproblems which previouslywere intractable.

An interest in learning how to apply MATLAB®'s capabilities to performKalmanfiltering applications. It is assumed that students taking this courseunderstandthe basic concepts of Kalman filtering, including a good workingknowledgeof matrix algebra. Familiar with MATLAB® would also be helpful.

The principal objective of this course is to is to understand the usesofand to gain competence in the in application of MATLAB®'s capabilitiesinsolving digital signal processing problems. Specific learning objectivesforthis course are:

• To develop intuitive skills for modern estimation process by examples of "classic" problems and their solutions;
  
• To understand MATLAB®'s notations and methods for formulating Kalman filters in solving estimation and prediction problems
  
• To gain skills in writing MATLAB® Kalman filter programs; and,
  
• To gain experience in using MATLAB® on Kalman filtering applications through hands-on workshops;
  

MATLAB® has become the de facto standard in advanced mathematical analysisbyengineers and scientists throughout the world. This course is a comprehensivehands-ontraining program on the application of MATLAB® to the implementationof Kalmanfilters. In recursive estimation, the central topics are state-representationofsystem dynamics, measurement models, and the definition of the estimationerrorto be minimized. Once these are understood, a formal statement ofthe estimationproblem follows naturally. The solution will be presentedin the intuitivelyappealing predictor - corrector form of the Kalman estimatorequation. Successfulapplication of Kalman techniques often requires experienceand good judgmentin constructing appropriate mathematical models. Typicalconsideration willbe illustrated by working with several examples suchas ballistic missiletracking, estimation of orbital parameters, and theprediction of locationand velocity of submarine targets.

Following the introductory material, applications and extensions of theKalmanfilter will be presented and discussed. Central to the basic propertiesofthe Kalman Filter are the properties of the covariance equation -- amatrix-Ricattiequation. The properties of this equation, such as controllability,observability,and stability, are discussed in detail. As a logical extensionof Kalmanfiltering, smoothing is presented and the important smoothingalgorithmsare developed. Lastly, the extended Kalman filter problem isdescribed andillustrated by using a simple satellite attitude estimationproblem as anexample of the application of the extended Kalman filter process.

Further insight is provided by hands-on student participation throughtheuse of real-time MATLAB® programs and visualization tools developed forhands-onstudent participation. Students taking this class will receiveextensivecourse notes and a student version of MATLAB® .

MATLAB® is a trade mark of The Math Works, Inc.

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