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Kalman Filtering



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This course provides a thorough knowledge of Kalman Filtering, its theoretical origin (Kalman Filter derivation), and how to apply Kalman Filtering to real-world physical systems. Pertinent theoretical and applications background material from probability, random process, estimation, and linear systems is addressed. Dynamic and measurement modeling for Kalman Filtering includes reviews of state-space formulations and required elements from linear systems theory. Fee per person: $2415.

UCLA Extension


UCLA Extension



Who Should Attend?

Engineers and scientists

The Kalman filter is probably the most successful and widely-used part of so-called "modern control theory." It has been used as the central piece of the algorithm for many applications in aircraft/ship/ground vehicle navigation, spacecraft attitude determination, orbit determination, missile guidance and control, RF antenna/laser terminal target acquisition/tracking, RF/optical signal acquisition and tracking, seismic data processing, medical signal processing, and other fields in the industry.

This course is designed for practitioners, such as system engineers, system analysts, software engineers, hardware engineers, and project managers, as well as military operational personnel who want to develop, streamline, or enhance their knowledge and experiences in Kalman filters. Instruction provides a solid foundation for both the basic theory and practical application of Kalman filtering. Specific case studies are provided to illustrate the latter, including GPS navigation, integrated inertial navigation, precision navigation using GPS carrier-phase, spacecraft stellar-inertial attitude determination, precision clock, and radar/laser target tracking.

The course is unique in providing participants with a ready-to-use, step-by-step approach for employing Kalman filtering to their practical applications. Skills are taught based on the instructors' combined 40 years of experience in Kalman filter design, analysis, tuning, implementation, validation, and verification. Detailed discussions are provided on the hardware and software architectures of Kalman filter-based systems, as well as system integration issues, such as time-tagging and precision time matching of sensor measurements, numerical stability, and divergence prevention. Lectures are further augmented by computer lab sessions using MATLAB to help participants develop insights through hands-on experience. The lab sessions have been further enhanced for this course based on positive feedback received from prior participants.

Using the knowledge and skills gained through this course, participants should be able to design Kalman filters for their specific fields; analyze the performance; develop the system, hardware, and software architecture; and resolve problems encountered in system integration, validation, and verification.

UCLA Extension has presented this highly successful short course since 2005.

Course Materials

The texts, Applied Optimal Estimation, Arthur Gelb, editor (MIT Press, 1974) and Stochastic Models, Estimation, and Control, Volumes I-III, Peter S. Maybeck (Academic Press, 1984); lecture notes; and published papers are distributed on the first day of the course. The notes are for participants only and are not for sale.

Daily Schedule

Day One


Review of Probability and Random Process Theory

Review of Linear and Nonlinear Systems

Basic Estimation Theory

Kalman Filter: Architecture and Algorithm

Case Study 1: Kalman Filters for Precision Clock

Computer Lab Session 1: Design and Analysis of Kalman Filter for Precision Clock

Day Two


Kalman Filters: Derivation

Kaman-Bucy Filter

Numerical Stability and Alternative Forms

Application Approach: General Guidelines

Case Study 2 : GPS Navigation

Computer Lab Session 2: Develop an Estimator for 2D GPS (I)

Day Three


Case Study 3: Spacecraft Stellar/Inertial Attitude Determination (SIAD)

Case Study 4: Radar/Laser Tracking

Computer Lab Session 3: Radar Tracking

Case Study 5: Integrated Strap-Down Inertial Navigation

Case Study 6: Precision Navigation Using GPS Carrier-Phase

Day Four


Computer Lab Session 4: Kalman Filter Development

Computer Lab Session 5: Kalman Filter Development

Units 2.4 CEU (24 hours of instruction)

Sponsor Background:

UCLA Extension is one of the largest providers of continuing education in the United States. For more than 40 years, it has presented quality technical and management short courses for engineers and managers seeking to keep abreast of new and rapidly changing technologies. The instructors -- drawn from academia, industry, and government -- are well-respected experts in their fields who present both theory and practice.

The courses range from two-to-five days in length and attract participants from across the United States and Internationally. Subject areas include electrical, materials, and mechanical engineering as well as computer and communications engineering and technical management. Nearly 100 courses per year are held on the UCLA campus in Los Angeles. Many of them are also presented under contract at company locations across the country and abroad.


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