Kalman Filtering

Complete Seminar Details

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

REVIEWS AND BASIC KALMAN FILTER THEORY

Review of Probability and Random Process Theory

• Probability Theory
• Random Variables, Vectors, and Distributions
• Normal Distribution
• Moments
• Random Process
• White Noise
• Markov/Gaussian Markov Process

Review of Linear and Nonlinear Systems

• Discrete Time System
• Continuous Time System
• Observability/Controllability
• Stability

Basic Estimation Theory

• Bayesian Estimation Theory
• Least Square Estimate
• Minimum Variance Estimation
• Batch vs. Recursive Estimation Algorithms

Kalman Filter: Architecture and Algorithm

• Basic Kalman Filter: Architecture and Algorithm
• Intuitive Interpretation and Understanding
• Extended Kalman Filter: Architecture and Algorithm
• Generic Recursive Estimator Architecture
• Fixed Gain Estimator

Case Study 1: Kalman Filters for Precision Clock

• Clock Model
• Simple First-Order Filter
• Second-Order Filter
• Third-Order Filter

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

Day Two

MORE KALMAN FILTER THEORY AND PRACTICAL APPLICATION CONSIDERATIONS

Kalman Filters: Derivation

• Orthogonality Approach
• Innovation Approach

Kaman-Bucy Filter

• From Discrete to Continuous
• Steady-State Filter

Numerical Stability and Alternative Forms

• Li/Wu Approach
• Alternative Forms of Kalman Filter Equations
• UDU Factorization

Application Approach: General Guidelines

• Stability Process Model
• Establishing Measurement Model
• Evaluate Model Uncertainty
• Evaluate Process Noise
• Time-Matching
• Divergence and Working with White Noise Assumption
• Numerical Stability

Case Study 2 : GPS Navigation

• GPS Fundamentals
• GPS Measurements and Errors
• Memory-Less Estimates vs. Kalman Filtering

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

Day Three

MORE APPLICATIONS AND CASE STUDIES

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

• Architecture
• Attitude Propagation Approache
• Attitude Propagation Error Model
• Star-Tracker and Error Model
• Kalman Filter Design for Attitude Determination
• Example: GOES SIAD Design

Case Study 4: Radar/Laser Tracking

• Radar and Laser LOS Tracking Problem
• Math Model
• Kalman Filter Design

Computer Lab Session 3: Radar Tracking

Case Study 5: Integrated Strap-Down Inertial Navigation

• Gyros and Error Models
• Accelerometers and Error Models
• Strapdown Inertial Navigation Equations
• Inertial Navigation Error Model
• Aiding Sensors
• GPS/Inertial Integration: Overview
• Time-Matching and Lever-Arm Compensation

Case Study 6: Precision Navigation Using GPS Carrier-Phase

• GPS Carrier-Phase Measurements
• GPS Carrier-Phase-Based Precision Navigation
• GPS Carrier-Phase-Based Attitude Determination

Day Four

HANDS-ON SESSIONS

Computer Lab Session 4: Kalman Filter Development

Computer Lab Session 5: Kalman Filter Development

Units 2.4 CEU (24 hours of instruction)

Sponsor Background:

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.