| With Applications to Orbits/Target Tracking/GPS and Navigation|
ATI's Applications-Oriented Kalman Filtering course
This applications-oriented course provides a
comprehensive overview of the Kalman filter. The course
begins with a brief review of probability, stochastic
processes, dynamics and modeling of systems. This is
followed with an in-depth discussion of estimation theory
and methods, concluding with the derivation of the
Kalman filter algorithm.
The remainder of the course focuses on the practical
use of the Kalman filter. Methods of implementing the
Kalman filter algorithms are discussed, including
initialization and convergence.
Applications of the Kalman filter are presented in
several areas including: target tracking, orbit
determination, navigation and the Global Positioning
System (GPS). Participants will receive a complete set of
Dr. C. Allen Butler is a recognized expert in the field of
Multi-Sensor Correlation, Kalman Filtering and Multi-Target
Tracking, with over 15 years
experience in both theoretical and
engineering development of correlation
and tracking systems. As a senior
associate with D. H. Wagner Associates,
he has worked on the development of
several Navy, Air Force, and Army
tracking and fusion systems. He
recently developed and implemented
new algorithms for the Composite
Combat Identification (CCID) program under the Navy's
Missile Defense FNC.
Dr. Donald A. Kelly received his Ph.D. in Electrical
Engineering from Colorado State University and MSEE
from the University of Colorado. Dr. Kelly has more than
17 years experience in engineering,
specializing in estimation and navigation.
He is an expert in estimation and Kalman
filtering with applications to orbit
determination, multi-target tracking and
real-time systems, and navigation/GPS.
Dr. Kelly is principal of AdvanTech, which
specializes in navigation/GPS, systems
engineering, and software engineering.
Most recently, he has supported the
Navy in developing real-time Kalman trackers, and
supported the Air Force in systems engineering and
analysis for air-to-air and air-to-surface weapon systems.
Previously he was involved in spacecraft attitude and orbit
Contact these instructors (please mention course name in the subject line)
What you will learn:
- Batch and recursive estimation; when to use which method.
- Kalman filter implementation and diagnostics.
- Applications to orbit determination and target tracking.
- Current literature sources and software packages.
- Fundamentals. A review of probability, statistics, stochastic and random
processes. The basics of matrix manipulation and linear system theory.
Discussions of covariances, correlation, and Gaussian distribution.
- Dynamics and Modeling. Formulation of process and measurement
models. Forming the state-space representation from differential dynamic
equations. Structure of linear and nonlinear models, including time variant
and time invariant cases.
- Estimation Theory. Definition of filtering, prediction and smoothing.
Derivation of a linear, unbiased, minimum variance, optimal estimator.
Least-squares, weighted-least-squares, maximum likelihood, and Bayesian
estimation algorithms. Handling of a priori information, development of
recursive estimation approaches.
- Derivation of the Kalman Filter. Step-by-step derivation of the Kalman
filter algorithm. Discrete and continuous versions. Various alternate forms of
the Kalman filter and suggestions for when to use which Kalman filter form.
- Implementation Issues Using the Kalman Filter Algorithms.
Initialization and convergence criteria. Modeling errors and concerns,
process and measurement noise issues. Various integration algorithms and
techniques. Square-root filter algorithm and fading memory method.
Linearization of nonlinear systems.
- Advanced Topics Current Literature and Software Packages. Adaptive
Kalman filtering, identification methods. Using Kalman filtering for process
control. Recent developments in Kalman filtering and applications.
- Target Tracking. An overview of the basics of target tracking are presented,
followed by the formulation of two kinematic tracking process models.
Applications of target tracking for missile guidance and radar target tracking
are discussed. The Hyperbolic In-Air Tracking System (HITS) is discussed,
emphasizing the tracking algorithms, real-time code, and accuracy.
- Orbit Determination. A discussion of the dynamics involved for spacecraft
orbit is followed by the development of a process model for orbit
determination. A range/range-rate measurement model is derived, and
examples using both batch and recursive methods are presented. The
dynamic model for spacecraft orbit is developed, and a lab exercise
- GPS and Inertial Navigation. An overview of the Global Positioning
System (GPS) is presented, followed by a discussion on inertial navigation
systems. Integrated INS/GPS models for aircraft and smart munitions are
developed, including the design of a reduced-order flight filter.
Tuition for this three-day course is $1790 per person at one of our scheduled public courses. Onsite pricing is available. Please call us at 410-956-8805 or send an email to ATI@ATIcourses.com.