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Course 546 Details

NEW! Course 546: Inertial Systems, Kalman Filtering and GPS / INS Integration (2.4 CEUs) On-Site Only
Instructors: Dr. Alan Pue, Johns Hopkins University, APL and  Mr. Michael Vaujin, Consultant


This 4-day course on aided navigation will thoroughly immerse the student in the fundamental concepts and practical implementations of the various types of Kalman filters that optimally fuse GPS receiver measurements with a strapdown inertial navigation solution. The course includes the fundamentals of inertial navigation, inertial instrument technologies, technology surveys and trends, integration architectures, practical Kalman filter design techniques, case studies, and illustrative demonstrations using MATLAB®.


  • Familiarity with principles of engineering analysis, including matrix algebra and linear systems.
  • A basic understanding of probability, random variables, and stochastic processes.
  • An understanding of GPS operational principles in Course 356, or equivalent experience.

Who Should Attend?

  • GPS/GNSS professionals who are engineers, scientists, systems analysts, program specialists and others concerned with the integration of inertial sensors and systems.
  • Those needing a working knowledge of Kalman filtering, or those who work in the fields of either navigation or target tracking.

Equipment You Should Bring

  • A laptop (PC or Mac) with full version of MATLAB 5.0 (or later) installed. 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.
  • These course notes are searchable and you can take electronic notes with the Adobe Acrobat 9 Reader we will provide you.

Materials You Will Keep

  • A color electronic copy of all course notes will be provided on a USB Drive or CD-ROM. Bringing a laptop to this class is highly recommended; power access will be provided. 
  • A black and white hard copy of the course notes, printed 3 slides to a page. 
  • Public Venue Attendees: Introduction to Random Signals and Applied Kalman Filtering, 3rd edition, by R. Grover Brown and Patrick Hwang, John Wiley & Sons, Inc., 1996. (Note: This arrangement does not apply to on-site contracts. Any books for on-site group contracts are negotiated on a case by case basis.)

Attendee Testimonials    PDF Course Outline     Dates and Locations     On-Site Information

Day 1, Morning

Introduction to INS/GPS Integration
  • Inertial navigation
  • Integration architectures
  • Example applications
Vectors and Coordinate Systems
  • Vector definitions
  • Coordinate transformations
  • Vector kinematics
Navigation Coordinate Systems
  • Earth model
  • Navigation coordinates
  • Earth relative kinematics

Day 1, Afternoon

Inertial Navigation Mechanization
  • Gravity model
  • Navigation equations
  • Implementation options
Inertial Sensor Technologies
  • Accelerometer technologies
  • Ring laser gyros
  • Fiber optic gyros
MEMS Technologies and INS Testing
  • Instrument technologies
  • INS technology survey and trends
  • INS testing

Day 2, Morning

Strapdown Computations
  • Quaternions
  • Orientation vector
  • Coning and sculling compensation
Navigation System Errors
  • Tilt angle definitions
  • Navigation error dynamics
  • Simplified error characteristics
System Initialization
  • INS static alignment
  • Transfer alignment
  • Simplified error analysis

Day 2, Afternoon

Inertial Aiding
  • Aiding techniques
  • Kalman filters
  • Aiding examples
GPS Receivers
  • Interfaces and timing
  • Measurement processing
  • Measurement errors
INS Aiding of Receiver Signal Tracking
  • Code and carrier tracking
  • Track loop design trades
  • Interference suppression

Day 3, Morning

Random Process Review
  • Random variables, probability densities
  • Gaussian & multivariate expectation
  • Covariance matrix, random process
  • Autocorrelation, power spectral density
  • Stationary & non-stationary linear response
  • Shaping filters
State Space Modeling
  • Models derived from differential equations
  • PSDs and block diagrams
  • Discrete time solution
  • Mean & covariance response
  • Markov & integrated Markov Examples
The Kalman Filter
  • Derivation and examples

Day 3, Afternoon

Kalman Filter Methods of Implementation
  • Tuning examples
  • Sequential vs. batch measurement processing
  • Measurement decorrelation
  • Matrix partitioning
Building Extended Kalman Filters
  • Radar tracking of vertical body motion with non-linear dynamics
  • Sled tracking of horizontal motion with non-linear measurements
  • Computer demos for both
Aided Navigator Example, Loosely Coupled
  • Local level psi-angle implementation
  • 15 state, PVT GPS aided
  • Practical implementation Considerations
  • Computer demo

Day 4, Morning

Smoothing & Prediction
  • Prediction recursive equations
  • Smoothing, fixed point
  • Fixed lag, fixed interval
  • Computer demos of all
Square Root Filtering
  • Motivation, UD factorization,
  • Square root covariance filtering,
  • Square root covariance smoothing
  • Computer demo
Square Root Information Filters
  • Motivation and theoretical development
  • Another aided navigator demo

Day 4, Afternoon

Adaptive Filtering
  • Residual analysis, on-line, off-line
  • Iterative residual analysis methods
  • Multiple model adaptive estimation
  • Computer demo
Unscented Kalman Filters
  • Unscented transforms & sigma points
  • Augmented & non-augmented filters
  • Application to navigation
  • Performance vs. EKF
  • Computer demo
Advanced Suboptimal Analysis
  • Effects of mis-modeling
  • Optimal covariance analysis
  • Two-pass error budget design analysis
  • Computer demo

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