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Course 557 Details

Course 557: Inertial Systems, Kalman Filtering and GPS / INS Integration (3.0 CEUs; EXPANDED TO 5 FULL DAYS) (Public and On-Site)

Instructors: Dr. Alan Pue, Johns Hopkins University, APL and Mr. Michael Vaujin, Consultant

Description

Course 557 (formerly called Course 556) has been expanded to a full five days based on attendee requests. This course on GNSS-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.

The extra half-day will allow for a fuller and more detailed development of the design of an aided navigation system, combined with a more detailed discussion of the use of lower quality IMUs, and advanced filtering techniques.

Prerequisites

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 the 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 Registration Form

Day 1, Morning

Introduction to INS/GPS Integration

Inertial navigation
Integration architectures
Example applications

Vectors, Matrices, and State Space

Vectors and matrices
State-space description
Examples

Random Processes

Random variables
Covariance matrices
Random process descriptions

Day 1, Afternoon

Kalman Filter

Filtering principles
Least squares estimation
Kalman filter derivation

Filter Implementation

Filter processing example
Off-line analysis
Filter tuning

Navigation Coordinate Systems

Earth model
Navigation coordinates
Earth relative kinematics

Day 2, Morning

Inertial Navigation Mechanization

Gravity model
Navigation equations
Implementation options

Inertial Sensor Technologies

Accelerometer technologies
Optical gyros
MEMS technologies
Technology survey

Strapdown Systems

Quaternions
Orientation vector
Coning and sculling compensation

Day 2, Afternoon

Navigation System Errors

Tilt angle definitions
Navigation error dynamics
Simplified error characteristics

System Initialization

INS static alignment
Transfer alignment
Simplified error analysis

Loosely-Coupled INS/GPS Design

Measurement processing
Filter design and tuning
Navigation systems update

Day 3, Morning

INS Aiding of Receiver Tracking

Code and carrier tracking
Track look deign trades
Interference suppression
Autocorrelation, power spectral density
Deep integration

Tightly coupled INS/GPS Design

Measurement processing
Filter parameter selection
Pseudo-range and delta pseudo-range measurement models

Multi-Sensor Integration

Terrain aiding and relative GPS
Carrier phase differential integration
GPS interferometer/INS integration

Day 3, Afternoon

Building Extended Kalman Filters

Linearized and extended Kalman filters
Radar tracking of a vertical body motion with non-linear dynamics
Radar tracking of an accelerating body with non-linear measurements

Implementation Considerations

Keeping a covariance matrix well-conditioned, symmetric, and positive definite
Sequential vs batch measurement processing
Methods of measurement correlation and de-correlation

Discreet Implementation of the Strapdown Equations

Attitude updates and TOV of the acceleration
Propagating the position DCM
High rate vs low rate routines
Effects of errors in initialization & IMU data

Day 4, Morning

Aided Psi-Angle Navitator

Description and demonstration of a loosely coupled 15 state Psi-angle wander azimuth navigator flying an aircraft type trajectory
Homework problems

Partials of Measurement Equations

Techniques for taking partials
Psi-angle and Phi-angle feedback to strapdown
Homework solutions

Initialization and Process Noise

Strapdown and covariance matrix initialization
Process noise for vertical deflections/anomaly & velocity/attitude random walk
Typical sensor error models: random constant, random walk & first order Gauss Markov

Day 4, Afternoon

Aided Phi-Angle Navigator

Description and demonstration of a Phi-angle north-slaved navigator
Modeling position error as latitude/longitude error
Modeling position error as navigation frame tilt error
Comparison of popular state dynamics matrix elements
Navigation in ECEF coordinates

Ground Alignment & Integrated Velocity Matching

Gyro-Compassing, zero velocity & zero earth rate observations
Small azimuth static alignment & leveling
Integrated true velocity error, mapping into delta-range
Large azimuth static alignment, advanced methods
Aiding with a 3 axis magnetometer

Attitude Matching & Use of Inexpensive IMUs

Attitude matching & boresight error states
Considerations for use of very inexpensive IMUs
Non-holonomic motion constraints
Process noise for un-modeled states
Matrix partitioning for computational efficiency
Using consider states

Day 5, Morning

Measurement Editing & Adaptive Filters

Online and offline residual analysis
Advanced methods of outlier detection & rejection
Multiple Model Adaptive Estimation
Application to carrier phase integer ambiguity resolution

Methods of Smoothing

Optimal prediction & Fixed Interval smoothing
Fixed Point & Fixed Lag smoothing
Application to navigation testing

Square Root Filtering

Day 5, Afternoon

Suboptimal Covariance Analysis

Effects of mis-modeling errors
Optimal & sub-optimal (two pass) covariance analysis
Error budget & reduced state analysis

Unscented Kalman Filters

Sigma points & the Unscented Transform
Performance against the EKF
Augmentation & application to navigation
Spherical Simplex Sigma Points
Square Root UKFs

Particle Filtering & 2nd Order EKFs

Bootstrap particle filter (PF)
Multi-modal position solutions
2nd Order EKFs (2EKF)
Cage Match! PF vs 2EKF vs UKF vs EKF