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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

Expanded to a full five full days based on attendee requests, this course on GPS-aided navigation will thoroughly immerse you 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®.

Five fulls days allow for a fuller and detailed development of the design of an aided navigation system, combined with a 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. However, 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 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 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

Numerical Preliminaries and Considerations

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

Discreet Time Strapdown Implementation

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 an aided Psi-angle wander azimuth navigator flying an aircraft type trajectory

Aided Phi-Angle Navitator

Description and demonstration of an aided Phi-angle north-slaved navigator flying and aircraft type trajectory
Modeling position error as latitude/longitude error
Modeling position error as navigation frame tilt error
Comparison of popular state dynamics matrix elements

Partials of Measurement Equations

Techniques & tricks for taking partials, examples
Psi-angle and Phi-angle feedback to strapdown
Pros and cons of the 3 different Navigator types

Day 4, Afternoon

Initialization and Process Noise

Strapdown and covariance matrix initialization
Process noise for gravity & random walk
Common sensor error models: random constant, random walk & Gauss Markov

Measurement Editing and 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
Applications to navigation testing

Day 5, Morning

Square Root Filtering

Square root covariance filtering and smoothing
Information filter derivation
Square root information filters
UD factorization and filtering

Suboptimal Covariance Analysis

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

Unscented Kalman Filters

Sigma points and the unscented transform
Performance against the EKF
Augmentation and application to navigation
Spherical Simplex Sigma Points
Square Root UKFs

Day 5, Afternoon

Ground Alignment and Integrated Velocity

Gyro-Compassing, zero velocity & zero earth rate observations
Large azimuth static alignment, advanced methods
Small azimuth static alignment & leveling
Ground alignment observability examples
Integrated true velocity error, mapping into delta-range

Attitude Matching and Using Inexpensive IMUs

Attitude matching & boresight error states
Considerations for use of very inexpensive IMUs
Non-holonomic motion constraints
Magnetometer aiding
In class measurement equation exercise
Matrix partitioning for computational efficiency

Particle Filtering

Bootstrap particle filter (PF)
Multi-modal position solutions
Particle filter example
Applications to navigation