GPS/GNSS/IMU Integration for Robustness/Accuracy Training

GPS/GNSS/IMU Integration for Robustness/Accuracy Training


GPS/GNSS/IMU Integration for Robustness/Accuracy Training Course Description

This four-day GPS/GNSS/IMU Integration for Robustness/Accuracy Training provides extensive coverage of multisensor integration by flight-validated methods. The instructor is the author of innovations in carrier phase, integrity, inertial error propagation (Matlab program for long term, commonality with tracking for short-term), and practical estimation techniques. It can benefit anyone involved in GNSS, inertial navigation or tracking, or any integrated combination.

Motivation was prompted by vulnerability jamming and spoofing in current operations, drawing urgent attention toward robustness in satellite navigation (GNSS). Primary attention is given to GNSS (satellite) and inertial navigation, either used separately or together, with additional sensors (e.g., magnetometer, radar) also included. Both navigation and tracking of external objects are addressed, illuminating similarities and differences among applications.

Most operations don’t require pinpoint instantaneous location in minuscule volumes, but dynamic accuracy remains crucial (e.g., projecting over a minute ahead for collision avoidance). Prudence then urges precision in dynamics while accepting adequate position without laborious efforts vulnerable to catastrophic errors. The goal is met through sequential differencing of carrier phase and separate correction with pseudorange measurements, all subjected to rigorously derived integrity testing. Tight integration only begins to describe the approach.

The course begins with fundamentals, showing clear intuitive connection of mathematics to physical examples, followed by a natural transition to advanced material. Practical realities are given top priority, by delivering maximum effectiveness from the simplest permissible representations.

GPS/GNSS/IMU Integration for Robustness/Accuracy TrainingRelated Courses:

Duration:4 days

Skills Gained:

to prepare and integrate raw GNSS measurements (pseudorange and carrier phase, with raw data adhering to a different time base (from gyros, accelerometers, magnetometers)
to achieve state-of-the-art performance from low-cost equipment, counteracting long-term drifts
to follow direct step-by-step procedures, leaving you with entirely new depth of understanding closed form solution for inertial error propagation, tilt and velocity errors; intuitive results for durations up to a tenth Schuler period
analytical characterization for average rate of drift from pseudoconing
an extensive array of motion-sensitive errors for gyros and accelerometers, including rectification effects
dramatic simplification of inertial error propagation and in Kalman filter models
commonality of short-term INS error propagation with simple track formulation
carrier phase benefits including elimination of all problems involving integer ambiguity and interoperability
description of FFT-based GPS processing and major benefits it offer
multiple advancements in RAIM including independent extension to each separate measurement tracking application
extensive description of related operations (transfer alignment, SAR motion compensation, etc.)

Customize It:

With onsite Training, courses can be scheduled on a date that is convenient for you, and because they can be scheduled at your location, you don’t incur travel costs and students won’t be away from home. Onsite classes can also be tailored to meet your needs. You might shorten a 5-day class into a 3-day class, or combine portions of several related courses into a single course, or have the instructor vary the emphasis of topics depending on your staff’s and site’s requirements.

Course Content:

Basic motion

2-D and 3-D position, velocity, acceleration
Absolute and relative motions
Coordinate frames of interest
Euler angles, direction cosines, and quaternions

Matrix math

Summations and simultaneous equations
Physical and probabilistic representations
Complex dynamics reduced t
intuitive form

Further properties of motion

Rotational (gimbal lock)
Coupled translation/rotation
Gravitation vs gravity over a spheroidal earth
Vibration and its ramifications

Inertial nav fundamentals

Mechanical and computational stabilization of platforms
Space stable and geographic references
Specific force from accelerometers
Absolute angular rate from gyros
Velocity and attitude from processing of increments

Further Inertial nav issues

Coning and sculling
Motion-sensitive degradations

IMU role in aiding; beginnings of integration

Uncoupled vertical channel
Schuler and short-term error propagation solutions
Wander azimuth


Fundamentals and definitions
KF, EKF, block vs recursion
Penrose, augmentation
1-state and 2-state examples
Bierman UD factorization


General block diagram
Subtle ramifications of c
State minimization
Model fidelity
Suboptimal: when and when NOT

Span of influential updates

Data window
MATLAB program for illustration
Consequences of violation
Un-observability and false observability

Navigation with GNSS data

From ICD message t
SV position & velocity
-range and carrier phase
Backup t
transmit time
Classical 4-SV solution


Across receivers, SVs, and time
Correlations introduced
MATLAB pre-whitening algorithms


Classical FDI/FDE
Extended RAIM
Single-measurement RAIM
Residual monitoring
Outlier editing in real time

GNSS/Inertial integration

Conventional (pre-GPS) form
Low cost for avoidance of overdesign
Loose, tight, ultra-tight, deep
Pivotal value of Morrison insight
Dramatic simplification of dynamics

1-sec changes in carrier phase

Advantage over delta range/Doppler/delayed states
Formation of residuals
Formation of sensitivities

Robust configuration: Segmented GNSS/IMU

Block diagrams, symbolic and detailed
Long list of robustness features
Rationale for precision in dynamics only
Extension t
precise positioning


6-state, 7-state, 9-state
Channel separation: when and when NOT
Mitigation of nonlinearities
Concurrent stabilization

Tracking Application similarities and differences

Orbit determination
Re-entry vehicle
TWS littoral surveillance

Illustrative Applications

Transfer alignment
SAR motion compensation
Mutual Surveillance
Collision avoidance
Cooperative Engagement

Experimental results

Sparse data with and without cueing
Decimeter/sec in flight without IMU
cm/sec in flight with IMU

Practical issues

Processing of magnetic heading data
Coordination of simulation, test, real-time operation
MATLAB program for long term coast


Extended coast durations (welcome back, 1970!)
Beware of aliasing; MATLAB program example
Classical/Current/Future Integration

Extended operation

Additional sensors (air data, Doppler, DME, eLoran, r-f, vision, terrain or mag patterns)
Support of additional processes (interferometry, conformal arrays, beamforming, null steering)
Additional applications (UAV, UWV, driverless cars, etc.)

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Time Frame: 0-3 Months4-12 Months

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