GPS/GNSS/IMU Integration for Robustness/Accuracy

Course Length:



This three and a half-day course 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.

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 simplest permissible representations. Optional exercises can therefore use any version of Matlab from within the past ten years. Principles shown in class will conform to formulations documented in the instructor’s text GNSS Aided Navigation & Tracking: Inertially Augmented or Autonomous that will be provided to each attendee.

What you will learn:

  • To prepare and integrate raw GNSS pseudorange and carrier phase measurements with raw data from gyros, accelerometers, and magnetometers adhering to a different time base.
  • 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 an 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 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 offers
  • Multiple advancements in RAIM, including independent extension to each separate measurement * Extensive description of tracking applications

Course Outline:

  1. Basic Motion. Motion in 1, 2, and 3 dimensions. Relative motion. Modes. Coordinate frames.
  2. Motion Involving Rotation. Angles. Gimbal lock. Direction cosines. Quaternions. Motion over ellipsoid.
  3. Inertial Navigation Fundamentals. 1- & 3-axis platforms. Gyros. Accelerometers. Geographic-vs-wander azimuth.
  4. Inertial Navigation Processing. Rotation and translation increments. Quantization effects. Task lists.
  5. Inertial Navigation Errors. Schuler. Closed form solutions. Intuitive insights. Motion-induced drift.
  6. Updating to Follow Dynamics. Thorough 1-axis channel (North, vertical) scrutiny. Sync. Estimation intro.
  7. Linear Estimation Development. From simple to full general case. Development followed by several examples.
  8. Estimation Algorithmic Designs. Practical issues. Transition matrix. Modeling. Extended & suboptimal forms.
  9. Performance with Departures from Theoretical Idealizations. Block & sequential forms. Nonlinearity. Inexact values. Crucial decisions.
  10. Satellite Navigation Fundamentals. 1, 2, 3, and 4 dimensions. Elliptical orbit parameters. Timing effects.
  11. Navigating with GPS. Range and pseudorange. ECEF. GPS orbits. ICD. 4_SV snapshot. GDOP.
  12. GPS/INS. Full & reduced dynamics. Differencing. Loose/tight/ultra. Process noise.
  13. Integrity. Definitions, approaches, outcomes. RAIM & extensions. Parity. Examples.
  14. GPS Carrier Phase: Catastrophic Error Avoidance. Integrated doppler. Sequential changes. Residuals. Sensitivities. Benefits.
  15. Block and Sequential Formulation. Exploiting the relation. GPS/INS segmentation. Full formulation with RAIM.
  16. Tracking Air-to-Air, Surface-to-Air, Air-to-Surface. Active or passive. Ballistic, projectile or orbiting. Cooperative or not.
  17. Track Support Functions. Transfer alignment. SAR. Stabilization. Surveillance. Collision avoidance.
  18. Real-world GPS Results with and without INS. Van & flight test. Flight paths, pseudorange & precise phase residuals.
  19. Unaided (“Free”) Inertial Coast Performance. Straight & turning flight. Position, velocity, and attitude error history.
  20. Robustness/Resilience. All functions’ data rates, features, challenges. Raw data on interface!!
  21. System Operational Considerations. Fusion. I/O. Timing. Software. V&V. Integration. Coordination. Confidence.


REGISTRATION:  There is no obligation or payment required to enter the Registration for an actively scheduled course.   We understand that you may need approvals but please register as early as possible or contact us so we know of your interest in this course offering.

SCHEDULING:  If this course is not on the current schedule of open enrollment courses and you are interested in attending this or another course as an open enrollment, please contact us at (410)956-8805 or Please indicate the course name, number of students who wish to participate. and a preferred time frame. ATI typically schedules open enrollment courses with a 3-5 month lead-time.   To express your interest in an open enrollment course not on our current schedule, please email us at

For on-site pricing, you can use the request an on-site quote form, call us at (410)956-8805, or email us at


  • James L. Farrell, Ph.D., is a former ION Air Nav Representative, a senior member of IEEE, a former local board member of AIAA, and a registered professional engineer in Maryland. Technical experience includes teaching appointments at Marquette and UCLA, two years each at Minneapolis Honeywell and Bendix-Pacific, plus 31 years at Westinghouse in design, simulation, and validation/test for modern estimation algorithms in navigation and tracking applications. He is author of Integrated Aircraft Navigation and of GNSS Aided Navigation and Tracking (2007), as well as chapters in books edited by C.T. Leondes and Cary Spitzer. He was a columnist for Washington Technology, and has written over a hundred journal and conference manuscripts. Active in RTCA (Washington D.C.) for the past several years, he served as co-chairman of Working Group #5 (Fault Detection and Isolation) within Special Committee SC- 159 for GPS Integrity. He has continued his teaching (on University campus as well as in both industry and conference seminars), while consulting for private industry, DOD, and University research.

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