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Geomatics Program | School of Forest Resources and Conservation | University of Florida

Course Syllabus

pring XXXX – Section XXXX

SUR6535: GPS-INS Integration

Catalog Description

Principles of inertial navigation and its integration with GPS; coordinate frames, modeling linear motion and rotational motion, mechanization of inertial navigation sensor measurements, space state representation of system errors and linear state equations.

Credits: 3

Timeline: Lecture R 5-7

Office Hours open door


Dr. Ahmed Mohamed

Office: 406A Reed Lab, Phone: 392-3465 Email:


Classroom lectures prepared and presented by a different student each week; discussions moderated by the instructor; lab project data collected, analyzed and presented by students under instructor’s supervision


  1. Distinguish between dynamic and kinematic modeling and Identify observables and contemporary systems suitable for kinematic modeling

  2. Review basic mathematical techniques used in kinematic modeling, identify reference frames, and perform transformations between them

  3. Explore the geometric figure of Earth and its gravitational and gravity fields and model gravity on the reference ellipsoid

  4. Discuss basic linear motion modeling equations in inertial, terrestrial, and navigation reference frames

  5. Analyze the state model for kinematic geodesy

  6. Model the rotational motion matrix using DCM, Quaternion, and Euler’s angles

  7. Mechanize the inertial navigation system (INS) equations in terrestrial and navigation reference frames

  8. Propagate INS errors in inertial, terrestrial, and navigation frames using linear state models

  9. State the optimal estimation problem through the Kalman filter approach

  10. Derive the Kalman filter algorithm in the navigation context

  11. Apply the discrete Kalman filter algorithm to the problem of GPS-aided inertial navigation system

  12. Lab project: Collect, process, and analyze GPS and INS data sets in a dynamic environment and present and discuss results in professional/academic setting.


Course attendees are assumed to have solid mathematics background especially vector calculus and matrix algebra

Co-requisite(s): None

Course Text (Required)

Schwarz KP and M Wei 2000. INS/GPS Integration for Geodetic Applications. Department of Geomatics Engineering, University of Calgary. Hard copies and pdf files available from the instructor (author permission granted).

Other Text

AGARD: Strapdown Inertial Systems, AGARD Lecture Series No. 95. North Atlantic Treaty Organization, May 1978.
Britting, K.R. Inertial Navigation Systems Analysis, Interscience, New York, 1971
Brown, R.G. and P.l.C. Wang Introduction to Random Signal Analysis and Kalman Filtering, Second edition, John Wiley and Sons, New York, 1992
Chatfield, A.B. Fundamentals of High Accuracy Inertial Navigation. Vol. 174, Progress in Astronautics and Aeronautics, American Institute of Aeronautics and Astronautics, Inc. Reston, Virginia 1997
Farrell, J.L. and Mathew Barth, The Global Positioning System and Inertial Navigation, McGraw Hill, New York, 1999
Gelb,A. (ed.) Applied Optimal Estimation. MIT Press, Cambridge, Mass., 1974
Heiskanen, W.A. and H.Moritz Physical Geodesy. Freeman and Company, 1967
Hofmann-Wellenhof, B., H. Lichtenegger J. Collins. GPS - Theory and Practice, Springer-Verlag, 1997
Jekeli C. Inertial Navigation Systems With Geodetic Applications, Walter de Gruyter, October 2000

Kleusberg, A. and PJ.G. Teunissen GPS for Geodesy. Lecture Notes in the Earth Sciences # 60, Springer Verlag, 1996

Lawrence, Anthony, Modern Inertial Technology, Springer, New York 1998.
Merhav S. Aerospace Sensor Systems and Applications. Springer-Verlag, New York, 1996.
Parkinson, Bradford W. and James J. Spilker (eds). Global Positioning System: Theory & Applications. AIAA 1996

Rogers, Robert M. Applied Mathematics in Integrated Navigation Systems. American Institute of Aeronautics and Astronautics; Third edition 2007

Salychev, 0.S. Inertial Surveying: ITC Ltd Experience, Baumann MSTU Press, 1995.

Seeber, G. Satellite Geodesy: Foundations, Methods and Applications, de Gruyter, Berlin, 1993.
Siouris, G.M. Aerospace Avionics Systems, Academic Press Inc., San Diego, 1993
Stieler, B. and H. Winter Gyroscopic Instruments and Their Application to Flight Testing, AGARDograph No. 160, vol 15, North Atlantic Treaty Organization, September 1982
Schwarz, K.P. Inertial Surveying and Geodesy, Reviews of Geophysics and Space Physics, Vol. 21, No. 4, May 1983
Schwarz, K.P. and M. Wei. A Framework for Modelling Kinematic Measurements in Gravity Field Applications, Bulletin Géodésique, Vol. 64, pp. 331-346, 1990
Schwarz, K.P., M.A. Chapman, M.E. Cannon, P. Gong An Integrated INS/GPS Approach to the Georeferencing of Remotely Sensed Data. Photogrammetric Engineering and Remote Sensing, 59, 11. pp. 1667- 1674, Nov. 1993
Schwarz, K.P. and M. Wei Modelling INS/GPS for Attitude and Gravity Applications. Proc. Third International workshop on High Precision Navigation, Stuttgart, April 1995. Published by Dümmler, Bonn, 200-218, 1995
Schwarz, K.P. and M. Wei INS/GPS Integration for Geodetic Applications. Lecture Notes ENGO 623, U of C, 1996
Titterton, D. and J. Weston. Strapdown Inertial Navigation Technology. IEE; 2005

Wong, RV.C. Development of a RLG Strapdown Inertial Survey System. UCSE Publication No. 20027, Department of Surveying Engineering, University of Calgary, 1988.


Matlab or similar


Lecturing: Reed Lab 302



Assignments, Project, and Quizzes

In addition to the class seminar that each student is required to prepare (in collaboration with the instructor) and present, each student is required to write one journal-style paper of their choosing and one homework assignment of chapter-end problems. The journal-style paper is graded based on originality, literature review, and completeness. Paper topics are provided by the instructor from which students can choose; students, however, are also encouraged to present their own topics of research as a paper assignment. Homework assignment will be graded based on completeness and correctness to the topics discussed in the classroom. The project involves collecting INS/GPS or related data, process them, and present the results. Evaluation of the project is based on completeness of data, developmental effort to process and analyze the data, and on quality of results presentation. Class presentation is peer evaluated by the students and is based on clarity, completeness, and correctness. Quizzes and final exam are in-class written exams for one hour and two hours, respectively.

Course Evaluation

2 Assignment Papers 20%

2 Quizzes 20%

Class Presentation 20%

Project 20%

Final Exam 20%

Total 100%

Grading System

90-100 A

85-89.9 B+ 80-84.9 B

75-79.9 C+ 70-74.9 C

65-69.9 D+ 60-64.9 D

0-59.9 E

Academic Honesty, Software Use, UF Counseling Services, Services for Students with Disabilities

In 1995 the UF student body enacted a new honor code and voluntarily committed itself to the highest standards of honesty and integrity. When students enroll at the university, they commit themselves to the standard drafted and enacted by students.

In adopting this honor code, the students of the University of Florida recognize that academic honesty and integrity are fundamental values of the university community. Students who enroll at the university commit to holding themselves and their peers to the high standard of honor required by the honor code. Any individual who becomes aware of a violation of the honor code is bound by honor to take corrective action. The quality of a University of Florida education is dependent upon community acceptance and enforcement of the honor code.

The Honor Code: We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity.

On all work submitted for credit by students at the university, the following pledge is either required or implied: “On my honor, I have neither given nor received unauthorized aid in doing this assignment.

The university requires all members of its community to be honest in all endeavors. A fundamental principle is that the whole process of learning and pursuit of knowledge is diminished by cheating, plagiarism and other acts of academic dishonesty. In addition, every dishonest act in the academic environment affects other students adversely, from the skewing of the grading curve to giving unfair advantage for honors or for professional or graduate school admission. Therefore, the university will take severe action against dishonest students. Similarly, measures will be taken against faculty, staff and administrators who practice dishonest or demeaning behavior.

Students should report any condition that facilitates dishonesty to the instructor, department chair, college dean or Student Honor Court.

(Source: 2007-2008 Undergraduate Catalog)

It is assumed all work will be completed independently unless the assignment is defined as a group project, in writing by the instructor.

This policy will be vigorously upheld at all times in this course.

Software Use:

All faculty, staff and students of the university are required and expected to obey the laws and legal agreements governing software use. Failure to do so can lead to monetary damages and/or criminal penalties for the individual violator. Because such violations are also against university policies and rules, disciplinary action will be taken as appropriate.

Campus Helping Resources

Students experiencing crises or personal problems that interfere with their general well-being are encouraged to utilize the university’s counseling resources. Both the Counseling Center and Student Mental Health Services provide confidential counseling services at no cost for currently enrolled students. Resources are available on campus for students having personal problems or lacking clear career or academic goals, which interfere with their academic performance. The Counseling Center is located at 301 Peabody Hall (next to Criser Hall). Student Mental Health Services is located on the second floor of the Student Health Care Center in the Infirmary.

Alcohol and Substance Abuse Program (ASAP)

Center for Sexual Assault / Abuse Recovery & Education (CARE)

Eating Disorders Program

Employee Assistance Program

Suicide Prevention Program

Students with Disabilities

The Disability Resource Center coordinates the needed accommodations of students with disabilities. This includes registering disabilities, recommending academic accommodations within the classroom, accessing special adaptive computer equipment, providing interpretation services and mediating faculty-student disability related issues.

0001 Reid Hall, 392-8565,

Time Guidelines

Subject to change, the following section times are a suggested guide in order to meet learning goals…




Lecture Topic


1. Kinematic Methods in Geodesy


Course Outline

This document


Modeling Motion

Ch. 1 pp. 1-4


Ch. 1 pp. 4-14

2. Mathematical Background and Coordinate Frames


Reference Frames

Ch. 2 pp. 14-16

Basic Mathematical Techniques

Ch. 2 pp. 16-20

Transformation Between Reference Frames

Ch. 2 pp. 20-24

3. The Earth and Its Gravity Field


Geometric Figure of the Earth

Ch. 3 pp. 24-27

Gravitational and Gravity Fields of the Earth

Ch. 3 pp. 27-29

Normal Gravity in Different Frames

Ch. 3 pp. 29-32

4. Modeling Linear Motion


Modeling Equations in an Inertial Frame

Ch. 4 pp. 34-35

Modeling Equations in The Conventional Terrestrial Frame

Ch. 4 pp. 36-37

Modeling Equations in The Local level Frame

Ch. 4 pp. 37-38

State Model for Kinematic Geodesy

Ch. 4 pp. 38-42

5. Modeling Rotational Motion


Parameterization of The Rotation Matrix

Ch. 5 pp. 43-45

Quaternion Integration

Ch. 5 pp. 45-47


Euler’s Method

Ch. 5 pp. 47-50

6. INS Mechanization Equations


Mechanization Equations in The Conventional Terrestrial Frame

Mechanization Equations in The Local Level Frame

Ch. 5 pp. 50-57

Ch. 5 pp. 57-63


Initialization and Alignment of Inertial System

Rogers Ch. 11

Quiz 1

All of the Above


Spring Break

7. Modeling INS Errors


Linear State Model

Ch. 6 pp. 64-65

Error Equations in the Inertial Frame

Ch. 6 pp. 65-71


Error Equations in the Conventional Terrestrial Frame

Ch. 6 pp. 71-75

Error Equations in the Local Level Frame

Ch. 6 pp. 76-83

8. The Discrete Kalman Filter


Statement of the Kalman Filtering Problem

Ch. 8 pp. 92-95

Derivation of the Kalman Filter Algorithm

Ch. 8 pp. 95-100

The Discrete Kalman Filter Algorithm

Ch. 8 pp. 100-111




Quiz 2

All of the Above

9. GPS/INS Project


GPS-INS Data Collection

GPS-INS Data Processing

GPS-INS Analysis




Final Exam

All of the Above


Instructor iconThe instructor who turns to this last section of the instructor’s manual, devoted to the twentieth century, will either be fresh and sparkling as a new

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