Purdue Engineering Professional Education

logo header header
Toll-Free in U.S. (877) 598-4233
CE59700 - Adjustment of Geospatial Observations

Fall 2015

Days/Time: TBA / TBA
Credit Hours: 3

Learning Objective:
This course prepares the student to carry out modeling and least squares estimation for a wide variety of environments and data observation types. Although many of the examples will be drawn from the Geomatics and Geospatial domains, the techniques would be useful in any Science or Engineering discipline. The emphasis is on fundamental principles so that the student will be able to able to apply them to new problems not specifically addressed in the course. In addition to estimation, the student will be able to perform error/covariance propagation to make quantitative statements about uncertainties of the results, and to evaluate statistical hypothesis tests. The major least squares techniques presented will be implemented and tested by students using the Matlab programming language. The student will become conversant with both linear and nonlinear models as well as sequential estimation, the kalman filter and the extended kalman filter.

This course presents a thorough and comprehensive look at the topic of fitting data to a mathematical model. The techniques presented will free the scientist or engineer from dependence on restrictive software applications, and allow customization of solutions using weighting, constraints, parameter dependencies, and robust techniques which minimize the influence of blunders. Example applications include 2D/3D ranging, 2D/3D triangulation, GPS pseudo ranges, vehicle tracking and navigation, curve and surface fitting, coordinate transformations, leveling, and image triangulation. Pre-analysis and design techniques permit the precision of unknown parameters to be determined in advance, prior to expending time and effort in field measurements. Tentative Syllabus

Topics Covered:
Models, model elements, observations, random variables, errors; Adjustment, least squares methods: mixed model (general LS), observations only, indirect observations; Observations statistics, variance, covariance, weight; Linear applications: regression, curve fitting, surface fitting, coordinate transformation, leveling; Constrained minimization, lagrange multipliers; Nonlinear problems, newton iteration; Nonlinear applications: 2D/3D triangulation, traverse, 2D/3D ranging, GPS pseudoranging; Post adjustment statistics; Error propagation, confidence intervals, confidence regions, error ellipses, circular error, CE/LE; Applications requiring mixed model (general LS): curve and surface fitting; Network design, preanalysis; Comparison with commercial software solutions; Blunder detection, robust estimation, L1 norm minimization, IRLS, data snooping, reliability; Sequential estimation techniques, kalman filter and extended kalman filter; Tricks & hints: numerical derivatives, sequential formation of normal equations.

Graduate standing.

Applied/Theory: 65/35

Web Address:

Web Content:
Web Content: Follow link from web URL to current semester course offering. Note: Prior years' sites are there; use for reference and help. Coverage will be about the same. Homeworks and exams will be different.

Homework (approx. 6-7), 25%. Emailed to bethel@ecn.purdue.edu.Need to become familiar with Matlab (it's easy!). Successful completion of homework problems is essential element of mastering this subject. Assistance is available so a dedicated student can always complete homeworks.


1 Midterm Exam 37.5% and a Final Exam 37.5%

No required textbook. References --Linear Algebra, Geodesy, and GPS, by Strang and Borre, Wellesley-Cambridge Press, 1997 GPS Satellite Surveying, by Leick, Wiley, latest edition

Computer Requirements:
ProEd Minimum Computer Requirements. Numerical & Graphics Software: either Matlab Student Version which you can purchase, or Matlab Professional Version available via Purdue GoRemote (http://goremote.ics.purdue.edu).

ProEd Minimum Requirements: view

Tuition & Fees: view

Other Requirements:
You will need to become familiar with Matlab, later in the term we may do a GUI application.

James S. Bethel
765 494-6719
Purdue University
Civil Engineering Building
550 Stadium Mall Drive
West Lafayette, IN 47907-2051
765 494-0395
Instructor HomePage