This course has been discontinued
A simplified definition of error propagation is 'the process of accumulation and/or cancellation of random errors in a measurement, direct or indirect'. It involves certain mathematical procedures for determining the random error (uncertainty) in an indirect measurement; that is, when the final measurement is the result of computations, be it a simple average, an inverse computation from plane coordinates, or more complex geometric relationships. Error propagation applies to random errors, not to systematic errors.
The broad goals of this 8-hour online course are teaching the student to apply error propagation equations and to gain a deeper understanding of the nature of measurement. The course is divided into five sections:
1. Basic Equations for Error Propagation
2. Error Propagation by Rate of Change
3. Graphical Analysis of Error Propagation
4. Using Calculus for Error Propagation
5. Applications of Random Error Analysis
This course is primarily for licensed surveyors and surveying technicians, licensed engineers and engineering technicians who deal with surveying and mapping, geodesists, photogrammetrists, geographic/land information system personnel, and anyone else who uses measurements and must analyze measurement errors. It is also excellent preparation for licensing exams in surveying and engineering, both fundamentals and principles and practice.
The Body of this course is presented in PDF format. You will need Acrobat Reader.
There is a test included at the end of this course.
At the conclusion of this course, you will:
- Be able to analyze survey measurement systems to arrive at the equations needed to make calculations for propagation of random errors in measurements.
- Be able to arrive at the expected uncertainty in measurements determined by indirect means through learning how to analyze random errors.
- Be able to judge whether or not expected errors in surveys meet required standards, and also gain insights as to how to derive measurement specifications to meet specific standards.
- Be better prepared for licensing exams in surveying and engineering as related to errors and error propagation.
Background is not needed in calculus, as the mathematical concepts required for understanding the material in this course are included herein. However, basic mathematics, equivalent to college algebra and trigonometry is recommended. It is assumed that the student has some experience and/or coursework in using basic surveying instruments, such as optical and electronic theodolites, self-leveling levels, electronic distance instruments and total stations, steel tapes, and stadia measurements. It is also assumed that the student understands field operations and calculations associated with traversing, leveling, and similar basic surveying measurements. A glossary of terms is included as an aid in understanding error terminology related to this course.
Many problem examples are used in the course to help explain the material. The quiz at the end of the course consists of a mixture of questions and short problems, totalling 30 items. The problems will require an ordinary scientific calculator to solve. Care has been taken to keep the level and extent of the course, including the quiz problems, appropriate for the credit hours assigned. In this regard, extensive and involved problems have not been included, but merely mentioned as applications, with guidance as to how the coursework can be applied to them.
Three other courses by this instructor are useful, but not required, prerequisites for this course. They are: (1) 'The Theory of Measurement', (2) 'Significant Figures and Round-Off Errors', and (3) 'Statistical Analysis of Random Errors'. However, anyone who has a good understanding of measurement theory should be able to successfully complete this course.