Observation Theory: Estimating the Unknown

Are you an engineer, scientist or technician? Are you dealing with measurements or big data, but are you unsure about how to proceed? This is the course that teaches you how to find the best estimates of the unknown parameters from noisy observations. You will also learn how to assess the quality of your results. TU Delft’s approach to observation theory is world leading and based on decades of experience in research and teaching in geodesy and the wider geosciences. The theory, however, can be applied to all the engineering sciences where measurements are used to estimate unknown parameters. The course introduces a standardized approach for parameter estimation, using a functional model (relating the observations to the unknown parameters) and a stochastic model (describing the quality of the observations). Using the concepts of least squares and best linear unbiased estimation (BLUE), parameters are estimated and analyzed in terms of precision and significance. The course ends with the concept of overall model test, to check the validity of the parameter estimation results using hypothesis testing. Emphasis is given to develop a standardized way to deal with estimation problems. Most of the course effort will be on examples and exercises from different engineering disciplines, especially in the domain of Earth Sciences. This course is aimed towards Engineering and Earth Sciences students at Bachelor’s, Master’s and postgraduate level. 3b:T4a

• How to translate real-life estimation problems to easy mathematical models
• Practical understanding of least squares estimation and best linear unbiased estimation, and how to apply these methods
• How to assess and describe the quality of your estimators in the form of precision and confidence interval
• How to check the validity of your estimation results

• Calculus (high school level)
• Probability concepts like expectation, variance, the normal distribution and other probability density functions
• Basic matrix manipulation (by hand and with e.g. Python or Matlab)