In this module you will learn how to develop a systematic approach to translate real-life problems into mathematical models. This will be in the form of a so-called system of observation equations, comprising four fundamental blocks:

1. vector of observations,
2. vector of unknown parameters,
3. linear (or linearized) functional relation between observations and unknowns, and
4. stochastic characteristics of observations in the form of dispersion (or covariance matrix) of the observation vector.

In addition, you will learn about different concepts, such as linear vs. nonlinear models, functional vs. stochastic models, consistent vs. inconsistent models, over/under-determined models, redundancy, and solvability of observation-equation systems. All the aforementioned concepts are explained by various practical examples.

Learning objectives

In this module you will learn to …

• … formulate the mathematical model for a set of estimation problems (both functional and stochastic model).
• … identify the various properties of mathematical models.