ABSTRACT
In this chapter we will present a very simple scenario that has the typical elements of an estimation problem of the kind Kalman Filtering is meant to help solve. We have tried to propose a system that will likely be familiar to any reader who has an engineering background, or even to a hobbyist or do-it-yourselfer. Our main goal is to help the reader in identifying, within this familiar situation, the concepts that play critical roles in the definition and implementation of the Kalman Filtering estimation process. These include state variable(s), measurement(s), system model(s), etc. We will emphasize that several of the variables in the scenario are, in fact, random variables, and, as such they have levels of uncertainty that must be expressed by appropriate statistical characteristics, such as their means and variances. We will also introduce the two governing relationships that are used to represent the model, the measurements and their interactions, employing the variable names that are commonly used when this kind of situation is addressed through Kalman Filtering.
