Multiple Random Sequences Considered Jointly
Armando B. Barreto, Malek Adjouadi, Francisco Raul Ortega, Nonnarit O-larnnithipong · 2020
In our study of Kalman Filtering, it is most likely that we will not be handling a single random variable, in isolation, at a time. Instead, it is very likely that we will be dealing with circumstances where two or more random variables (possibly as two or more discrete-time series) will need to be considered jointly. The study of random variables provides a well-established framework for these cases and, fortunately, it is conceptually a natural extension of the ideas we have explored before, with some additional ideas that can only be applied when two or more random variables are being considered jointly. For the sake of simplicity, and also to have the opportunity to visualize the key concepts, the discussion here will be focused on cases when only two random variables are considered jointly. That is, we will consider “Joint distributions” of two random variables, which are referred to as “Bivariate distributions”. However, the overall conclusions that we will reach are also applicable to the cases with more than two variables, such as the cases we will study in later chapters.