== Formulation of any state estimation problem ==

Let <math>\vec{X} \in \mathbb{R}^n</math> represent the state of a system and <math>\vec{Y} \in \mathbb{R}^r</math> represent the vector containing all the measured information about the state. Physical properties of the system being measured will be known beforehand and can be written as some function of state vector <math>\vec{X}</math>, say <math>\vec{f}(\vec{X}): \mathbb{R}^n \rightarrow \mathbb{R}^r</math>. Ideally, without any measurement errors, <math>\vec{f}(\vec{X}): </math> should be equal to <math>\vec{Y}</math> but the presence of uncertainty makes them unequal, thus