State Information

State Information is the processs through which we determine a system's sate $x$ using indirect measurements $y$

State Systems

Example

Let’s try to find a dog’s breed $x(t)=\text{fixed}$ > $X=\text{Dog Breed}$ > $Y=[\text{Yellow Fur},\text{Short Hair}]$ Our data is in two categories: deterministic and stochastic

• Deterministic:
  • No randomness/noise
  • All dynamics are known
  • Measurements are perfect
• Stochastic:
  • Randomness/noise in system
  • Some dynamics that are unknown
  • Measurements have error

• Filters
  • The algoriths used to sift out information from measurements
  • $Y\to \boxed{Filter}\to X$
• Orbit Determination:
  • Using state estimation to determine position & velocity (orbit) of an object in space

NOTE

State Estimation

• $\text{range}=e$
• $\text{range rate}=\dot{e}$
• $\vec{Y}=\left[\begin{array}{c}e\\ \dot{e}\end{array}\right]\underrightarrow{\text{filters}}\vec{X}=\left[\begin{array}{c}\vec{r}\\ \vec{v}\end{array}\right]\underrightarrow{\text{transform}}\text{O.E.s}=\left[\begin{array}{c}\alpha \\ e\\ i\\ \omega \\ \Omega \\ \nu \end{array}\right]$
• $\vec{Y}=\left[\begin{array}{c}{y}_1\\ y_2\\ y_3\end{array}\right]\underrightarrow{\text{Filters}}\vec{X}=\left[\begin{array}{c}\vec{r}\\ \vec{v}\end{array}\right]+\text{State Uncertainty}$