Kalman Filter 09/28

After all-hands we had a Kalman Filter meeting where we learned about state-space modelling and discussed preliminary goals for Kalman Filtering.

STATE-SPACE MODELLING

State-space modelling is a way of representing a physical system (often with high order diff eqs) by way of max first-order differential equations like so:

$//<![CDATA[ \begin{array}{l}\dot{x} = A\vec{x} + Bu(t)\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}y = C \vec{x} + Du(t)\end{array} //]]>$

Where  $//<![CDATA[ \begin{array}{l}A\end{array} //]]>$,  $//<![CDATA[ \begin{array}{l}B\end{array} //]]>$,  $//<![CDATA[ \begin{array}{l}C\end{array} //]]>$, and  $//<![CDATA[ \begin{array}{l}D\end{array} //]]>$ are matrices.

Example: