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:
\dot{x} = A\vec{x} + Bu(t)
y = C \vec{x} + Du(t)
Where A, B, C, and D are matrices.
Example:
Say we have a system that can be described with
\ddot{\theta} = k\dot{\theta} + n\theta + u(t)
and
y(t) = \theta