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:

Where , , , and  are matrices.

Example:

Say we have a system that can be described with

and

To model this, let 

.

We need to find matrices  and  such that

.

We find that 

.