Could someone help me understand the logic behind choosing a particular state space vector for an EKF?
Context: Say there is a 4 wheeled robot that operates only in 2D. It is equipped with an inertial unit (a/g/m) and wheel encoders (I understand that these alone might not satisfy accuracy constraints, but consider this as a hypothetical case).
Now, some literature has the state as [q, x, y, vx, vy]' while a few others as [q, q_dot, x, y, vx, vy]'. My question is, what is the advantage with having certain 'rate terms' as opposed to only the normal parameters? Also, what about including bias terms in there?
How do I go about selecting an appropriate state space vector for any use-case (in general)? Is there a set of intuitive/mathematical steps to consider/follow?