I'm trying to work my way through a text on robotics and specifically trying to make sense of Kalman filters. I've used them before but I'd like to be able to understand and make my own for new systems.
The question I have asks for the minimal state vector for a car with position X and velocity V at time t. The acceleration (A) is assigned randomly at each point in time. I have to come up with a minimal state vector so the the resulting system is Markovian.
Here's my answer so far:
The initial state vector should just be S = [X,V,A] since those are the three components that were given? The Markovian part is confusing to me. This means that the state vector can only have components that do not depend on past measurements? In which case it should only be S = [X,A] since acceleration was given to be random and position has no time dependence?