State Vector for autonomous cars distance measurements

Hey guys,

I am currently trying to build two cars which drive one after the other and thereby keep their distance. We are working on this project as a team and are given some code from the previous year already.
In the previous year, distance and velocity has been measured using an ultrasonic-distance sensor and some edge-detection to figure out the rounds per second the wheels go. These measurements have been filteres with a 1-dimensional Kalmanfilter. Now, I wonder, can we further improve the Kalmanfilter?

Here is my thinking: The Kalmanfilter is 1-dimensional so far. The state-vector of the filter must, therefore, only contain two states: x-coordinate and velocity in x-direction. Is it possible to change this state-vector, such that we obtain an x- and y-coordinate and velocity in x- and y-direction? Do we need to get additional sensors for this to work?

I'd be helpful for any help, really. I am just starting to get familiar with all of this.