# How can I determine the Transition Matrix of a Kalman-Filter ?

I am trying to set up a Kalman-Filter to filter position-measurements of a self-driving car. To do so, I consider a state-vector with 5 elements and am now trying to set up the Transition Matrix.

As you can see in the following picture, I do not have a clear understanding of the car dynamics. How does my steering for example contribute to my x-position? Since steering is the rate of change of the vehicle heading, it must somehow be linked to acceleration. Can anyone help me to figure out A ?

I would be so grateful! In both cases robot travels towards its' heading direction but in world coordinate frame the heading is different. • That's great, thx so much! Just two questions about your answer: The matrix you have given assumes that the steering is constant. Does this mean we are constantly steering in the same direction? ..I have a feeling this cannot be and I probably just misunderstand the last equation. Second: What if we consider control input? In a car, we can control acceleration. But this would have to be considered in a separate matrix, right? So that x_t = A x_{t-1} + B u_{t-1}, where u is the input vector – user503842 Jan 2 at 17:41
• allright, thx again! Just to be clear: The control input matrix is what I am referring to as matrix B in my previous comment, am I right? – user503842 Jan 3 at 21:46