# Kalman Filter Process Noise Covariance

I want to model the movement of a car on a straight 300m road in order to apply Kalman filter on some noisy discrete data and get an estimate of the position of the car.

In a Kalman filter the matrix $A$ and process noise covariance $Q$ is what describes the system. I have chosen $A$ according to the following model:

\begin{align} \begin{bmatrix}p_{k+1} \\v_{k+1}\end{bmatrix} &= A \begin{bmatrix}p_k \\v_k\end{bmatrix} \\ \begin{bmatrix}p_{k+1} \\v_{k+1}\end{bmatrix} &= \begin{bmatrix}1 & \Delta t \\0 & 1\end{bmatrix} \begin{bmatrix}p_k \\v_k\end{bmatrix} \end{align}

where $p$ is position and $v$ is velocity.

My question is how to define the process noise covariance $Q$? The process details are unknown to me but they should be the same for any urban car movement. I have looked for articles that describe the process noise variance for forward and sidewise movement of a car but I haven't found anything.

I'm sorry if the question is not very mathematical but since Kalman filters are maths I figured someone here should have worked with car models in the past.

• Kalman filters we originally invented to help anti-aircraft guns track their targets. They relied on the first two derivatives of the planes position. Perhaps some of these historical examples can be changed from planes to cars. I would suggest l tracking them down. – Wintermute Jul 18 '16 at 16:14