# What to do when the control input of the Kalman filter is unknown?

I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope.

Say at time $t-dt$, the compass reports a reading $\theta_{t-dt}$, and the gyroscope reports a reading $\omega_{t-dt}$. Then I assume from time $t-dt$ to $t$, the rotation rate can be regarded as a constant. Thus, my current heading direction is $$\theta_{t}=\theta_{t-dt}+\omega_{t-dt}\cdot dt$$ As can be seen, the $\theta$ can be easily time-updated.

But what about my $\omega$? The robot is not at my control. So its rotation rate at next moment is unpredictable.

How should I do the time update in this case?