Background:
I am a newbie in DSP. 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.
My Understanding:
I am thinking about representing my state as a 2D vector $(x, \dot{x})$, where $x$ is the current heading direction and $\dot{x}$ is the rotation rate reported by the gyroscope.
Questions:
- If my understanding is correct, there will be no control term, $u$ in my filter. Is it true? What if I take the state as a 1D vector $(x)$? Then does my $\dot{x}$becomes the control term $u$? Will these two methods yield different results?
- As we know, the main noise source comes from the compass when the compass is in a distorted magnetic field. Here, I suppose the Gaussian noise is less significant. But the magnetic distortion is totally unpredictable. How do we model it in the Kalman Filter?
- In Kalman Filter, is the assumption that "all the noises are white" necessary? Say, if my noise distribution is actually a Laplacian distribution, can I still use a Kalman Filter? Or I have to switch to another filter, like Extended Kalman Filter?