What do we expect by setting a too low measurement error in a Kalman Filter model, much lower than the noise existing in the measurements? And why?
Let's say we simulate some measurements and we add some noise to them with variance $0.1$, but we set $Q$ to $0.001$. I have run some toy experiments with these values already, but the results are not really that clear and I thought I would require a more theoretical answer before drawing any conclusions.
My guess is that since we will not account for the measurements' noise through $Q$, the model will be overconfident about the measurements and the estimates can diverge from the real state values as more noise will be used to update the estimate's parameters.