I am designing a Kalman Filter for a signal which features a certain kind of noise and I do not know how to model it properly in the filter. The noise is constructed from a white noise source, called $w(t)$ by taking the difference of the current noise-sample and the last noise sample ($\Delta t$ is the sample-time):
$\eta(t) = w(t) - w(t-\Delta t)$
From my current point of view this is basically high-pass filtered noise or some kind of differentiated white noise (I read purple noise somewhere) with a sinusiodal power spectral density.
Question 1: Do you agree on my thoughts above?
Question 2: How can this noise be modeled in terms of a Kalman Filter? Would a Markov-model be suitable? How to express the color of this noise in a Kalman Filter?