[bonoboTP]

> In my very ignorant world view Kalman filters make some prediction from some input.

The word "filter" indicates that it turns one sequence (usually a time series of measurements) into another sequence (an estimate for underlying states). You can think of it as denoising the sequence of measurement by using knowledge about how the underlying system behaves. For example, if our GPS measurement says we suddenly jumped 100 meters compared to a second ago, we can weigh this against our prior knowledge that a car (the underlying system) is not likely to make such a sudden position change.

The Kalman filter weights the incoming measurement against what our model would predict. Both the prediction and the measurement are probabilistic and they are weighted according to the uncertainties of them. The more certain source of information is weighted higher.

> For example, I want to predict a time series let's say the number of visitors of a site. I know some characteristics of the series (periodic, seasonal), but how should I go about it?

That's not what the Kalman filter is for as you are not trying to denoise some sequence of noisy measurements.