There are multiple versions of the Kalman filter.
The idea behind the filter is this:
You keep track of a vector of states of the system (i.e. position, speed, acceleration and noise) and update it for each new data. When post-processing data you can initialize de filter on a forward pass and then use the backwards for estimation.
You have a model of how ...
My 2 cents on your questions:
All Global Navigation Satellite Systems (GNSS) have ground track repeating with a time that varies according to the GNSS. Evidence of this for GPS, GLONASS and Galileo is given e.g., in a nice table reported in the text book Hofmann-Wellenof, 2008, p. 398
The nonidealities you talk about (e.g., solar radiation pressure), are ...