I am struggling with quotes like
The EnKF applies a Markov chain Monte Carlo (MCMC) method ... (1, p. 6)
In fact, the Kalman filter is a MCMC algorithm in the case of a linear and Gaussian state space model with known parameters. (2, p. 5)
I cannot find the construction of a Markov chain in the description of neither linear nor ensemble Kalman filter. Could anyone please clarify how this is meant?
 Evensen, Geir. "The ensemble Kalman filter for combined state and parameter estimation." Control Systems, IEEE 29.3 (2009): 83-104.
 Johannes, Michael, and Nicholas Polson. "MCMC methods for financial econometrics." The Handbook of Financial Econometrics 65 (2002).