While convergence properties of many sampling selection methods can be proven to hold in a context of approximation of Feynman-Kac solutions using sequential Monte Carlo simulations, there is one particular sampling selection method introduced by Baker (1987), closely related with "systematic sampling" in statistics, that has been exclusively treated on an empirical basis. The main motivation of the paper is to start to study formally its convergence properties, since in practice it is by far the fastest selection method available. One will show that convergence results for the systematic sampling selection method are related to properties of peculiar Markov chains.