Computer simulation experiment is very important in the phase of project design, the availability of simulated result highly depends on the scheme of error simulation. Time series observations are normally correlated. This paper first discusses the formula of correlated error propagation, then derives the formula of simulating time series correlated errors. This formula is then used to simulate correlated ephemerides errors of CHAMP, then the ephemerides are used to recover the gravity vector at satellite altitude with finite differential formula. The formulae derived in this paper are verified with the difference between the recovered gravity vectors and the true values' which are directly computed with the same gravity model as that generating the ephemerides.