A sequential orbit determination algorithm is given which models auto-correlated gravity errors for nearcircular orbits. Using results from geodesy theory it is demonstrated that gravity modeling error auto-correlation cannot be approximated with the Kalman white process noise model. The resulting auto-correlated orbit error process is transformed from the status of non-Markov to Markov at the expense of an assumption which imposes symmetries on certain covariance functions. It is emphasized that the character of the trajectory estimation problem is significantly changed by recognizing and using the auto-correlation property associated with gravity modeling errors. I. Introduction S EQUENTIAL orbit determination procedures enjoy significant operational advantages over the older methods1 of batch least-squares differential corrections: ephemeris integration across overlapping measurement time intervals is eliminated thereby significantly reducing computation time, force modeling discontinuities are easily bridged with a significant reduction in the time required to remove transients due to uncertainties associated with the discontinuities, and the extended Kalman filter provides a structure to formally account for stochastic force modeling errors. With the richer structure associated with sequential procedures, one would have hoped to say that they enjoy a consistent and significant accuracy improvement over the< older batch methods. In the author's experience this has not been realized. Herein the author will attempt to show that a fundamental reason for this disappointment is to be found in the failure of stochastic force modeling errors to satisfy the white process noise hypothesis of the Kalman filter. Particularly we will show in Sec. V that gravity modeling errors are autocorrelated with respect to time so that any white noise approximation will yield a nonoptimal procedure. The problem of interest is stated in Sec. Ill, using the notation and definitions introduced in Sec. II. An approximate solution which accounts for gravity modeling error auto-correlation is given in Sec. IV. The remaining sections (V-IX) are devoted to the derivation of the solution given in Sec. IV. Equation (6), given in the solution, follows Eq. (26) in Sec. IX from a derivational point of view.