Statistical estimates are developed for the position of a moving surface target at any time from observations, subject to random errors, taken of its position from a manned orbital laboratory MOL. The exact position of the MOL, being determined by observations subject to random errors, is also unknown. To develop the estimates, the simplifying assumption that the earths surface is a plane and that the target moves linearly are made. The further assumption is made that the estimated coordinates of position of the target from the MOL are jointly normal as are the observations of the postion of the MOL from the ground. The observations are independent but may have different distributions. From the equations derived, it is possible to decide, in a given situation with known accuracies of the radars involved, whether it is better to make an estimate of the direction of travel with each pass or to estimate position only and to estimate the direction of travel after collecting the position data on subsequent passes. Also from the equations developed, how much an increase in the number of observations will increase the accuracy of the estimated position and direction can be determined.