We consider the problem of initializing the tracking filter of a target moving with nearly constant velocity when positiononly (1D, 2D, or 3D) measurements are available. It is known that the Kalman filter is optimal for such a problem, provided it is correctly initialized. We compare a single-point and the well-known two-point difference track initialization algorithms. We analytically show that if the process noise approaches zero and the maximum speed of a target used to initialize the velocity variance approaches infinity, then the single-point algorithm reduces to the two-point difference algorithm. We present numerical results that show that the single-point algorithm performs consistently better than the two-point difference algorithm in the mean square error sense. We also present analytical results that support the conjecture that this is true in general.