To see how the observer's position affects tracking one could look at one's thumb an arm's length in front of one's eyes and look at the thumb one eye at a time. The thumb will move sideways relative to its background. Moving one's head back and forth sideways while looking through one eye will also affect the thumb position relative to the background but even though the head is moved it doesn't significantly affect the angular change that result from switching eyes. This is because the distance of the thumb hasn't changed and the range parallax depends of the relative positions of the eyes so the effect of the head's motion is canceled out. Motion of the head sideways will still affect the position of the thumb on the background and as a consequence its direction relative to the head.
Switching eyes corresponds to the simultaneous sighting method used to determine the object's position. The motion of the Earth doesn't affect range measurements relative to its center. Changes in bearing due to the Earth's motion are part of the object's relative motion. The Earth and the Moon orbit a common center known as the Earth-Moon barycenter. As a result of the Earth's rotational motion an observer's position is periodically altered by the Earth's diameter in half a day. The Earth's motion relative to the Earth-Moon barycenter shifts the Earth's position by roughly a Earth diameter in half a month. The result is that range measurements are more likely to be affected by the least squares method than paired observation parallax method. Making observations relative to the Earth-Moon barycenter would result in a better agreement of the object positions from the two methods. We would prefer to remove the way an observer affects the observations as much as possible. The Earth-Moon barycenter would be the better choice for comparison of observations that span a month of time. The perspective could be changed after the least squares fit is done.
The precision needed to make predictions of where an object will be from one night to the next based on tracking information is not as great as that needed to do orbit calculations. Care needs to be taken to ensure that a common perspective is being used when when working with sets of observations.