Implementing Kalman filter or extended or unscented with only position information
from the generality of your question then yes you can design a Kalman filter which would accept the target position as the only measurement possibly corrupted with noise. 

Then the Kalman filter will try to estimate the true position of the target based on the noisy position measurement and the assumed motion model. Hence in effect the Kalman filter would be reducing the measurement noise of the target position measuring device. 

The states of the filter would be defined based on the assumed motion model: a constant acceleration model would use for example the position, velocity and acceleration as the internal states which are being estimated (when the acceleration is unknown) or another model would use a deterministic input for the known acceleration and use two states instead.