To start, you have to write a probabilistic model of your system. Let us denote, your outputs (observations) as $\bf{y}_t$'s and the true positions as $\bf{x}_t$'s. To use Kalman filter, you have to be sure that underlying noise is Gaussian and your observation and transition models (I will explain in the sequel) are linear.
First, write a reasonable observation model such that,
$$ \mathbf{y}_t = H_t \mathbf{x}_t + \mathbf{w}_t $$
In this model, you aim to model how your true positions are corrupted and become observations. Thus you have to determine $H_t$. For example, if you are using a camera and want to know 3D positions, then observation model is a camera matrix which projects the real world points to 2D points. In your case, you have to know sensor characteristics (or model it).
Second, you have to write a transition model, this requires to use physical knowledge of the underlying system. For instance, if we model a ball and try to model its evolution in time, certainly we have to write a motion model. Transition model can be written as,
$$ \mathbf{x}_t = F_t \mathbf{x}_{t-1} + \mathbf{\eta}_t $$
Notice that, in both models, the noise terms are Gaussian and $H$ and $F$ are linear. To use Kalman filter, you have to know these models, i.e., you should have a probabilistic model which explains the underlying physical structure. Then you can use the Kalman filtering recursions, which are straightforward from this point.
