Kalman Filter to estimate 3D position of a node
As I said in the comments, just follow the 1D case from Wikipedia and augment it with the extra $y$ and $z$ dimensions (and velocities):
$$
\mathbf{x}_k = \left [ 
\begin{array}{c}
x\\ \dot{x}\\ y\\ \dot{y}\\ z\\ \dot{z} 
\end{array}
\right]
$$

You will also need to augment $\mathbf{F}$ and $\mathbf{G}$:
$$
\mathbf{F} = \left[ \begin{array}{cccccc}
1 &amp; \Delta t &amp; 0 &amp; 0 &amp; 0 &amp; 0\\
0 &amp;        1 &amp; 0 &amp; 0 &amp; 0 &amp; 0\\
0 &amp; 0 &amp; 1 &amp; \Delta t &amp; 0 &amp;  0\\
0 &amp; 0 &amp; 0 &amp;        1 &amp; 0 &amp; 0\\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; \Delta t \\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp;        1 \\
\end{array}
\right]
$$
$$
\mathbf{G} = \left[ \begin{array}{c}
\frac{\Delta t^2}{2}\\
\Delta t\\
\frac{\Delta t^2}{2}\\
\Delta t\\
\frac{\Delta t^2}{2}\\
\Delta t\\
\end{array}
\right]
$$

And then $\mathbf{H}$ is just
$$
\mathbf{H} = \left[ \begin{array}{cccccc}
1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0\\
0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0\\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 0\\
\end{array}
\right]
$$
so that $\mathbf{z}_k$ is
$$
\mathbf{z}_k =  \left[ \begin{array}{c}
x\\
y\\
z
\end{array}
\right]
$$