I am working on multiple object tracking. The next state of a state variable given the current state is characterized by the equation $x(k+1) = Fx(k) + noise$. $F$ is a state motion model matrix. It models the motion of state variable $x$. For a state variable $x$, with entries$[x_1, \dot{x_1}, x_2, \dot{x_2}]$, $x_1$ is the position and $\dot{x_1}$ is the velocity for measurement 1. Similarly, $x_2$ and $\dot{x_2}$ are position and velocity respectively for measurement 2. If the motion is modeled as constant velocity (CV), then $F$ is given as
$$ F_{\textrm{CV}} = \begin{bmatrix} 1 & T & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & T \\ 0 & 0 & 0 & 1 \end{bmatrix}.\tag{1} $$
Likewise, if the motion is modeled as constant turn (CT) model, the CT matrix is given as
$$ F_{\textrm{CT}} = \begin{bmatrix} 1 & \frac{\sin \omega T}{\omega} & 0 & -\frac{1-\cos \omega T}{\omega} \\ 0 & \cos \omega T & 0 & -\sin \omega T \\ 0 & \frac{1 - \cos \omega T}{\omega} & 1 & \frac{\sin \omega T}{\omega} \\ 0 & \sin \omega T & 0 & \cos \omega T \end{bmatrix}.\tag{2} $$
These are characterized by laws of motion. But if there are more than 2 measurements, I can simply write the CV matrix as
$$ F_{\textrm{CV}} = \begin{bmatrix} 1 & T & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & T & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & T \\ 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix}\tag{3}. $$
But how can we extend the CT model for multiple measurements? I think unlike CV model, CT model entries are non zero for other measurements. So I cannot simply add zeroes just like I did in (3). Please help me understand this.
