*3.3. Motion Model*

We take the CV model as an example of a linear model, also known as a non-maneuver model:

$$
\begin{bmatrix} \dot{\mathbf{x}} \\ \dot{\mathbf{x}} \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} \mathbf{x} \\ \dot{\mathbf{x}} \end{bmatrix} + \begin{bmatrix} 0 \\ 1 \end{bmatrix} w\left(t\right), \tag{22}
$$

where *x* is the location of the target, *x*˙ is the velocity of the target, *x*¨ is the acceleration of the target, *w* (*t*) is zero mean white noise. Let *T* denotes the sampling interval, then the discrete-time model is given by:

$$
\begin{bmatrix} \dot{\mathbf{x}}\_{k+1} \\ \dot{\mathbf{x}}\_{k+1} \end{bmatrix} = \begin{bmatrix} \mathbf{1} & \mathbf{T} \\ \mathbf{0} & \mathbf{1} \end{bmatrix} \begin{bmatrix} \mathbf{x}\_{k} \\ \dot{\mathbf{x}}\_{k} \end{bmatrix} + \begin{bmatrix} \mathbf{T}^{2}/2 \\ \mathbf{T} \end{bmatrix} w\left(t\right). \tag{23}
$$
