Algorithm 2: Motion tracking model.

for $t+1=t_0+1$ to the end of the frame sequence  1.take M candidate states ${\{{\widehat{X}}_{t+1}^j\}}_{j=1}^M\sim N(X_t,\overrightarrow{\sigma })$ around the point $(x_t^c,y_t^c)$  2.build up the M descriptors ${\{{\overrightarrow{v}}_{t+1}^j\}}_{j=1}^M$ and their measurements ${\{{\widehat{Y}}_{t+1}^j\}}_{j=1}^M$  3.compute the motion model $p({\widehat{X}}_{t+1}^j|X_t)$ (Equation (8))  4.compute the observation model $p({\widehat{Y}}_{t+1}^j|{\widehat{X}}_{t+1}^j,X_t)$ by Equation (10)  5.estimate the a posteriori prob. $p({\widehat{X}}_{t+1}^j|{\widehat{Y}}_{t+1}^j,X_t)$ using Equation (11)  6.find the most likely target state $X_{t+1}$ by Equation (12)  7.create the target descriptor ${\overrightarrow{v}}_{t+1}^{tg}\in {\mathbb{R}}^s$  8.create the background descriptors ${\overrightarrow{v}}_{t+1,(a_x,b_x)}^{bg}\in {\mathbb{R}}^s$

end