Smoothness Penalty

$P=\frac{1}{T}{\sum }_{t=1}^T\frac{{\left(\left(x_{t+1}-x_t\right)-\left(x_t-x_{t-1}\right)\right)}^2}{{\left(x_{t+1}-x_t\right)}^2+{\left(x_t-x_{t-1}\right)}^2}$

From this we get nice properties such as

• enforced angle smoothness
• enforced constant velocity
• partly enforced noise cancellation