How does autocorrelated noise models converge to white noise models when considering kinematic tracking models?

56 Views Asked by At

In the article: A jerk model for tracking highly maneuvering targets see http://eprints.iisc.ac.in/2710/

The jerk model is explained. What happens with the process noise matrix Q if the limit is taken ($\alpha\rightarrow\infty, \sigma^2\rightarrow\infty$). The author suggests that the model reduces to a constant white noise jerk model. It does not seem to work, does anyone know if these limits can be taken? If we define $q = \frac{2 * \sigma_j^2 }{ \alpha}$, then take the limit of $\alpha$ and $\sigma^2$ to infinity, then entry q_23 inside the noise matrix Q should converge to zero but instead it converges to $\frac{q}{2}$. Any help is appreciated.

1

There are 1 best solutions below

1
On

Looking at the paper, it does seem that $q_{23}$ should go to zero as $\alpha \rightarrow \infty$. From the paper

$$ q_{23} = \frac{1 + \alpha^2 T^2 - 2 \alpha T + 2 \alpha T e^{-\alpha T} + e^{-2 \alpha T} - 2 e^{-\alpha T}}{2\alpha^4} $$

The $e^{-\alpha}$ terms will go to zero as $\alpha \rightarrow \infty$, and the $\alpha^4$ in the denominator will grow faster than the $\alpha^2$ in the numerator.

Am I misunderstanding what you mean?