# Maximum likelihood estimator (ML Data Association) EKF

This question is an extension to my previous problem (Data association with ekf). My problem here is in the line 16 in the aforementioned link.

16.     $j(i) = \underset{k}{\operatorname{arg\,max}} \ \ det(2 \pi S^{k})^{-\frac{1}{2}} \exp\{-\frac{1}{2} (z^{i}-\hat{z}^{k})^{T}[S^{k}]^{-1} (z^{i}-\hat{z}^{k})\}$

When I compute this line, I'm getting huge number 1.0e+09 * 3.5230. This is probability density function. Why is the pdf getting bigger than 1 in a huge way?

Just like Jacob said. The integral of pdf from $\int_{-\infty}^{\infty}{f(t) dt}=1$ for some pdf $f(t)$. This does not mean the pdf cannot be more than one at some point (i.e. infinitesimal interval). Thinking about dirac delta function might help.