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?
Getting a value larger than 1 in a pdf is normal. Remember that the pdf does not actually evaluate to a probability itself, but to a density. Only the integral over the function has to evaluate to 1. For a continuous variable the probability of getting exactly one particular value approaches zero. In this case you can only give the probability that the variable is within a certain interval, or you can compare the relative probability.
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.
