# existence probability of an object in fusion

I want to compute an existence probability of an object in a sensor fusion on the high level (having from each sensor list of objects already filtered with e.g. Kalman Filter).

There are these formulae:

$$LR(G)_{old} = \frac{p(Ex_{out})_{old}}{1 - p(Ex_{out})_{old}}$$ $$\alpha = \frac{p(Ex_{in})_{old}}{p(Ex_{in})_{old}*(1 - p(Ex_{in})_{new})}$$ $$LR(G)_{new} = LR(G)_{old} * \alpha$$ $$p(Ex_{out})_{new} = \frac{LR(G)_{new}}{1 + LR(G)_{new}}$$

Where $p(Ex)$ is the probability of existence and $LR$ is the Likelihood Ratio.

The idea is that $p(Ex)_{in}$ is some probability existence of local object, which was fused into the global $p(Ex_{out})$, and its probability influences that global one. $old$ would mean values from previous cycle.

How do you condition that computation to avoid situations of dividing by zero, obtaining NaN, or Inf? Also, if $p(Ex_{in})_{new}$ is almost 1, then $\alpha$ will be huge, increasing output, and increasing it enormously in each later cycle, so that the object will live forever. How to prevent it?

• Where did "this formula" come from? Perhaps if you go back to the original paper, book, or whatever, it would make these things clear? – TimWescott Jul 13 '13 at 0:57

2. the factors $1 - p\left(Ex_{out}\right)_{old}$ and $1 - p\left(Ex_{in}\right)_{new}$ occur in both the numerator and denominator, and can be canceled out, making the expression more opaque, but numerically more tractable.