09. Binary Bayes Filter Algorithm

Input

The binary Bayes filter algorithm computes the log odds of the posterior belief denoted by l _t .
Initially, the filter takes the previous log odds ratio of the belief _t-1 and the measurements z _t as parameters.

Computation

Then, the filter computes the new posterior belief of the system l _t by adding the previous belief l _t-1 to the log odds ratio of the inverse measurement model $log \frac{p(x|z_{t})}{1-p(x|z_{t})}$ and subtracting the prior probability state also known by initial belief $log \frac{p(x)}{1-p(x)}$ . The initial belief represents the initial state of the system before taking any sensor measurements into consideration.

Output

Finally, the algorithm returns the posterior belief of the system l _t , and a new iteration cycle begins.