  In the problem "Localization and trilateration with the minimum number of
landmarks", we faced the 3-Guard and classic Art Gallery Problems. The goal of
the art gallery problem is to find the minimum number of guards within a simple
polygon to observe and protect its entirety. It has many applications in
robotics, telecommunications, etc. There are some approaches to handle the art
gallery problem that is theoretically NP-hard. This paper offers an efficient
method based on the Particle Filter algorithm which solves the most fundamental
state of the problem in a nearly optimal manner. The experimental results on
the random polygons generated by Bottino et al. \cite{bottino2011nearly} show
that the new method is more accurate with fewer or equal guards. Furthermore,
we discuss resampling and particle numbers to minimize the run time.
