In the problem Localization and trilateration with minimum number of landmarks, we faced 3-guard and classic Art Gallery Problem. The goal of the art gallery problem is to find the minimum number of guards within a simple polygon to observe and protect the entire of it. It has many applications in Robotics, Telecommunication and so on and there are some approaches to handle the art gallery problem which 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 near optimal. The experimental results on the randomly polygons generated by Bottino shows that the new method is more accurate with less or equal guards. Furthermore, we discuss the resampling and particle numbers to minimize the running time.

翻译：在本地化和与最低地标数的三角问题中,我们面临三维和经典美术馆问题。 美术馆问题的目标是在一个简单的多边形内找到最起码的卫兵人数, 以观察和保护整个美术馆。 它在机器人学、 电信学等方面有许多应用, 并且有一些方法可以处理美术馆问题, 这个问题理论上是NP- 硬的。 本文提供了一种基于粒子过滤算法的有效方法, 它能解决问题最根本的状态, 并且几乎是最佳的。 博蒂诺产生的随机多边形的实验结果显示, 新的方法在卫兵人数越来越少或相等的情况下更准确。 此外, 我们讨论重标和粒子数, 以尽量减少运行时间 。