# Occupancy Grid Mapping(占用栅格地图构建)

一、栅格的定义 将连续空间离散化成一个个栅格。然后每个栅格用一个布尔随机变量来描述： ![Alt text](/files/-LWOCwoR9T77axtfByIq) 二、传感器测量模型 激光传感器的一次测量可以确定一条线段上所有栅格是否被占用（不是一般性，假设是单线激光雷达），相应的附一个概率值，总共有如下四中情况 ![Alt text](/files/-LWOCwoTSACo9DWKHe6e) 三、带入贝叶斯公式 在（随机）先验的地图下，通过读取激光雷达传感器的测量数据，对地图用贝叶斯公式进行实时更新： ![Alt text](/files/-LWOCwoVE3_0z9-kdRov) 四、Log-odd 定义odd运算，然后再取log，可以将贝叶斯公式中的相乘各项化为相加，达到变量分离方便迭代更新的目的： ![odd的定义](/files/-LWOCwoXTPOOxcgt5fl2) ![取对数](/files/-LWOCwoZmKrT1bbnUK31) ![log odd更新](/files/-LWOCwoak8FXYrLYxH5o)


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