A simple scheme is presented for mapping the 2D probability density for an observer's position, defined by any number of lines of position (LOPs) on the surface of the Earth, assuming that the LOPs result from uncorrelated observations that have normally distributed errors. Although the mapping can be used to determine the position fix corresponding to the LOPs (which is consistent with other methods), its intended use is computing the total probability that the observer is located within (or outside) some specified area of interest, such as a zone of avoidance around a navigational hazard. Numerical experiments with areas where the average total interior probability is known, such as the triangles and polygons formed by nearly convergent LOPs, show that the method provides correct answers. The numerical experiments also revealed that theoretical probabilities associated with commonly used error ellipses are overstated for navigational solutions based on small numbers of LOPs.

中文翻译：

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修复 LOP 几何的概率

提出了一个简单的方案来绘制观察者位置的二维概率密度，该位置由地球表面上任意数量的位置线 (LOP) 定义，假设 LOP 是由具有正态分布误差的不相关观测结果产生的。虽然映射可用于确定与 LOP 相对应的位置锁定（这与其他方法一致），但其预期用途是计算观察者位于某些特定感兴趣区域内（或外）的总概率，例如航行障碍周围的避让区。在已知平均总内部概率的区域（例如由几乎收敛的 LOP 形成的三角形和多边形）的数值实验表明，该方法提供了正确的答案。