Abstract We consider the problem of quantifying uncertainty for converging beam triple LIDAR when the input uncertainty follows a uniform distribution. We determine expressions for the range (i.e. set of reachable points) for the reconstructed velocity vector as a function of any particular setting of the nominal input parameters and determine an explicit lower (and upper) bound on the (averaged) volume (with respect to Lebesgue measure), in R 3 , of that range. We show that the size of any such bound is inversely proportional to the absolute value of the triple scalar product of the unit vectors characterizing the Doppler measurement directions (optimized over the uncertainty region) in R 6 associated with the nominal angle settings under consideration. This leads to the conclusion that the nominal LIDAR configurations that minimize output uncertainty ought to be those in which the value of the triple scalar product of the Doppler unit vectors is at its largest.

中文翻译：

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会聚光束三重激光雷达的体积不确定性界限和最佳配置

摘要 当输入不确定性遵循均匀分布时，我们考虑了量化收敛光束三重激光雷达的不确定性问题。我们确定重构速度矢量的范围（即一组可达点）的表达式作为标称输入参数的任何特定设置的函数，并确定（平均）体积（相对于Lebesgue 测度），在 R 3 中，该范围。我们表明，任何此类界限的大小与表征多普勒测量方向（在不确定区域上优化）的单位矢量的三重标量积的绝对值成反比，R 6 中与所考虑的标称角度设置相关联。