光电经纬仪组网测量位置估计的Cramer-Rao限

Cramer-Rao lower bounds of position estimation in a photoelectric theodolite-based network

在由多台光电经纬仪组成的测量网中,提出一种基于目标位置估计Cramer-Rao限(CRLB)的精度分析方法,并给出了光电经纬仪组网测量布站应遵循的原则。Cramer-Rao限给出了无偏参数估计变量的下限,可以定量分析不同数量、不同位置的经纬仪组网测量的目标位置估计精度,为制订经纬仪组网布站方案提供依据。仿真计算和实际应用结果表明,两台经纬仪与目标所构成的夹角θ应满足60o<θ<120o;采用3台或4台经纬仪组网对目标位置估计性能有较大改善,但进一步增加经纬仪的数量,性能改善不明显。

Referring to a measuring network composed of two or more photoelectric theodolites, an approach for precision analysis based on Cramer-Rao Lower Bounds (CRLB) of target position parametric estimation is proposed and the principles to locate the netted photoelectric theodolites is also given in the paper. The Cramer-Rao lower bound gives a lower limit to the variance of any unbiased parameter estimation, which makes quantitative analysis possible for target position estimation of the netted theodolites in different amount and position and provides a basis for the layout of the netted theodolites. Numerical simulation and actual application show that the angle θ between two theodolites and the target satisfies 60° less than or equal θ less than or equal 120°; the performance of target position parametric estimation with three or four netted theodolites is superior to that with two theodolites. However, with the increase of still more netted theodolites, the performance will be improved a little on the former level.