针对含有不完全随机有偏测量序列的状态估计问题,给出了统计意义下的修正递推估计误差方差Cramer-RaoT界(CRLB)求解算法.首先建立了不完全随机有偏量测离散系统的数学模型,进而推导了枚举的CRLB和统计意义的CRLB计算式,该统计意义的CRLB为枚举CRLB的下界,其计算量远小于枚举CRLB求解的计算量.最后,以给定探测概率和偏差发生率下的一类光电跟踪系统为例,进行了数字仿真.
A modified recursive Cramer-Rao lower bound(CRLB) of the statistical estimation error variance is derived for the state estimation with incomplete and stochastic-biased measurement sequences. Firstly, a mathematical model of the discrete-time system with incomplete and stochastic-biased measurements is built; and then, the enumeration CRLB and the statistical CRLB are derived, respectively. The proposed statistical CRLB is a lower bound of the enumeration CRLB, but its calculation complexity is far lower than that of the enumeration CRLB. Simulation is performed in an optical-electrical tracking system with pre-specified detection probability and biased occurrence probability.