不完全量测下Cramer-Rao下界与数据丢失位置的关系

随机探测/丢失序列的引入使得状态估计中的Cramer-Rao下界(Cramer-Rao lower bound, CRLB)具有随机性; 在探测概率小于1的不完全量测系统中, 针对CRLB与数据丢失位置(Location of missing data, LMD)之间呈现出的某种关联现象, 讨论了离散随机系统中LMD对CRLB的影响; 利用Lyapunov不等式, 给出了一定条件下变形CRLB与LMD满足单调递减函数关系这一新结论; 同时在给定探测率下, 给出了一组CRLB上下界计算方法, 数字仿真表明探测率越高, 上下界越接近理论CRLB.

Research on the Relationship between Cramer-Rao Lower Bound and Location of Missing Data with Incomplete Measurements

Since the stochastic detection/miss sequences are introduced, Cramer-Rao lower bound (CRLB) for state estimation becomes stochastic. Considering a correlation phenomenon between CRLB and location of missing data (LMD) for incomplete measurements systems in the case where the probability of detection is less than unity, the influence of LMD upon the CRLB is discussed for discrete-time random system. It is a novel result that under certain conditions the modified CRLB is a monotonically decreasing function of LMD by use of Lyapunov inequality. Moreover, a pairs of upper and lower bounds of CRLB are also presented for a deterministic probability of detection. The numeral simulations reveal that the upper and lower bounds of CRLB approach the theoretic CRLB as the probability of detection increases.