Cramér-Rao Lower Bound of Target Localization Method Based on TOA Measurements

The Cramér-Rao bound of target localization method based on time-of-arrival measurements is analyzed. For the localization error analysis, the CRLB is derived under the assumptions that the measurement errors are independent and characterized by zero-mean Gaussian distributed process with identical variance, which is not satisfied in the situation of localizing noncooperative targets. Cramér-Rao bound is deduced by using the fact that the variances of TOA measurements of different sensors are affected by the signal-to-noise ratio of the echo signal and are different from each other. Simulations of Monte Carlo experiments are carried out so as to verify the analytical results. 对基于到达时间估计的水下主动目标定位方法的定位误差克拉美罗界进行了分析，针对现有误差分析过程中时间测量误差假设不适用于非合作目标情况的问题，提出了时间测量误差可变的定位误差分析方法，推导了时间测量误差随目标位置变化时定位误差的克拉美罗下界，并进行了计算机蒙特卡罗仿真实验，结果表明经过修正后的克拉美罗下界整体上小于修正前克拉美罗下界，且在定位范围内，修正后克拉美罗下界的分布变化趋势与蒙特卡罗统计实验的定位方差分布变化趋势更加相符。