时钟抖动下加速度测量值的数值双积分误差

摘要

采用蒙特卡洛分析法,对由于时钟抖动造成的加速度计定位误差进行了系统的分析.仿真结果表明,在存在时钟抖动的情况下,加速度测量值是渐近服从高斯分布的,这个结果与理论分析相吻合.对积分距离的方差与时钟抖动之间的关系进行了分析,理论及仿真分析结果都表明了噪声的数值双积分的积分误差与时钟抖动的大小成正比.当输入一个幅值为1g,周期为1 s的正弦波加速度信号时,1 s后数值双积分的积分误差与时钟抖动的比例系数为0.261 1.%The positioning error of accelerometers due to a clock jitter is analyzed by Monte Carlo analysis method. The simulation results reveal that the distribution of acceleration measurements with the clock jitter is approximately Gaussian distribution, which is well coincident with the theoretical analysis. Moreover, the relation between the variance of integration distance and the clock jitter is analyzed. Both the theoretical and simulation results indicate that the error of numerical double integration due to the clock jitter increases proportional to the clock jitter. When the input acceleration signal is a sine wave with a amplitude of 1g and a period of 1 s, the ratio between the integration error of numerical double integration and the clock jitter is 0.261 1 after 1 s.