动态总方差设计及其快速算法

Design of dynamic total variance and its fast algorithm

Allan方差法分析随机误差时存在2点缺陷,一是长相关时间下估计值震荡较大,二是无法跟踪信号的动态变化。本文融合总方差法和动态Allan方差法的思想和优势,提出了动态总方差法。首先使用窗函数截取原始数据,然后对窗内数据进行延拓,对延拓后的数据进行总方差分析,得到原始信号的局部随机特性,随着窗函数的滑动可以得到原始信号的随机变化特性。经验证,动态总方差法同时解决了Allan方差法存在的2个缺陷。最后设计了半球谐振陀螺(HRG)的线振动试验验证此算法的有效性,分析结果表明动态总方差法在分析精度和使用的数据量上具有优势。但是动态总方差法又存在计算量大、分析速度慢的问题,因此本文又推导出了动态总方差法的递推公式,从而给出了动态总方差的快速算法。

There exist two shortcomings in Allan variance approach when it is used to analyze random error. First,the vibration of estimated value is large in long-term correlation. Second it can’t follow the dynamic change of signal. This paper integrates the thought and advantage of total variance and dynamic allan variance,and proposes the dynamic total variance approach. Firstly,original data is truncated by window function. Secondly,we continue the data in the window. Then the data after continuation is analyzed by total variance,so that local random characteristic is acquired. With the window sliding,the change of random characteristic of original signal with time is obtained. Through verification,the dynamic total variance can solve the two shortcomings of Allan variance approach. Eventually,linear vibration trial of hemispherical resonator gyro（ HRG） is designed to clarify this new algorithm,which indicates that dynamic total variance possesses advantages in analysis accuracy and data quantity that it used. However,this new algorithm has the problem of excessive calculation and low speed of analysis,so we derive recursive formula of it,based on which fast algorithm is provided.