基于状态空间模型的IIR滤波运算不确定度评估

摘要

针对IIR滤波运算如何依据GUM准则进行结果不确定度评估的问题,将滤波器转化为对应的状态空间模型,消除了由于输出量的递归导致无法直接利用GUM准则进行不确定度评估的问题,并推导出了直接计算输出量不确定度的递推公式.该方法采用迭代计算,实现简单,可实时运行.软件仿真并与蒙特卡洛法计算结果比较表明,该方法能够准确计算带有噪声的被测信号通过系数具有不确定度的IIR滤波器后输出量的不确定度.%To solve the problem of uncertainty evaluation for IIR filter calculation in line with GUM,a state-space representation for the filter is used.As a result the output of the filter depends only on the current input and the current state-space vector,the dependence on past inputs and past outputs,which causes unable to evaluation uncertainty under GUM framework,is absorbed in the state-space vector,and the uncertainty calculation formula is given.The proposed method applies iterative computation and thus can be realized in an easy way,and also enables real-time applications.The proposed procedure is illustrated by simulation,for instance,a noise-corrupted signal and a IIR filter with coefficients are uncertain.