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当高超声速风洞自由飞试验的测量数据被有色噪声污染时,传统的Cramér-Rao界作为参数估计准度的度量往往过于乐观。文本采用一种修正协方差方法来处理传统的最大似然估计的残差,以便计算出有色残差情况下精确的Cramér-Rao下界,对辨识参数结果进行不确定度评价。以10°半锥角尖锥模型为例,通过大量的Monte Carlo仿真试验和风洞试验验证了修正协方差方法的有效性。结果表明,在风洞试验测量存在有色噪声情况下,修正协方差方法给出的标准差均值约为传统的Cramér-Rao界方法给出的标准差的3~5倍,与参数估计的统计标准差一致,客观反映了参数辨识结果的精准度。
The traditional Cramér-Rao community is often over-optimistic as a measure of parameter estimation accuracy when measured data from free-flight hypersonic wind tunnel tests are contaminated with colored noise. The text uses a modified covariance method to deal with the residuals of the traditional maximum likelihood estimation in order to calculate the exact Cramér-Rao lower bound in the case of colored residuals and evaluate the uncertainty of the identification parameters. Taking the 10 ° cone angle cone model as an example, the effectiveness of the modified covariance method is verified by a large number of Monte Carlo simulations and wind tunnel tests. The results show that the standard deviation of the modified covariance method is about 3 ~ 5 times of the standard deviation given by the traditional Cramér-Rao method in the presence of colored noise in the wind tunnel test. Compared with the statistical standard of parameter estimation Poorly consistent, objectively reflect the accuracy of parameter identification results.