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本文分析了以前ARMA建模中的一些方法。这些方法只用到相关序列的一部分。对于没有误差的ARMA序列来说,这样做是充分的,因为ARMA过程的信息已经全部包含在其相关序列的一部分中。但是对实测的相关序列,我们可以利用相关序列的全部来减小误差对参数估计的影响。另外,这些方法在实际上还不能保证得到的谱估计是非负的。基于上述考虑,本文提出了一种有约束的最小二乘拟合方法。该方法利用实测相关序列的全体,并且保证得到的谱估计是非负的。
This article analyzes some of the previous ARMA modeling methods. These methods only use part of the relevant sequence. This is sufficient for an ARMA sequence without errors because the information of the ARMA process is all contained in part of its associated sequence. However, for the measured correlation sequence, we can use the whole of the correlation sequence to reduce the influence of the error on the parameter estimation. In addition, these methods do not actually guarantee that the spectral estimation obtained is nonnegative. Based on the above considerations, this paper presents a constrained least-squares fitting method. This method uses the whole of the measured sequence and assures that the resulting spectral estimation is nonnegative.