Maximum likelihood autoregressive (AR) model parameter estimation problem with independent snapshots observed under white Gaussian measurement noise is studied. In addition to the AR model parameters, the measurement noise variance is also included among the unknowns of the problem to develop a general solution covering several special cases such as the case of known noise variance, noise-free snapshots, the single snapshot operation etc. The presented solution is based on the expectation-maximization method which is formulated by assigning the noise-free snapshots as the missing data. An approximate version of the suggested method, at a significantly reduced computational load with virtually no loss of performance, has also been developed. Numerical results indicate that the suggested solution brings major performance improvements in terms of estimation accuracy and does not suffer from unstable AR filter estimates unlike some other methods in the literature. The suggested method can be especially useful for small-dimensional multiple-snapshot noisy AR modeling applications such as the clutter power spectrum modeling application in radar signal processing.

研究了在高斯白噪声下观测到的具有独立快照的最大似然自回归（AR）模型参数估计问题。除了AR模型参数外，测量噪声方差还包括在问题的未知数中，以开发出涵盖几种特殊情况的通用解决方案，例如已知噪声方差，无噪声快照，单快照操作等。提出的解决方案基于期望最大化方法，该方法通过将无噪声快照分配为缺失数据来制定。还开发了一种建议方法的近似版本，可显着减少计算量，而几乎不损失性能。数值结果表明，与文献中的某些其他方法相比，建议的解决方案在估计精度方面带来了重大的性能改进，并且不会遭受不稳定的AR滤波器估计的困扰。所提出的方法对于小尺寸多快照噪声AR建模应用（例如雷达信号处理中的杂波功率谱建模应用）特别有用。