Moon Todd K, Gunther Jacob H
Electrical and Computer Engineering Department, Utah State University, Logan, UT 84332, USA.
Entropy (Basel). 2020 May 19;22(5):572. doi: 10.3390/e22050572.
Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation.
估计自回归（AR）随机过程的参数是一个已得到充分研究的问题。在许多应用中，只能获得AR过程的带噪测量值。加性噪声的影响在于，即使测量噪声是白噪声，系统也可建模为具有有色噪声的AR模型，其中相关矩阵取决于AR参数。由于存在相关性，使用多个堆叠观测值进行计算较为便利。使用逆协方差加权对AR参数进行加权最小二乘估计可显著提供更好的参数估计，且随着堆叠深度的增加，改进效果也会增强。该估计算法本质上是一个具有时变协方差矩阵的向量RLS自适应滤波器。文中介绍了估计未知协方差的不同方法，以及一种估计AR和观测噪声方差的方法。符号表示扩展到向量自回归（VAR）过程。仿真结果表明在系数误差和频谱估计方面性能有所提升。
