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.

中文翻译：

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使用迭代协方差更新从噪声观测估计自回归参数

估计自回归 (AR) 随机过程的参数是一个经过充分研究的问题。在许多应用中，只有 AR 过程的噪声测量可用。加性噪声的影响是系统可以建模为带有有色噪声的 AR 模型，即使测量噪声是白色的，其中相关矩阵取决于 AR 参数。由于相关性，使用多个堆叠观测值进行计算是有利的。使用逆协方差加权对 AR 参数执行加权最小二乘估计可以提供明显更好的参数估计，随着堆栈深度的增加而改进。估计算法本质上是一个向量RLS自适应滤波器，具有时变协方差矩阵。介绍了估计未知协方差的不同方法，以及估计 AR 和观测噪声方差的方法。该符号扩展到向量自回归 (VAR) 过程。仿真结果证明了系数误差和频谱估计方面的性能改进。