Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

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

Fast adaptive identification of autoregressive signals subject to noise

Adaptive identification of autoregressive (AR) signals subject to white measurement noise is studied. A fast adaptive algorithm, which is based on the recently proposed improved least-squares (LS) method, is developed. The variance of the white measurements noise, which specifies the source of the noise-induced bias in the standard LS estimate, is calculated by means of extra noisy measurements of the AR signal. With a good estimate of the measurement noise variance being attained more quickly, the convergence speed of the developed adaptive identification algorithm can be accelerated. Numerical results are presented to demonstrate the promising performance of the new fast adaptive identification algorithm