Non-iterative Subspace-based Method for Estimating AR Model Parameters in the Presence of White Noise with Unknown Variance

We consider the problem of estimating the parameters of autoregressive (AR) processes in the presence of white observation noise with unknown variance, which appears in many signal processing applications such as spectral estimation, and speech processing. A new non-iterative subspace-based method named extended subspace (ESS) method is developed. The basic idea of the ESS is to estimate the variance of the observation noise via solving a generalized eigenvalue problem, and then estimate the AR parameters using the estimated variance. The major advantages of the ESS method include excellent reliability and robustness against high-level noise, and also estimating the AR parameters in a non-iterative manner. Simulation results help to evaluate the performance of the ESS method, and demonstrate its robustness.

[1]  Alimorad Mahmoudi,et al.  Inverse filtering based method for estimation of noisy autoregressive signals , 2011, Signal Process..

[2]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[3]  Sergiy A. Vorobyov,et al.  An array processing approach to pilot decontamination for massive MIMO , 2015, 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[4]  Ivan Ganchev Ivanov.  Stochastic Modeling and Control , 2012 .

[5]  Alimorad Mahmoudi,et al.  Two-dimensional noisy autoregressive estimation with application to joint frequency and direction of arrival estimation , 2018, Multidimens. Syst. Signal Process..

[6]  Umberto Soverini,et al.  Identification of autoregressive models in the presence of additive noise , 2008 .

[7]  Reza Sameni,et al.  Online filtering using piecewise smoothness priors: Application to normal and abnormal electrocardiogram denoising , 2017, Signal Process..

[8]  B.W. Dickinson,et al.  An introduction to statistical signal processing with applications , 1979, Proceedings of the IEEE.

[9]  Alimorad Mahmoudi,et al.  Parameter estimation of autoregressive signals from observations corrupted with colored noise , 2010, Signal Process..

[10]  Howell Tong.  Autoregressive model fitting with noisy data by Akaike's information criterion (Corresp.) , 1975, IEEE Trans. Inf. Theory.

[11]  R. Guidorzi,et al.  A noise-compensated estimation scheme for AR processes , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[12]  Robert W. Heath,et al.  Channel Estimation and Hybrid Precoding for Millimeter Wave Cellular Systems , 2014, IEEE Journal of Selected Topics in Signal Processing.

[13]  Wei Xing Zheng.  On Estimation of Autoregressive Signals in the Presence of Noise , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  R. Viswanathan,et al.  An introduction to statistical signal processing with applications , 1979 .

[15]  Lijuan Jia,et al.  On convergence of a BCLS algorithm for noisy autoregressive process estimation , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[16]  Bogdan Dumitrescu,et al.  Conditional independence graphs for multivariate autoregressive models by convex optimization: Efficient algorithms , 2017, Signal Process..

[17]  Karl Meerbergen,et al.  The Quadratic Eigenvalue Problem , 2001, SIAM Rev..

[18]  Petre Stoica,et al.  Adaptive algorithms for constrained ARMA signals in the presence of noise , 1988, IEEE Trans. Acoust. Speech Signal Process..

[19]  Carlos E. Davila.  A subspace approach to estimation of autoregressive parameters from noisy measurements , 1998, IEEE Trans. Signal Process..

[20]  Wei Xing Zheng.  Fast identification of autoregressive signals from noisy observations , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[21]  Wei Xing Zheng.  Autoregressive parameter estimation from noisy data , 2000 .

[22]  Wei Xing Zheng,et al.  Novel parameter estimation of autoregressive signals in the presence of noise , 2015, Autom..

[23]  Alimorad Mahmoudi,et al.  Estimation of the parameters of multichannel autoregressive signals from noisy observations , 2008, Signal Process..

[24]  Suman Dutta,et al.  Automated classification of non-motor mental task in electroencephalogram based brain-computer interface using multivariate autoregressive model in the intrinsic mode function domain , 2018, Biomed. Signal Process. Control..

[25]  Eric Grivel,et al.  Jeffrey's divergence between autoregressive processes disturbed by additive white noises , 2018, Signal Process..

[26]  S. Kay.  Noise compensation for autoregressive spectral estimates , 1980 .

[27]  Paul Honeine,et al.  Kernel autoregressive models using Yule-Walker equations , 2013, Signal Process..