Spectral estimation for noisy signals observed through a linear system

Spectral estimation for autoregressive moving-average (ARMA) processes observed through a known linear system is considered. An algorithm based on a system identification/parameter estimation technique known as the recursive prediction error method is presented for spectral estimation. The algorithm is formulated in the state space to incorporate the constraints imposed by the linear system. The linear system may represent the distortion introduced by the sensor or the channel. Several simulation examples are presented to illustrate the performance of the estimator for various types of data.

[1]  Lennart Ljung,et al.  Analysis of a general recursive prediction error identification algorithm , 1981, Autom..

[2]  L. Ljung.  Convergence analysis of parametric identification methods , 1978 .

[3]  L. Ljung.  Asymptotic gain and search direction for recursive identification algorithms , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[4]  Lennart Ljung,et al.  The Extended Kalman Filter as a Parameter Estimator for Linear Systems , 1979 .

[5]  K. Åström,et al.  Uniqueness of the maximum likelihood estimates of the parameters of an ARMA model , 1974 .

[6]  Benjamin Friedlander.  A recursive maximum likelihood algorithm for ARMA spectral estimation , 1982, IEEE Trans. Inf. Theory.

[7]  Benjamin Friedlander.  Recursive lattice forms for spectral estimation , 1982 .

[8]  Lennart Ljung,et al.  A theoretical analysis of recursive identification methods , 1978, Autom..

[9]  John B. Moore,et al.  Recursive prediction error methods for adaptive estimation , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[10]  F.S. Hill.  Introduction to discrete signal processing , 1978, Proceedings of the IEEE.

[11]  P. Young,et al.  Refined instrumental variable methods of recursive time-series analysis Part I. Single input, single output systems , 1979 .

[12]  B. Friedlander,et al.  System identification techniques for adaptive noise cancelling , 1982 .

[13]  L. Ljung,et al.  Asymptotic normality of prediction error estimators for approximate system models , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.