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.