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This thesis estimates the frequency response of a network where the only data is the output obtained from an Autoregressive-moving average (ARMA) model driven by a random input. Models of random processes and existing methods for solving ARMA models are examined. The estimation is performed iteratively by using the Yule-Walker Equations in three different methods for the AR part and the Cholesky factorization for the MA part. The AR parameters are estimated initially, then MA parameters are estimated assuming that the AR parameters have been compensated for. After the estimation of each parameter set, the original time series is filtered via the inverse of the last estimate of the transfer function of an AR model or MA model, allowing better and better estimation of each model's coefficients. The iteration refers to the procedure of removing the MA or AR part from the random process in an alternating fashion allowing the creation of an almost pure AR or MA process, respectively. As the iteration continues the estimates are improving. When the iteration reaches a point where the coefficients converse the last VIA and AR model coefficients are retained as final estimates.
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Brown, Gerald G.; Rutemiller, Herbert (1977-10);Applications in operations research often employ models which contain linear functions. These linear functions may have some components (coefficients and variables) which are random. (For instance, linear functions in ...
Kislack, Arthur (Monterey, California. U.S. Naval Postgraduate School, 1969-12);A method is proposed for the estimation of the transfer function of a linear, time-invariant system with no numerator dynamics, from random input and output data. The method employed utilizes the Fast Fourier Transform ...
Wester, Roderick C. (Monterey, California. Naval Postgraduate School, 1990-06);This thesis treats the topic of multi-dimensional autoregressive (AR) spectral estimation. An iterative algorithm for the solution of toeplitz block- toeplitz matrix equations is presented. This leads to a fast solution ...