Identification of MA processes using cumulants: several sets of linear equations
Diego Pablo Ruiz, Maria Carmen Carrion, Antolino Gallego, Juan Antonio Morente · IEE Proceedings - Vision Image and Signal Processing · 1996
Several new sets of linear equations relating the coefficients of a moving average (MA) system with its (k – 1)th- and kth-order polyspectra, with k>2 are presented. These equations are used to identify the nonminimum phase MA model parameters from the statistics of the noisy output. The system is driven by an (unobservable) independent and identically distributed nongaussian process and the noise is additive and coloured gaussian with unknown power spectrum. Four estimators based on the method of least-squares using linear relations between third- and fourth-order statistics are proposed and discussed. These methods make use of more higher order statistics information than other linear methods do, and the uniqueness of the solutions can normally be guaranteed by the linearity of the equations. Results from computer simulations confirm the expected theoretical advantages of the proposed methods in coloured noise environments and allow one to draw a comparison among proposed and other published linear methods.