In this paper we develop a new linear approach to identify the parameters of a moving average (MA) model from the statistics of the output. First, we show that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. Then, this
result is used to obtain a new well-conditioned linear method
to estimate the MA parameters of a non-Gaussian process. The
proposed method presents several important differences with
existing linear approaches. The linear combination of slices used
to compute the MA parameters can be constructed from dif-
ferent sets of cumulants of different orders, providing a general
framework where all the statistics can be combined. Further-
more, it is not necessary to use second-order statistics (the autocorrelation slice), and therefore the proposed algorithm still
provides consistent estimates in the presence of colored Gaussian noise. Another advantage of the method is that while most
linear methods developed so far give totally erroneous estimates if the order is overestimated, the proposed approach does
not require a previous estimation of the filter order. The simulation results confirm the good numerical conditioning of the
algorithm and the improvement in performance with respect to existing methods.
CitationRodríguez Fonollosa, J. A.; Vidal Manzano, J. System identification using a linear combination of cumulant slices. IEEE Transactions on Signal Processing, 1993, vol. 41, núm. 7, p. 2405-2412.
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