System identification using a linear combination of cumulant slices

Abstract-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 ex-pressed 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 au-tocorrelation slice), and therefore the proposed algorithm still provides consistent estimates in the presence of colored Gauss-ian noise. Another advantage of the method is that while most linear methods developed so far give totally erroneous esti-mates if the order is overestimated, the proposed approach does not require a previous estimation of the filter order. The sim-ulation results confirm the good numerical conditioning of the algorithm and the improvement in performance with respect to existing methods. I