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 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.