Parameters and order estimation for non-Gaussian ARMA processes

There has been a lot of interest in using higher-order statistics (such as cumulants) in signal processing and system identification problems. There are several reasons behind this interest. First, higher-order cumulants are blind to all kinds of Gaussian processes, hence cumulants suppress additive colored Gaussian noise. Therefore if the signal to be analysed is contaminated by additive Gaussian noise, the noise will vanish in the cumulant domain. Thus, a greater degree of noise immunity is possible. Second, cumulants are useful for identifying nonminimum phase systems or for reconstructing nonminimum phase signals if the signals are non-Gaussian. That is because cumulants preserve the phase information of the signal. Third, cumulants are useful for detecting and characterizing the properties of nonlinear systems. The emphasis of this paper is based on the first property. We address the problem of estimating the orders and the parameters of a non-Gaussian autoregressive moving-average (ARMA) and autoregressive with exogenous input (ARX) processes using third order cumulants. The ARMA processes are widely used in signal modeling and spectrum estimation.