Blind Estimation of ARMA Systems

1 : In this paper, we present an approach to blind estimation of non-minimum phase ARMA models using fourth order statistics. The algorithm follows a Residual Time Series (RTS) procedure, which sequentially identiies the AR and MA parts. In step 1 of the RTS concept, the AR estimation is geared to deliver the shortest impulse response of the overall system, so that a new fast approach to MA system identiication can be applied in step 2. Investigations have shown that, in order to obtain a given ARMA estimation quality, the Yule-Walker based AR identiication requires much more data samples of the channel output signal than does the subsequent MA estimation based on eigenvectors. In an attempt to decrease AR estimation bias and variance at a given blocklength, the Structured Total Least Squares (STLS) scheme has proved to achieve better pole estimates of channels with allpasses. However, the STLS technique can not improve on the standard least squares performance, if the cumulant estimation errors are highly correlated, which is true for systems with allpass-free poles close to the unit circle. For these reasons, the AllPass Separation (APS) approach has been conceived, which rst identiies the allpass-free poles using 2nd order statistics, thereby decorrelating the cumulant estimation errors at the overall system's output. This is why, in a 2nd step, the STLS can be applied successfully. Brieey, for the allpass-free poles, APS beneets from high quality 2nd order estimates while STLS yields the best identiication of allpass-poles known to the authors.