Kalman filter design using the Levinson algorithm and output statistics

In this paper we present a new method to identify the minimum parameter autoregressive moving-average (ARMA) model of a system. The model identified, when used as a one-step ahead predictor, produces a minimum error variance estimate. The parameters are found from output statistics by solving a set of linear equations. The ARMA model found is equivalent to the Kalman filter innovations model but we avoid solving a Riccati-type equation. The equivalence is demonstrated through a numerical example.