Rank pattern-based selection of input/output ARMA model order

Rational transfer functions are standard models for radar targets and adaptive beamforming. Fitting these models essentially involves estimating the transfer function “poles and zeroes.” A key preliminary step in this estimation process is to determine the numbers of poles and zeros, or equivalently to determine the order of the corresponding ARMA model. A pattern-based method of order selection using matrix ranks is proposed for input/output (I/O) ARMA models, where ARMA model inputs and outputs are each observed in additive noise with known variances. This I/O ARMA model encompasses two distinct scenarios: observational studies in which all observations—those of both inputs and outputs—are erred, and controlled experiments in which outputs are observed with error while inputs are known without error. The proposed rank pattern method exploits the eigenvalue structure of the covariance matrices associated with the observed data and performs well for short data records at moderate SNRs.