Least squares model reduction

TLDR: This method calculates a low order autoregressive moving average (ARMA) predictor equation from a high order ARMA equation that minimizes the sum of the squares of the prediction errors when the input is white noise.

Abstract: A model reduction method based on the least squares algorithm is derived. This method calculates a low order autoregressive moving average (ARMA) predictor equation from a high order ARMA equation. The low order ARMA equation minimizes the sum of the squares of the prediction errors when the input is white noise. This is almost equivalent to minimizing the sum of the squares of the error in the impulse response function. Transfer function models can also be used and a steady-state gain constraint can be incorporated into the procedure. The merits of this method of model order reduction are shown with three examples. In these examples, the proposed method produced results that compared favorably with highly regarded existing model reduction techniques which require many more computations.