A simplified NARMAX method using nonlinear input-output data

Abstract

A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling (GMDH) method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.

Estimation of time series noise covariance using correlation technology

“…Autoregressive moving average (ARMA) is one of the most widely used methods in the area of system identification [1]. Consider an arbitrary time series {y k } (stationary or nonstationary), where the clean signal {s k } is corrupted by additional zero-mean Gaussian noise {v k } with variance R v , namely…”

“…Sinha and Tom [10] uses Carew's method as an initial estimate, and utilizes stochastic approximation to account for nonstationary process, but this additional step may be prohibitively slow. Odelson et al [11,12] developed an autocovariance least-squares (ALS) method for estimating noise covariance in model-based control methods like model predictive control, but the least-square equations they use is with (m 2 + 1) independent variables and (N × N ) equations towards equation (1), where N is a user chosen number. In the following work by Rajamani and Rawlings [13], the number of equations has been reduced to N and only uses (m + 1) independent variables.…”

“…In this paper, we developed a new concisely autocovariance least-square (CALS) method for estimating time series noise covariance by solving least-square equations with only 3 or 2 independent variables (depending on whether the noise and clean signal are correlated or not) and N equations towards equation (1), which is much more simpler than that in [11∼13, 17]. The time series does not imperatively have to be stationary.…”