System Order Determination by Using LDL<sup>T</sup> Decomposition and Information Criteria

Abstract

In this paper, we present a new order determination method of applying the LDLT decomposition and information criteria. A statistical test is available for the system order determination, and is based on the relation between the system order and the rank of the correlation matrix of the Hankel matrix consists of input-output data. We apply LDLT decomposition and Akaike's Information Criterion (AIC) [3] to determine the rank, so that we can determine the system order by the minimum AIC estimate (MAICE). AIC requires the heavy computation because the maximum likelihood estimates should he obtained by solving the nonlinear optimization problem. Thus we apply a subspace method, e.g., N4SID (Numerical algorithms for Subspace State Space System IDentification) [4], to simplify the computation of the log-likelihood functions. But in subspace methods, stability of the obtained model cannot he guaranteed. When the model obtained is unstable, the maximum likelihood estimates cannot be obtained. So we apply the method [6] that can guarantee the stability of the obtained model to MAICE.