Numerical conditioning and asymptotic variance of subspace estimates (Q1433070)

The authors discuss some new asymptotic variance formulas for the estimated parameters \((A,B,C,D)\) of a stationary linear system with observable exogenous inputs \(u\). The system is assumed in ``innovation representation'' \[ x(t+1)=Ax(t)+Bu(t)+Ke(t),\quad y(t)=Cx(t)=Du(t)+e(t),\tag{1} \] where the white noise \(\{e(t)\}\) has the meaning of (stationary) one-step prediction error of \(\{y(t)\}\), given the infinite past history of \(\{y(t)\}\), \(\{u(t)\}\) up to time \(t-1\). Explict expressions have been provided pinpointing the sensitivity dependence the asymptotic variances of the estimates on the index of collinearity.