Descriptor Wiener state estimators (Q5925933)

The authors consider a linear discrete stochastic singular system NEWLINE\[NEWLINEMx(t+ 1)= \Phi x(t)+\Gamma w(t),\qquad y(t)= Hx(t)+ v(t),NEWLINE\]NEWLINE with the state \(x(t)\in \mathbb{R}^n\), the measurement \(y(t)\in \mathbb{R}^m\), \(M\), \(\Phi\), \(\Gamma\), and \(H\) are constant matrices, \(M\) is a singular square matrix, i.e., \(\text{det }M= 0\). A new time-domain Wiener filtering approach is presented. Compared with the Kalman filtering approach, the solution of the Riccati equations is avoided, so that the computational burden is reduced.