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New approaches to Wiener filtering and Kalman filtering for descriptor systems. (Chinese. English summary) Zbl 0978.93073

The authors consider the following descriptor system: \[ M x(t+1)=\Phi x(t)+\Gamma w(t),\quad y(t)=H x(t)+v(t), \] where \(x(t)\in {\mathbb R}^n\), \(y(t)\in {\mathbb R}^m\), \(M\) is singular and \(\det (zM-\Phi)\not\equiv 0, \forall z\in {\mathbb C}\), \(w(t)\) and \(v(t)\) are white noise with zero mean, and the system is completely observable. Using a decomposition of matrices and a time series analysis method, based on an autoregressive moving average (ARMA) innovation model and white noise theory, they present Wiener state estimators and steady-state Kalman estimators for the above-mentioned system. By the way, they handle the optimal filtering, smoothing, and prediction problems in a unified framework. According to their presented approach there is no need for solving Diophantine equations and Riccati equations. Two simulation examples are given to illustrate their approach and its effectiveness.

MSC:

93E10 Estimation and detection in stochastic control theory
93C55 Discrete-time control/observation systems
93C35 Multivariable systems, multidimensional control systems
93E15 Stochastic stability in control theory
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