Wiener State Estimator for Non-regular Descriptor System

Using the modern time-series analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimator, non-regular descriptor discrete-time stochastic linear systems are researched. Under assumption 1~3, an asymptotically stable reduced-order Wiener state estimator for descriptor systems is given by using projection and block matrix theories. Non-regular descriptor systems include general descriptor systems in them. And the algorithm is reduced-order. It avoids the solution of the Riccati equations and Diophantine equations. So that it reduces the computational burden, and is suitable for real time applications. Introduction Descriptor systems are often seen in such fields as circuit, economics and robotics, thus receiving more and more attention. In recent years, a number of very useful research results have been obtained in terms of regular descriptor systems [1~4]. However, research on non-regular descriptor systems is still lacking. In this paper, based on ARMA innovation model and white noise estimators, Wiener state estimators for non-regular descriptor systems are presented by using modern time series analysis method [5] and block matrix theory [6,7]. The presented Wiener state estimators have more universal significance since they can be applied to both non-regular and regular descriptor systems. Consider the discrete time descriptor stochastic system ) ( ) ( ) 1 ( t w t x t Mx Γ Φ + = + , (1) ) ( ) ( ) ( t v t Hx t y + = , (2) where the state n R t x ∈ ) ( , the measurement m R t y ∈ ) ( , q R t w ∈ ) ( , m R t v ∈ ) ( , constant matrices M 、Φ、 Γ and H are respectively n p× , n p× , q p× and n m× , and m n > . Assumption 1. ) (t w and ) (t v are correlated white noises. [ ] ij v w Q S S Q j v j w t v t w δ       =             T T T ) ( ) ( ) ( ) ( E , 0 T >      