RLS Filter Using Covariance Information and RLS Wiener Type Filter based on Innovation Theory for Linear Discrete-Time Stochastic Descriptor Systems
It is known that the stochastic descriptor systems are transformed into the conventional state equation, the observation equation and the other equation, by using the singular value decomposition. Based on the preliminary problem formulation for the linear discrete-time stochastic descriptor systems in section 2, this paper, in Theorem 1, based on the innovation theory, proposes the recursive least-squares (RLS) filter using the covariance information of the state vector in the state equation and the covariance information of the observation noise in the observation equation. The state equation and the observation equation are transformed from the descriptor systems. Secondly, in Theorem 2, based on the innovation theory, this paper proposes the RLS Wiener type filter for the descriptor systems. It might be advantageous that these filtering algorithms in this paper are derived based on the innovation theory in a unified manner.
A numerical simulation example is demonstrated to show the estimation characteristics of the proposed RLS Wiener type filtering algorithm for the descriptor systems.
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