access icon free Optimal linear filtering design for discrete-time systems with cross-correlated stochastic parameter matrices and noises

This study investigates the design of an optimal linear estimator for a class of discrete-time linear systems with correlated stochastic parameter matrices and noises. The considered systems are endowed with the following two main features: (i) cross-correlated stochastic matrices involved in the state and observation equations are assumed and (ii) the process and observation noises have cross-correlation at the same time instant. A decorrelation framework is established to reconstruct such systems. With the equivalent transformation of original dynamic systems resulting from decorrelating operations, the optimal linear recursive filter in the minimum mean square error sense is developed by employing the results of Kalman filtering. The discrete-time linear systems with multiple packet dropouts are modelled as a particular case, and then the proposed filter is applied directly to estimate the system state, while a comparative analysis between the new method and the existing approaches is provided. Simulations demonstrate the effectiveness of the presented algorithm.

Inspec keywords: stochastic processes; discrete time systems; linear systems; matrix algebra; Kalman filters

Other keywords: discrete-time linear systems; optimal linear estimator; discrete-time systems; multiple packet dropouts; observation equations; Kalman filtering; optimal linear recursive filter; cross-correlated stochastic matrices; equivalent transformation; minimum mean square error sense; original dynamic systems; cross-correlated stochastic parameter matrices; decorrelation framework; optimal linear filtering design; decorrelating operations

Subjects: Discrete control systems; Algebra; Simulation, modelling and identification; Other topics in statistics; Linear control systems

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