New scheme for discrete observer design with estimation error covariance assignment

This article presents an innovative method for solving an estimation error covariance assignment problem to design an observer for a stochastic linear system. In the proposed method, the covariance assignment problem is converted to the problem of finding an extra noise-like input to the observer. Using appropriate matrix manipulation, the Riccati equation of the estimation error covariance assignment problem, is converted to a new deterministic linear state-space model. Also, the extra noise-like input to the observer is modelled as an input to the new deterministic linear state-space model. Therefore, all the conventional and well-defined control strategies could be applied and there is no need to solve a complicated Riccati equation. Moreover, using the proposed method, a multi-objective estimation error covariance tracking problem would be easily converted to the problem of controlling a standard deterministic linear state-space system. Based on the integral control method, which is applied to the new state-space model, formulations for the proposed covariance feedback law are presented. The control law results in a stable closed-loop covariance system and assigns a pre-specified covariance matrix to the estimation errors.