ABSTRACT Unbiased estimation problem for constrained linear systems is considered, where the systems are subject to unknown inputs that exist in both the dynamic models and the sensor models, and unknown inputs and states are constrained by the corresponding linear equations without and with unknown parameters, respectively. Through system projection to guarantee that the reconstructed dynamical models satisfy the state constraints directly, the recursive least squares estimation of unknown parameters for state constraints is proposed, where left zero matrices are designed to decouple these unknown parameters in the equivalent dynamical models and unknown inputs in the sensor models. Then, the joint unbiased and minimum‐variance based estimators for states and unknown inputs are put forward, where the corresponding gain matrices are solved through special quadratic equations by considering the coupling between the states and the unknown inputs. Here, the unbiased estimators of unknown inputs based on minimum variance are presented instead of the least squares estimation, to avoid the inconvenience of the column rank deficiency of the direct feed‐through matrices. Finally, under what conditions the estimate error covariance matrices of the states converge is studied by using the associated algebraic Riccati equation. In the simulation examples, the proposed method is validated in terms of filtering precision comparison, convergence analysis and different levels of process/measurement noises.
Yang et al. (Thu,) studied this question.