State estimation with bounded deterministic errors

In this paper, an alternative method for state estimation of a linear stochastic system under additional bounded set-theoretic disturbance is proposed as a modification of the Bayesian formulation of the problem. The solution is not optimal, but only an approximation based on maximum likelihood approximation. This approach provides superior performance in comparison with classical unknown input observer approach, especially if the model error signal can be easily described by means of inequalities. Simultaneously, the computational complexity of the solution is quite feasible.