Upper bound filter under interval constraints and multiplicative noises

The filtering problem is considered for dynamic systems perturbed by additive and multiplicative noises under interval constraints. Interval constraints induce unknown inputs existing in the reconstructed dynamical model when transforming the state constrained problem into the unconstrained one, which makes the filter design based on minimising the estimate error covariance fail. Due to the coexistence of multiplicative noises and unknown inputs caused by interval uncertainty, a novel recursive upper bound filtering structure is designed for the considered system by a series of linear matrix inequalities. Then, the recursion of the upper bound of the estimate error covariance is realised through the scalar parameter optimisation, based on scaling the diagonal sub-block matrices and non-diagonal sub-block matrices of the innovation covariance which is dependent on the arriving measurement adaptively. Finally, a numerical example shows the effectiveness of the proposed method.