Multiple-model filtering with multiple constraints

The paper deals with state estimation of nonlinear stochastic systems, where the state is subject to nonlinear equality constraints reflecting some physical or technological limitations. Usually, this problem of constrained state estimation is solved within the Kalman filtering framework. The goal of the paper is to provide a generalization of the solution to a multiplemodel multiple-constraint problem, where the two-step method for constraint application is adopted. In addition, the model weight computation is analyzed and a weight correction for the constrained estimation is proposed. The proposed method is illustrated in a numerical example.