Equality-constrained state estimation for hybrid systems

The authors investigate the problem of state estimation for stochastic hybrid dynamical systems with state equality constraints. They divided this problem into three categories depending on the linearity or non-linearity of equality constraints as well as on the dependence of constraints on the operating mode. For the mode-independent equality-constrained linear case, they present sufficient conditions on process dynamics and filter initial conditions so that the classical interacting multiple model (IMM) algorithm yields state estimates satisfying the linear equality constraint for all subsequent times. For both linear and non-linear systems, the mode-dependent equality constraints must be enforced over time by the filter. They present a modified version of the IMM filter to enforce the equality constraints in such cases. Their numerical results show that the proposed methods provide more accurate estimates than the IMM unconstrained estimates.