Cascade Discrete-Continuous State Estimators for a Class of Monotone Systems

A cascade discrete-continuous state estimator is proposed for a class of monotone systems with both continuous and discrete state. The proposed estimator exploits the partial order preserved by the system dynamics in order to satisfy two properties. First, its computation complexity scales with the number of variables to be estimated instead of scaling with the size of the discrete state space. Second, a separation principle holds: the continuous state estimation error is bounded by a monotonically decreasing function of the discrete state estimation error, the latter one converging to zero. A multi-robot example is proposed.