Unscented Recursive Filtering for Inequality Constrained Systems

For nonlinear systems with state inequality constraints, the existing unscented recursive filtering methods utilize the constraint information in the sampling and update steps, rather than the prediction step. In practice, the constraints are known a priori and they are always satisfied by any true trajectory. To sufficiently incorporate the valuable information, this paper proposes a constrained unscented recursive filter, which applies the constraints to the whole filtering procedures. First, the constrained dynamic model is constructed by using the system projection technique, which optimally fuses the constraint information and the unconstrained dynamics. Next, the state evolutions of general inequality constraints and their special forms are derived, including linear inequality constraints (LIEC), quadratic inequality constraints (QIEC), and coexistence of LIEC and QIEC. Especially, it is proved that the dynamic model with constraints has a smaller uncertainty than the one without constraints, implying that introducing inequality constraint information definitely improves modeling accuracy. Finally, the numerical simulations in the context of target tracking verify the superiority of the proposed unscented recursive filter over the typical constrained ones for inequality constrained systems.