Cramer-Rao Lower Bound for State-Constrained Nonlinear Filtering

This letter presents a mean-square error lower bound for state estimation of nonlinear stochastic systems under given differentiable state constraints. Its recursive formulation permits incorporation of random process and measurement errors and is shown to be a generalization of the known lower bound for unconstrained problems. The bound is evaluated for the example of locating a ground vehicle fromnoisy measurements of its horizontal position and velocity incorporating a roadmap.