The unconstrained and inequality constrained moving horizon approach to robot localization

We present a moving horizon approach for estimating the state of a nonlinear dynamic system that may be subject to inequality constraints. The method takes advantage of a recent smoothing algorithm proposed in the literature based on interior point techniques. The approach exploits the same decomposition used for unconstrained Kalman-Bucy smoothers. Hence, the number of operations required by the algorithm scales linearly with the length of the horizon, making it suitable for online applications. We apply this method to the robot localization problem, showing that it is able to produce much more accurate results than the iterated Kalman filter with little additional computational effort.