Global estimation in constrained environments

This article considers the optimal estimation of the state of a dynamic observable using a mobile sensor. The main goal is to compute a sensor trajectory that minimizes the estimation error over a given time horizon taking into account uncertainties in the observable dynamics and sensing, and respecting the constraints of the workspace. The main contribution is a methodology for handling arbitrary dynamics, noise models, and environment constraints in a global optimization framework. It is based on sequential Monte Carlo methods and sampling-based motion planning. Three variance reduction techniques–utility sampling, shuffling, and pruning–based on importance sampling, are proposed to speed up convergence. The developed framework is applied to two typical scenarios: a simple vehicle operating in a planar polygonal obstacle environment and a simulated helicopter searching for a moving target in a 3-D terrain.