The theory of amorphous cloud trajectory prediction

Techniques are discussed for using cloud maps (observations) made on a moving cloud of particles to predict the cloud´s future location and shape. The amorphous cloud concept is used to model particle clouds in terms of surfaces moving through state space. Observations are modeled by possibly ´noisy´ surfaces obtained by projecting the state space cloud onto the observation space. Deterministic and maximum likelihood ´type´ prediction techniques are defined. Explicit algorithms are derived for deterministic prediction in the case of linear dynamics and ellipsoidal cloud maps. These algorithms include a closed-form bound and a non-linear programming technique that was successfully implemented. The analysis is motivated by the problem of a radar observing a cloud of chaff particles in orbit (on a ballistic trajectory) around the earth.