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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.