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Two approaches to a nonlinear state estimation problem are presented. The particular problem addressed is that of tracking a maneuvering target in three-dimensional space using spherical observations (radar data). Both approaches rely on semi-Markov modeling of target maneuvers and result in effective algorithms that prevent the loss of track that often occurs when a target makes a sudden, radical change in its trajectory. Both techniques are compared using real and simulated radar measurements with emphasis on performance and computational burden.