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This is the first part of a comprehensive and up-to-date survey of the techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. It surveys various mathematical models of target motion/dynamics proposed for maneuvering target tracking, including 2D and 3D maneuver models as well as coordinate-uncoupled generic models for target motion. This survey emphasizes the underlying ideas and assumptions of the models. Interrelationships among models and insight to the pros and cons of models are provided. Some material presented here has not appeared elsewhere.