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The approach of using a random matrix for extended object and group target tracking (EOT and GTT) is efficient. Designing and effectively applying this approach rely on modeling the extended object and group targets accurately. To describe complex dynamical variation and practical observation distortion of the extension in size, shape and orientation, two random matrix based models are proposed. True measurement noise can also be incorporated into the measurement model easily. Facilitated by special properties of the models, an approximate Bayesian approach is proposed to estimate the kinematic state and the extension jointly. For maneuvering EOT and GTT, a multiple-model approach is derived by moment matching. To evaluate what is proposed, simulation results of a scenario for maneuvering EOT are also given. The results illustrate the effectiveness of the proposed models and approach.