In this study, we extend traditional (single-target) hybrid systems to multi-target hybrid systems with a focus on the multi-maneuvering-target tracking system. This system consists of a continuous state, a discrete and switchable state, and a discrete, time-constant, and unique state. By defining a new generalized labeled multi-Bernoulli density, we prove that it is closed under the Chapman-Kolmogorov prediction and Bayes update for multi-target hybrid systems. In other words, we provide the exact derivation of a solution to this system, i.e., the multi-model generalized labeled multi-Bernoulli filter, which has been developed without strict proof.

在这项研究中，我们将传统（单目标）混合系统扩展到多目标混合系统，重点是多机动目标跟踪系统。该系统由连续状态，离散且可切换的状态以及离散，时间恒定且唯一的状态组成。通过定义一个新的广义标记的多伯努利密度，我们证明它在Chapman-Kolmogorov预测和贝叶斯更新的多目标混合系统下是封闭的。换句话说，我们提供了该系统解决方案的精确推导，即未经严格证明而开发的多模型广义标记多伯努利滤波器。