We demonstrate a heuristic approach for optimizing the posterior density of the data association tracking algorithm via the random finite set (RFS) theory. Specifically, we propose an adjusted version of the joint probabilistic data association (JPDA) filter, known as the nearest-neighbor set JPDA (NNSJPDA). The target labels in all possible data association events are switched using a novel nearest-neighbor method based on the Kullback-Leibler divergence, with the goal of improving the accuracy of the marginalization. Next, the distribution of the target-label vector is considered. The transition matrix of the target-label vector can be obtained after the switching of the posterior density. This transition matrix varies with time, causing the propagation of the distribution of the target-label vector to follow a non-homogeneous Markov chain. We show that the chain is inherently doubly stochastic and deduce corresponding theorems. Through examples and simulations, the effectiveness of NNSJPDA is verified. The results can be easily generalized to other data association approaches under the same RFS framework.

我们展示了一种启发式方法，用于通过随机有限集 (RFS) 理论优化数据关联跟踪算法的后验密度。具体来说，我们提出了联合概率数据关联 (JPDA) 过滤器的调整版本，称为最近邻集 JPDA (NNSJPDA)。所有可能的数据关联事件中的目标标签都使用基于 Kullback-Leibler 散度的新型最近邻方法进行切换，目的是提高边缘化的准确性。接下来，考虑目标标签向量的分布。切换后验密度后可以得到目标-标签向量的转移矩阵。该转移矩阵随时间变化，导致目标标签向量分布的传播遵循非齐次马尔可夫链。我们证明该链本质上是双重随机的，并推导出相应的定理。通过实例和仿真，验证了NNSJPDA的有效性。结果可以很容易地推广到同一 RFS 框架下的其他数据关联方法。