This work presents a tractable approach to multi-object posterior computation under a generic measurement likelihood function. While filtering is a popular solution, valuable historical information is discarded. Posterior inference, which captures the full history of the multi-object states, provides a more comprehensive solution but is notoriously difficult and has received limited attention. Our proposed approach uses Gibbs Sampling (GS) to generate samples from the multi-object posterior. In particular, we establish that the conditional distributions of the multi-object posterior are Bernoulli random finite sets with explicit existence probabilities and attribute densities. These conditionals are straightforward to evaluate and sample from, enabling the construction of an efficient Gibbs sampler with standard convergence guarantees. To demonstrate its versatility, we develop the first multi-scan multi-object smoothing algorithm for superpositional measurements. Numerical experiments show that the proposed method delivers robust performance in challenging low-SNR scenarios where detection based smoothing deteriorates. Moreover, posterior samples obtained from our approach provide statistical characterizations of key variables and parameters, highlighting the advantages of posterior inference. This approach enriches multi-object estimation techniques, which historically lacked smoothing capabilities for non-standard measurements.

翻译：本文提出了一种在通用测量似然函数下进行多目标后验计算的易处理方法。虽然滤波是常用的解决方案，但会丢弃有价值的历史信息。能够捕捉多目标状态完整历史的后验推断提供了更全面的解决方案，但众所周知其求解困难且受到的关注有限。我们提出的方法采用吉布斯采样从多目标后验中生成样本。具体而言，我们证明了多目标后验的条件分布是具有显式存在概率和属性密度的伯努利随机有限集。这些条件分布易于评估和采样，从而能够构建具有标准收敛保证的高效吉布斯采样器。为展示其通用性，我们首次开发了适用于叠加测量的多扫描多目标平滑算法。数值实验表明，在基于检测的平滑算法性能下降的低信噪比挑战性场景中，所提方法具有稳健表现。此外，通过该方法获得的后验样本能够提供关键变量和参数的统计特征，突显了后验推断的优势。该工作丰富了多目标估计技术，弥补了该类方法历史上缺乏针对非标准测量平滑能力的不足。