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<p>This paper introduces an advanced extended object tracking algorithm developed within the random finite sets (RFS) framework, utilizing a Poisson multi-Bernoulli mixture (PMBM) filter with forward-backward smoothing capabilities. The proposed solution combines a forward PMBM filter propagation with a novel backward multi-Bernoulli (MB) smoother, establishing a complete Bayesian framework for extended object tracking. The methodology begins with a rigorous derivation of the standard PMBM forward recursion, followed by the development of an MB backward smoothing procedure. A key theoretical contribution is the demonstration that the backward smoothing density, obtained through set integration of survival object components, maintains the MB distribution property. For practical implementation, we derive a closed-form solution using Gamma Gaussian inverse-Wishart (GGIW) distributions, enabling efficient estimation of both kinematic states and spatial extents. Computational efficiency is further enhanced through strategic application of Murty’s algorithm for optimal hypothesis management. Comprehensive simulation studies validate the algorithm’s performance, demonstrating significant improvements in tracking accuracy and computational efficiency compared to conventional approaches. The effectiveness of the proposed method is validated via an extensive simulation study.</p>

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A forward-backward smoothing algorithm for extended object tracking based on the PMBM filter

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年11月6日

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  • Xingxiang Xie,
  • Zhumei Song,
  • Kening Li,
  • Xiongwei Zhao

摘要

This paper introduces an advanced extended object tracking algorithm developed within the random finite sets (RFS) framework, utilizing a Poisson multi-Bernoulli mixture (PMBM) filter with forward-backward smoothing capabilities. The proposed solution combines a forward PMBM filter propagation with a novel backward multi-Bernoulli (MB) smoother, establishing a complete Bayesian framework for extended object tracking. The methodology begins with a rigorous derivation of the standard PMBM forward recursion, followed by the development of an MB backward smoothing procedure. A key theoretical contribution is the demonstration that the backward smoothing density, obtained through set integration of survival object components, maintains the MB distribution property. For practical implementation, we derive a closed-form solution using Gamma Gaussian inverse-Wishart (GGIW) distributions, enabling efficient estimation of both kinematic states and spatial extents. Computational efficiency is further enhanced through strategic application of Murty’s algorithm for optimal hypothesis management. Comprehensive simulation studies validate the algorithm’s performance, demonstrating significant improvements in tracking accuracy and computational efficiency compared to conventional approaches. The effectiveness of the proposed method is validated via an extensive simulation study.