δ-GLMB

Section IV-C证明δ-GLMB密度实际上是一个标记的多伯努利混合，但从存储和计算的角度来看，参数化效率较低[1]。
Section IV-C proves that the δ-GLMB density is in fact a labelled multi-Bernoulli mixture, but with a less efficient parameterisation from a storage and computational point of view [1].

注意，(39)中的标签MBM也可以写成(labelled) MBM₀₁参数化，类似于(38)中(9)的表达方式。我们建立了以下推论[1].。

Note that the labelled MBM in (39) can also be written in (labelled) MBM₀₁ parameterisation analogously to how (9) was expressed in (38). We establish the following corollary [1].

推论6。如果将出生过程是标记多伯努利或标记MBM，其目标具有唯一标签，且标签随时间固定，则标记MBM家族是标准点目标量测和动态模型的共轭先验[1]。
Corollary 6. If the birth process is labelled multi-Bernoulli or labelled MBM, whose targets have unique labels, and labels are fixed with time, the family of labelled MBM is a conjugate prior for the standard point target measurement and dynamic models [1].

我们需要对每个混合分量求解一个数据关联问题，即对前一个全局假设求解一个数据关联问题。在这种情况下，与MBM₀₁/δ-GLMB参数化相比，MBM参数化也具有优势，因为混合分量的数量更少。MBM₀₁/δ-GLMB参数化效率低下，这是导致MBM₀₁滤波器在预测和更新步骤方面具有这些优势的主要原因。一个MBM全局假设可以有效地表示多个δ-GLMB全局假设，而MBM滤波器的这种额外灵活性简化了预测和更新步骤，并且与我们是否使用标签无关[1]。
We need to solve a data-association problem for each mixture component, that is, for every global hypothesis in the prior. In this case, the MBM parameterisation is also advantageous due to the lower number of mixture components, compared to the MBM₀₁/ δ-GLMB parameterisations. The reason for these advantages in the prediction and update steps in the MBM filter is mainly due to the inefficient MBM₀₁/δ-GLMB parameterisations. One MBM global hypothesis can efficiently represent many δ-GLMB global hypotheses and this extra degree of flexibility in the MBM filter simplifies the prediction and update steps and it is independent of whether or not we use labels [1].

 

@article{Ref[1],
   author = {García-Fernández, Á F. and Williams, J. L. and Granström, K. and Svensson, L.},
   title = {Poisson Multi-Bernoulli Mixture Filter: Direct Derivation and Implementation},
   journal = {IEEE Transactions on Aerospace and Electronic Systems},
   volume = {54},
   number = {4},
   pages = {1883-1901},
   ISSN = {1557-9603},
   DOI = {10.1109/TAES.2018.2805153},
   year = {2018},
   type = {Journal Article}
} 

 

感谢 https://www.cnblogs.com/sunny99/ sumoier对本文的帮助