变维交互多模型和GPB2滤波器用于多模型系统中的跟踪
Variable Dimension IMM and GPB2 Filters for Tracking in Multiple Model Systems
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中文总结 AI 辅助
本文提出变维交互多模型（VD-IMM）和变维二阶广义伪贝叶斯（VD-GPB2）滤波器，通过贝叶斯建模和KLD最小化处理不同维度状态的多模型跟踪，仿真验证其优于现有方法。
中文摘要 AI 辅助
本文提出了针对具有不同维度状态的多模型系统的数学上严谨的滤波器，具体为变维交互多模型（VD-IMM）滤波器和变维二阶广义伪贝叶斯滤波器（VD-GPB2）。为此，我们首先提供了变维动态系统及其测量的贝叶斯建模。然后，对于变维线性高斯动态和测量模型，通过假设每个模式的后验具有高斯密度，并在每个预测步骤后执行Kullback-Leibler散度（KLD）最小化以保持每个模式的高斯密度形式，推导出VD-IMM滤波器。随后，执行贝叶斯更新步骤，保持每个模式的高斯密度。VD-GPB2滤波器考虑与VD-IMM滤波器相同的模型，也假设每个模式的后验是高斯分布。相比之下，VD-GPB2滤波器在预测步骤中为每个模式传播高斯混合。在更新步骤中，VD-GPB2滤波器执行KLD最小化以使每个模式具有高斯密度。仿真结果表明，与之前的替代方案相比，VD-IMM和VD-GPB2滤波器具有优势。
英文摘要
This paper presents mathematically principled filters for multiple-model systems with states of different dimensionality, specifically the variable-dimension interacting multiple model (VD-IMM) filter and the variable-dimension generalised pseudo-Bayesian filter of order 2 (VD-GPB2). To do so, we first provide a Bayesian modelling of a variable dimensional dynamic system, and its measurements. Then, for variable dimensional linear Gaussian dynamic and measurement models, the VD-IMM filter is derived by assuming a posterior that has a Gaussian density for each mode, and then performing a Kullback-Leibler Divergence (KLD) minimisation after each prediction step to keep the Gaussian density form for each mode. Subsequently, the Bayesian update step is performed, keeping a Gaussian density for each mode. The VD-GPB2 filter considers the same model as the VD-IMM filter and also assumes that the posterior for each mode is Gaussian. In contrast, the VD-GPB2 filter propagates a Gaussian mixture for each mode in the prediction step. In the update step, the VD-GPB2 filter performs a KLD minimisation to have a Gaussian density for each mode. Simulation results show the benefits of the VD-IMM and VD-GPB2 filters compared to previous alternatives.
发表机构
- Universidad Politécnica de Madrid（马德里理工大学）
机构由 AI 辅助整理，请以论文原文为准。
