For the mixed linear/nonlinear state-space model (ML/NLSSM) with asynchronously dependent noise processes (ADNP), this paper aims at designing Rao-Blackwellized particle smoothing (RBPS) algorithms via the sequential Monte Carlo sampling method to solve its fixed-interval smoothing problem. Asynchronous dependency leads to the current measurement depending not only on the current state, but also on the one-step previous state. This subtle feature makes the use of conditionally linear substructures in the ML/NLSSM complicated and thus brings a technical difficulty to the design of RBPS algorithms. In this paper, we first employ a noise de-correlation technique to covert the ML/NLSSM with ADNP into the one without noise dependency. Then for the converted ML/NLSSM, we propose a particle smoothing algorithm called the basic Rao-Blackwellized backward simulation (RBBSi) for the nonlinear substate. To further alleviate the computational complexity of the basic RBBSi, two improved versions of the basic RBBSi are developed via the Metropolis-Hastings sampling. For the (conditionally) linear substate, two analytical smoothing algorithms are provided by virtue of the forward-backward smoothing formula and the two-filter smoothing formula. By integrating the proposed algorithms, a unified implementation framework enveloping six RBPS algorithms is obtained. Finally, two target tracking examples demonstrate the effectiveness and superiority of the proposed RBPS algorithms.

中文翻译：

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用于具有异步相关噪声过程的混合线性/非线性状态空间模型的 Rao-Blackwellized 粒子平滑

针对具有异步相关噪声过程（ADNP）的混合线性/非线性状态空间模型（ML/NLSSM），本文旨在通过顺序蒙特卡罗采样方法设计Rao-Blackwellized粒子平滑（RBPS）算法来解决其固定区间平滑问题。异步依赖导致当前测量不仅取决于当前状态，还取决于一步的前一状态。这种微妙的特征使得ML/NLSSM中条件线性子结构的使用变得复杂，从而给RBPS算法的设计带来了技术难度。在本文中，我们首先采用噪声去相关技术将带有 ADNP 的 ML/NLSSM 转换为无噪声依赖性的技术。然后，对于转换后的 ML/NLSSM，我们提出了一种用于非线性子状态的粒子平滑算法，称为基本 Rao-Blackwellized 后向模拟（RBSi）。为了进一步减轻基本 RBBSi 的计算复杂性，通过 Metropolis-Hastings 采样开发了基本 RBBSi 的两个改进版本。对于（条件）线性子状态，利用前向-后向平滑公式和双滤波器平滑公式提供了两种解析平滑算法。通过整合所提出的算法，得到了包含六种RBPS算法的统一实现框架。最后，两个目标跟踪例子证明了所提出的RBPS算法的有效性和优越性。