标题： 具有多模态观测似然性的高维状态空间的粒子滤波器 显示英文标题

标题： Particle Filtering for Large Dimensional State Spaces with Multimodal Observation Likelihoods

摘要： 我们研究了粒子滤波（PF）中高效的重要性采样技术，当（a）观测似然（OL）频繁呈现多峰或重尾分布，或者（b）状态空间维度较大时（或两者兼有）。 当OL是多峰的，但状态转移概率密度函数（STP）足够窄时，最优的重要性密度通常是单峰的。在此假设下，已提出了许多技术。但是当STP较宽时，该假设不再成立。我们研究了现有技术如何推广到最优的重要性密度是多峰的场景，但在部分状态向量条件下是单峰的情况。推导出了测试该条件后验单峰性的充分条件。 使用PF准确跟踪所需粒子的数量N随着状态空间维度的增加而增加，因此对于高维跟踪问题，任何常规PF都是不切实际的。我们提出了一种部分解决此问题的方法。 一类重要的具有多峰OL的高维问题是使用传感器网络来跟踪大面积内的空间变化物理量（如温度或压力）。这些传感器可能是非线性的，并且可能具有不可忽略的故障概率。 显示英文摘要

摘要： We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavy-tailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow enough, the optimal importance density is usually unimodal. Under this assumption, many techniques have been proposed. But when the STP is broad, this assumption does not hold. We study how existing techniques can be generalized to situations where the optimal importance density is multimodal, but is unimodal conditioned on a part of the state vector. Sufficient conditions to test for the unimodality of this conditional posterior are derived. The number of particles, N, to accurately track using a PF increases with state space dimension, thus making any regular PF impractical for large dimensional tracking problems. We propose a solution that partially addresses this problem. An important class of large dimensional problems with multimodal OL is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and/or may have non-negligible failure probabilities.