This paper addresses the problem of filtering with a state-space model.
Standard approaches for filtering assume that a probabilistic model for
observations (i.e. the observation model) is given explicitly or at least
parametrically. We consider a setting where this assumption is not satisfied;
we assume that the knowledge of the observation model is only provided by
examples of state-observation pairs. This setting is important and appears when
state variables are defined as quantities that are very different from the
observations. We propose Kernel Monte Carlo Filter, a novel filtering method
that is focused on this setting. Our approach is based on the framework of
kernel mean embeddings, which enables nonparametric posterior inference using
the state-observation examples. The proposed method represents state
distributions as weighted samples, propagates these samples by sampling,
estimates the state posteriors by Kernel Bayes' Rule, and resamples by Kernel
Herding. In particular, the sampling and resampling procedures are novel in
being expressed using kernel mean embeddings, so we theoretically analyze their
behaviors. We reveal the following properties, which are similar to those of
corresponding procedures in particle methods: (1) the performance of sampling
can degrade if the effective sample size of a weighted sample is small; (2)
resampling improves the sampling performance by increasing the effective sample
size. We first demonstrate these theoretical findings by synthetic experiments.
Then we show the effectiveness of the proposed filter by artificial and real
data experiments, which include vision-based mobile robot localization.

本文提出了 Kernel Monte-Carlo Filter 方法，其中状态变量及观测值的关系仅通过若干组已知的观测值得知，该方法基于核平均嵌入的框架，通过简单有效的样本加权，样本采样，样本重采样等操作实现对状态量的准确后验推断，此方法在机器人定位等领域的应用效果显著。