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.
Estimating the location of a mobile device or a robot from wireless signal strength has become an area of highly active research. The key problem in this context stems from the complexity of how signals propagate through space, especially in the presence of obstacles such as buildings, walls or people. In this paper we show how Gaussian processes can be used to generate a likelihood model for signal strength measurements. We also show how parameters of the model, such as signal noise and spatial correlation between measurements, can be learned from data via hyperparameter estimation. Experiments using WiFi indoor data and GSM cellphone connectivity demonstrate the superior performance of our approach. To navigate reliably in indoor environments, a mobile robot must know where it is. This includes both the ability of globally localizing the robot from scratch, as well as tracking the robot's position once its location is known. Vision has long been advertised as providing a solution to these problems, but we still lack efficient solutions in unmodified environments. Many existing approaches require modification of the environment to function properly, and those that work within unmodified environments seldomly address the problem of global localization. In this paper we present a novel, vision-based localization method based on the CONDENSATION algorithm, a Bayesian filtering method that uses a sampling-based density representation. We show how the CONDENSATION algorithm can be rued in a novel way to track the position of the camera platform rather than tracking an object in the scene. In addition, it can also be used to globally localize the camera platform, given a visual map of the environment. Based on these two observations, we present a vision-based robot localization method that provides a solution to a difficult and open problem in the mobile robotics community. As evidence for the viability of our approach, we show both global localization and tracking results in the context of a state of the art robotics application.