Filtering with State-Observation Examples via Kernel Monte Carlo Filter.

Area of Science:

• Machine Learning
• Robotics
• Statistical Inference

Background:

• Standard state-space filtering requires explicit or parametric observation models.
• Many real-world scenarios lack explicit observation models, especially when state and observations differ significantly.
• Existing methods struggle with nonparametric observation models derived solely from state-observation examples.

Purpose of the Study:

• To propose a novel filtering method, the kernel Monte Carlo filter, for state-space models with unknown observation models.
• To enable nonparametric posterior inference using only examples of state-observation pairs.
• To analyze the theoretical properties of the proposed sampling and resampling procedures.

Main Methods:

• Utilizes kernel mean embeddings for nonparametric posterior inference.
• Represents state distributions as weighted samples.
• Employs kernel Bayes' rule for state posterior estimation and kernel herding for resampling.

Main Results:

• The kernel Monte Carlo filter effectively performs filtering without explicit observation models.
• Theoretical analysis shows sampling performance depends on effective sample size, and resampling improves it.
• Demonstrated effectiveness through synthetic, artificial, and real-world data, including robot localization.

Conclusions:

• The kernel Monte Carlo filter offers a powerful nonparametric approach for state-space filtering with example-based observation models.
• Kernel mean embeddings provide a robust framework for handling unknown observation models.
• The method shows promise for applications like vision-based mobile robot localization.