Goal inference with Rao-Blackwellized Particle Filters

TL;DR

This paper introduces a Rao-Blackwellized Particle Filter approach for inferring an agent's goal from noisy trajectory data, improving efficiency and providing bounds on inference accuracy.

Contribution

It develops a novel RBPF-based method for intent inference, with theoretical bounds and two estimators, demonstrating fast, accurate goal recovery in practice.

Findings

RBPF improves sample efficiency over standard particle filters

The reduced estimator performs nearly as well as the full estimator

Experiments show fast, accurate intent recovery for compliant agents

Abstract

Inferring the eventual goal of a mobile agent from noisy observations of its trajectory is a fundamental estimation problem. We initiate the study of such intent inference using a variant of a Rao-Blackwellized Particle Filter (RBPF), subject to the assumption that the agent's intent manifests through closed-loop behavior with a state-of-the-art provable practical stability property. Leveraging the assumed closed-form agent dynamics, the RBPF analytically marginalizes the linear-Gaussian substructure and updates particle weights only, improving sample efficiency over a standard particle filter. Two difference estimators are introduced: a Gaussian mixture model using the RBPF weights and a reduced version confining the mixture to the effective sample. We quantify how well the adversary can recover the agent's intent using information-theoretic leakage metrics and provide computable lower bounds on the Kullback-Leibler (KL) divergence between the true intent distribution and RBPF estimates via Gaussian-mixture KL bounds. We also provide a bound on the difference in performance between the two estimators, highlighting the fact that the reduced estimator performs almost as well as the complete one. Experiments illustrate fast and accurate intent recovery for compliant agents, motivating future work on designing intent-obfuscating controllers.