# Goal inference with Rao-Blackwellized Particle Filters

arXiv: https://arxiv.org/abs/2512.09269 · HTML: https://mlsanity.com/paper/2512.09269/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 7 of 7)

- [Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks](https://mlsanity.com/paper/1301.3853/) (2013)
- [Entropy Maximization for Markov Decision Processes Under Temporal Logic Constraints](https://mlsanity.com/paper/1807.03223/) (2018)
- [Privacy-Preserving Policy Synthesis in Markov Decision Processes](https://mlsanity.com/paper/2004.07778/) (2020)
- [Smoother Entropy for Active State Trajectory Estimation and Obfuscation in POMDPs](https://mlsanity.com/paper/2108.10227/) (2021)
- [Differential Privacy for Symbolic Systems with Application to Markov Chains](https://mlsanity.com/paper/2202.03325/) (2022)
- [Minimizing the Information Leakage Regarding High-Level Task Specifications](https://mlsanity.com/paper/1911.09889/) (2019)
- [Towards Differential Privacy for Symbolic Systems](https://mlsanity.com/paper/1809.08634/) (2018)

## Abstract (arXiv)

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.