Dynamic Correction of Erroneous State Estimates via Diffusion Bayesian Exploration

2025-12-01

AI Summary

In high-stakes emergency response, initial state estimation is often inaccurate due to scarce or biased information, severely constraining downstream decision-making. Conventional bootstrap particle filters suffer from static posterior support invariance (S-PSI): once a region is excluded from the prior, it remains permanently inaccessible, leading to irreversible state locking. This paper proposes a Diffusion Bayesian Exploration framework that—first in the literature—integrates entropy-regularized sampling with covariance-scaled diffusion dynamics, augmented by Metropolis–Hastings adaptive rejection sampling to dynamically break S-PSI. The method guarantees theoretically provable convergence and enables real-time belief correction. Experiments on real-world gas source localization show that, when the prior is accurate, our approach matches the performance of reinforcement learning (RL) and planning-based baselines; when the prior is erroneous, it significantly outperforms classical sequential Monte Carlo (SMC) perturbation and RL methods, and rigorously eliminates S-PSI.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

In emergency response and other high-stakes societal applications, early-stage state estimates critically shape downstream outcomes. Yet, these initial state estimates-often based on limited or biased information-can be severely misaligned with reality, constraining subsequent actions and potentially causing catastrophic delays, resource misallocation, and human harm. Under the stationary bootstrap baseline (zero transition and no rejuvenation), bootstrap particle filters exhibit Stationarity-Induced Posterior Support Invariance (S-PSI), wherein regions excluded by the initial prior remain permanently unexplorable, making corrections impossible even when new evidence contradicts current beliefs. While classical perturbations can in principle break this lock-in, they operate in an always-on fashion and may be inefficient. To overcome this, we propose a diffusion-driven Bayesian exploration framework that enables principled, real-time correction of early state estimation errors. Our method expands posterior support via entropy-regularized sampling and covariance-scaled diffusion. A Metropolis-Hastings check validates proposals and keeps inference adaptive to unexpected evidence. Empirical evaluations on realistic hazardous-gas localization tasks show that our approach matches reinforcement learning and planning baselines when priors are correct. It substantially outperforms classical SMC perturbations and RL-based methods under misalignment, and we provide theoretical guarantees that DEPF resolves S-PSI while maintaining statistical rigor.

Problem

• Corrects early state estimation errors in high-stakes scenarios
• Overcomes Stationarity-Induced Posterior Support Invariance in particle filters
• Enables real-time adjustment of beliefs with new evidence

Innovation

• Diffusion-driven Bayesian exploration for error correction
• Entropy-regularized sampling with covariance-scaled diffusion
• Metropolis-Hastings validation for adaptive inference