Dynamic Correction of Erroneous State Estimates via Diffusion Bayesian Exploration

TL;DR

The paper identifies S-PSI as a baseline-induced barrier in bootstrap particle filters that prevents corrections to severely misaligned initial state estimates. It introduces DEPF, a diffusion-enhanced PF framework that injects exploratory particles, applies entropy-aware diffusion guided by posterior covariance, and validates proposals with Metropolis–Hastings to expand the belief support only when contradicted by data. The approach yields theoretical guarantees and empirically superior performance in hazardous-gas localization tasks, outperforming RL-based and classical PF perturbation baselines, especially under severe prior misalignment. The results support DEPF as a robust inference module for real-time emergency management, enabling principled, data-driven corrections to early state estimates while preserving statistical rigor. Overall, DEPF offers a practical, generalizable mechanism to overcome prior misalignment in sequential Bayesian inference for high-stakes sensing and planning tasks.

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.

Figures (6)

• Figure 1: Flowchart of DEPF.
• Figure 2: Experimental Scenarios for Policy Errors in Emergency Response.
• Figure 3: Visualization of Policy Error Scenarios in Emergency Response.
• Figure 4: Impact of the number of particles and $\delta$ on DEPF performance under Severe Error.
• Figure 5: Gaussian Plume Model Visualization.

Theorems & Definitions (14)

• Proposition 3.2: S-PSI under \ref{['assump:S0']}
• Proposition B.1: S-PSI under the stationary bootstrap baseline
• proof
• Proposition D.1: Expansion of Support Range Beyond S-PSI
• proof
• Definition M.1: S-PSI: Stationarity–Induced Posterior Support Invariance
• Proposition M.2: S-PSI under the stationary bootstrap baseline
• Theorem M.3: DEPF resolves S-PSI
• Corollary M.4: Finite-step support–recovery bound
• Definition N.2: Stationarity-Induced Posterior Support Invariance (S-PSI)