Multi-model Stochastic Particle-based Variational Bayesian Inference for Multiband Delay Estimation

TL;DR

This paper introduces a multi-model stochastic particle-based variational Bayesian inference framework that improves multiband delay estimation accuracy, especially under challenging conditions like low SNR and closely spaced delay paths.

Contribution

The proposed MM-SPVBI method jointly addresses model selection and parameter estimation using multiple high-dimensional models with an auto-focusing sampling strategy.

Findings

Outperforms existing delay estimation methods in simulations.

Effectively handles low SNR and closely spaced delay paths.

Reduces complexity with hybrid posterior approximation.

Abstract

Joint utilization of multiple discrete frequency bands can enhance the accuracy of delay estimation. Although some unique challenges of multiband fusion, such as phase distortion, oscillation phenomena, and high-dimensional search, have been partially addressed, further challenges remain. Specifically, under conditions of low signal-to-noise ratio (SNR), insufficient data, and closely spaced delay paths, accurately determining the model order-the number of delay paths-becomes difficult. Misestimating the model order can significantly degrade the estimation performance of traditional methods. To address joint model selection and parameter estimation under such harsh conditions, we propose a multi-model stochastic particle-based variational Bayesian inference (MM-SPVBI) framework, capable of exploring multiple high-dimensional parameter spaces. Initially, we split potential overlapping primary delay paths based on coarse estimates, generating several parallel candidate models. Then, an auto-focusing sampling strategy is employed to quickly identify the optimal model. Additionally, we introduce a hybrid posterior approximation to improve the original single-model SPVBI, ensuring overall complexity does not increase significantly with parallelism. Simulations demonstrate that our algorithm offers substantial advantages over existing methods.