[Paper Review] Stein particle filtering

Jiaojiao Fan, Amirhossein Taghvaei+1 more|arXiv (Cornell University)|Jun 19, 2021

Target Tracking and Data Fusion in Sensor Networks23 references4 citations

TL;DR

This paper proposes a novel particle filtering framework based on Stein variational gradient descent (SVGD) that eliminates particle degeneracy by updating only particle locations, not weights, ensuring all particles remain uniformly weighted. The method achieves superior performance over standard particle filters in nonlinear and high-dimensional problems, with improved robustness via a sliding window extension that reuses measurements for enhanced stability.

ABSTRACT

We present a new particle filtering algorithm for nonlinear systems in the discrete-time setting. Our algorithm is based on the Stein variational gradient descent (SVGD) framework, which is a general approach to sample from a target distribution. We merge the standard two-step paradigm in particle filtering into one step so that SVGD can be used. A distinguishing feature of the proposed algorithm is that, unlike most particle filtering methods, all the particles at any time step are equally weighted and thus no update on the weights is needed. We further extended our algorithm to allow for updating previous particles within a sliding window. This strategy may improve the reliability of the algorithm with respect to unexpected disturbance in the dynamics or outlier-measurements. The efficacy of the proposed algorithms is illustrated through several numerical examples in comparison with a standard particle filtering method.

Motivation & Objective

• To address particle degeneracy in traditional particle filters, where most particles lose weight over time.
• To develop a particle filtering method that maintains uniformly weighted particles throughout iterations, preserving effective sample size.
• To leverage the Stein variational gradient descent (SVGD) framework for deterministic, non-Markovian sampling from posterior distributions.
• To improve robustness against model disturbances and outlier measurements through a sliding window mechanism that reuses observations.
• To demonstrate superior performance in nonlinear and high-dimensional filtering scenarios compared to standard particle filters.

Proposed method

• The algorithm replaces the standard two-step particle filtering process (importance sampling + resampling) with a single-step SVGD update that directly evolves particle locations to approximate the posterior.
• It uses the posterior distribution up to a normalization constant, derived from current particles and the next observation, as the target for SVGD.
• All particles are updated simultaneously via SVGD's kernel-based gradient flow, ensuring uniform weights and avoiding resampling.
• A sliding window extension is introduced, where posterior approximation is performed over a fixed window of time steps, allowing each measurement to contribute to multiple posterior updates.
• The sliding window version improves robustness by distributing the influence of each measurement across multiple time steps, reducing sensitivity to outliers or errors.
• The method is implemented iteratively, with particle locations updated at each time step using SVGD's update rule based on the score function of the unnormalized posterior.

Experimental results

Research questions

• RQ1 Can a particle filtering framework be designed to avoid particle degeneracy by eliminating the need for weight updates?
• RQ2 How does the performance of a Stein-based particle filter compare to standard particle filters like SIR in nonlinear and high-dimensional systems?
• RQ3 Does using a sliding window to recompute posteriors over multiple time steps improve robustness to measurement noise or model errors?
• RQ4 What is the impact of window size on the accuracy and computational cost of the filtering algorithm?
• RQ5 In what regimes (e.g., high state noise, low measurement noise) does the proposed method outperform traditional particle filters?

Key findings

• The proposed Stein particle filtering method achieves lower mean squared error (m.s.e.) in posterior mean and covariance estimation compared to the SIR particle filter in both linear Gaussian and Benes filtering examples.
• In the linear Gaussian case, the method with a window size of T=1 showed slightly better accuracy than T=3, likely due to lower dimensionality of the particle space.
• In the Benes filtering problem, the sliding window version with T=3 outperformed both the T=1 version and the SIR filter, demonstrating the benefit of reusing observations over time.
• The sliding window approach improved robustness to disturbances and outliers by distributing measurement influence across multiple time steps.
• The method is more computationally expensive than SIR due to iterative SVGD updates, but offers better performance in high-noise dynamics and low-noise measurement regimes.
• Empirically, the method performs best when state dynamics are highly random and measurement noise is relatively low—conditions that challenge most standard particle filters.