Resampling-free Particle Filters in High-dimensions

TL;DR

This work introduces a resampling-free particle filter that uses density-tracking flows to maintain particle diversity in high-dimensional state spaces. By deriving a velocity field from the continuity equation and a Laplacian-inversion kernel, the method updates particles with a combination of gradient-descent and attraction-repulsion forces, guaranteeing convergence to the posterior in a deterministic, dimension-robust manner. The approach is validated on a high-dimensional synthetic localization task and a 6D pose estimation task, where it outperforms standard Monte Carlo Localization and gradient-descent baselines, respectively, demonstrating superior accuracy and scalability. The results suggest that high-dimensional robotic systems can benefit from flow-based, resampling-free filters as DOFs grow, enabling more reliable state estimation in complex environments.

Abstract

State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in high-dimensional state spaces, these filters face challenges such as 'particle deprivation' which hinders accurate representation of the true posterior distribution. This paper introduces a novel resampling-free particle filter designed to mitigate particle deprivation by forgoing the traditional resampling step. This ensures a broader and more diverse particle set, especially vital in high-dimensional scenarios. Theoretically, our proposed filter is shown to offer a near-accurate representation of the desired posterior distribution in high-dimensional contexts. Empirically, the effectiveness of our approach is underscored through a high-dimensional synthetic state estimation task and a 6D pose estimation derived from videos. We posit that as robotic systems evolve with greater degrees of freedom, particle filters tailored for high-dimensional state spaces will be indispensable.

Figures (3)

• Figure 1: Example of the particle updates computed by our particle filter. Black lines indicate lines of constant likelihood $P_t$, the black arrow indicates increasing likelihood, red dots indicate particles. Sample update directions are indicated at four points: orange arrows indicate the gradient descent on the negative log-likelihood, and blue arrows indicate the attraction-repulsion force.
• Figure 2: Comparison of the performance (measured as KL divergence with the true posterior distribution) of our particle filter with standard Monte Carlo Localization (MCL) on a synthetic localization problem with adjustable dimensionality. $n$ denotes the number of particles. Margins indicate standard errors over $10$ trials. [Left] Performance over the course of particle filter iterations on a $10$-dimensional problem. [Right] Performance at the final iteration over varying dimensions.
• Figure 3: Performance Analysis of 6D Pose Estimation Methods on the "Cracker Box" Model: This figure presents a comparative analysis of the translation and rotation mean error between our proposed method and the conventional gradient descent approach. The evaluation is based on 1912 RGB video sequences of the "cracker box" model. Both methods were tested under identical configurations, using 80 particles. The mean error is computed over the $x, y, z$ coordinates and averaged for both translation and rotation. Specifically, the translation error measures the deviation in centimeters from the ground truth translation, while the (signed) rotation error quantifies the angular difference in degrees from the true rotation. Note that the rotation error can be positive or negative, with the optimal value being $0$.

Theorems & Definitions (2)

• Theorem 1
• proof