# The Manifold Particle Filter for State Estimation on High-dimensional Implicit Manifolds

arXiv: https://arxiv.org/abs/1604.07224 · HTML: https://mlsanity.com/paper/1604.07224/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2016.

## Built on by (most cited first, 5 of 5)

- [Tac2Pose: Tactile Object Pose Estimation from the First Touch](https://mlsanity.com/paper/2204.11701/) (2022)
- [HyperTaxel: Hyper-Resolution for Taxel-Based Tactile Signals Through Contrastive Learning](https://mlsanity.com/paper/2408.08312/) (2024)
- [Fusing RGBD Tracking and Segmentation Tree Sampling for Multi-Hypothesis Volumetric Segmentation](https://mlsanity.com/paper/2104.00205/) (2021)
- [UniTac2Pose: A Unified Approach Learned in Simulation for Category-level Visuotactile In-hand Pose Estimation](https://mlsanity.com/paper/2509.15934/) (2025)
- [Denoising Particle Filters: Learning State Estimation with Single-Step Objectives](https://mlsanity.com/paper/2602.19651/) (2026)

## Abstract (arXiv)

We estimate the state a noisy robot arm and underactuated hand using an Implicit Manifold Particle Filter (MPF) informed by touch sensors. As the robot touches the world, its state space collapses to a contact manifold that we represent implicitly using a signed distance field. This allows us to extend the MPF to higher (six or more) dimensional state spaces. Earlier work (which explicitly represents the contact manifold) only shows the MPF in two or three dimensions. Through a series of experiments, we show that the implicit MPF converges faster and is more accurate than a conventional particle filter during periods of persistent contact. We present three methods of sampling the implicit contact manifold, and compare them in experiments.