Contractor Filters
Abstract
We introduce Contractor Filters (CFs), a set-membership architecture for nonlinear continuous-time state estimation with bounded uncertainties and sporadic outliers. CFs represent feasible states symbolically by compositions of contractors rather than rematerializing a geometric enclosure after each update. This provides an abstraction layer between the set-theoretic filtering equations and their numerical realization, so prediction, correction, ambiguity, and outlier handling can be expressed within one algebra without prescribing a state geometry. We derive an exact nominal recursion and a guaranteed robust enclosure, with validated flow inclusions preserving soundness. Optional sub-paving compression then provides finite outer representations. CFs are evaluated against a robust particle filter on range-only and terrain-based localization under outliers, probabilistic model mismatch, association ambiguity, and multimodality. CFs retain the simulated truth in all tested configurations, while particle-filter reliability degrades under persistent bias and spatial aliasing. Contractor strength and compression budget control the trade-off between paving tightness and computational cost, while preserving the enclosure guarantee.
Related
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BibTeX
@misc{rohou2026contractor,
title = {{Contractor Filters}},
author = {Simon Rohou},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18040},
eprint = {2610.18040},
archivePrefix = {arXiv},
url = {https://ensta.hal.science/hal-05795637v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Contractor Filters
AU - Simon Rohou
PY - 2026
DA - 2026/10/12
PB - HAL
DO - 10.48550/arxiv.2610.18040
UR - https://ensta.hal.science/hal-05795637v1
AB - We introduce Contractor Filters (CFs), a set-membership architecture for nonlinear continuous-time state estimation with bounded uncertainties and sporadic outliers. CFs represent feasible states symbolically by compositions of contractors rather than rematerializing a geometric enclosure after each update. This provides an abstraction layer between the set-theoretic filtering equations and their numerical realization, so prediction, correction, ambiguity, and outlier handling can be expressed within one algebra without prescribing a state geometry. We derive an exact nominal recursion and a guaranteed robust enclosure, with validated flow inclusions preserving soundness. Optional sub-paving compression then provides finite outer representations. CFs are evaluated against a robust particle filter on range-only and terrain-based localization under outliers, probabilistic model mismatch, association ambiguity, and multimodality. CFs retain the simulated truth in all tested configurations, while particle-filter reliability degrades under persistent bias and spatial aliasing. Contractor strength and compression budget control the trade-off between paving tightness and computational cost, while preserving the enclosure guarantee.
ER -