# Multi-Agent Pose Uncertainty: A Differentiable Rendering Cram'er-Rao Bound

arXiv: https://arxiv.org/abs/2510.21785 · HTML: https://mlsanity.com/paper/2510.21785/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 18 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [Direct Sparse Odometry](https://mlsanity.com/paper/1607.02565/) (2016)
- [INeRF: Inverting Neural Radiance Fields for Pose Estimation](https://mlsanity.com/paper/2012.05877/) (2020)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [Kimera-Multi: Robust, Distributed, Dense Metric-Semantic SLAM for Multi-Robot Systems](https://mlsanity.com/paper/2106.14386/) (2021)
- [Photometric Bundle Adjustment for Vision-Based SLAM](https://mlsanity.com/paper/1608.02026/) (2016)
- [COVINS: Visual-Inertial SLAM for Centralized Collaboration](https://mlsanity.com/paper/2108.05756/) (2021)

## Abstract (arXiv)

Pose estimation is essential for many applications within computer vision and robotics. Despite its uses, few works provide rigorous uncertainty quantification for poses under dense or learned models. We derive a closed-form lower bound on the covariance of camera pose estimates by treating a differentiable renderer as a measurement function. Linearizing image formation with respect to a small pose perturbation on the manifold yields a render-aware Cram'er-Rao bound. Our approach reduces to classical bundle-adjustment uncertainty, ensuring continuity with vision theory. It also naturally extends to multi-agent settings by fusing Fisher information across cameras. Our statistical formulation has downstream applications for tasks such as cooperative perception and novel view synthesis without requiring explicit keypoint correspondences.