# Estimating Uncertain Spatial Relationships in Robotics

arXiv: https://arxiv.org/abs/1304.3111 · HTML: https://mlsanity.com/paper/1304.3111/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2013.

## Built on by (most cited first, 14 of 14)

- [SAM 3D: 3Dfy Anything in Images](https://mlsanity.com/paper/2511.16624/) (2025)
- [Multiview Compressive Coding for 3D Reconstruction](https://mlsanity.com/paper/2301.08247/) (2023)
- [Is Mapping Necessary for Realistic PointGoal Navigation?](https://mlsanity.com/paper/2206.00997/) (2022)
- [Emergence of Maps in the Memories of Blind Navigation Agents](https://mlsanity.com/paper/2301.13261/) (2023)
- [Beyond Robustness: A Taxonomy of Approaches towards Resilient Multi-Robot Systems](https://mlsanity.com/paper/2109.12343/) (2021)
- [Edge Robotics: Edge-Computing-Accelerated Multi-Robot Simultaneous Localization and Mapping](https://mlsanity.com/paper/2112.13222/) (2021)
- [Predictive World Models from Real-World Partial Observations](https://mlsanity.com/paper/2301.04783/) (2023)
- [SM3D: Simultaneous Monocular Mapping and 3D Detection](https://mlsanity.com/paper/2111.12643/) (2021)
- [Composition of Memory Experts for Diffusion World Models](https://mlsanity.com/paper/2605.18813/) (2026)
- [Real-Time Simultaneous Localization and Mapping with LiDAR intensity](https://mlsanity.com/paper/2301.09257/) (2023)
- [Localization of Autonomous Vehicles: Proof of Concept for A Computer Vision Approach](https://mlsanity.com/paper/2104.02785/) (2021)
- [Multi-Robot Relative Pose Estimation in SE(2) with Observability Analysis: A Comparison of Extended Kalman Filtering and Robust Pose Graph Optimization](https://mlsanity.com/paper/2401.15313/) (2024)
- [MR-SLAM: Immersive Spatial Supervision for Multi-Robot Mapping via Mixed Reality](https://mlsanity.com/paper/2605.16432/) (2026)
- [SLAM in Low-Light Environments: Project Report](https://mlsanity.com/paper/2607.17699/) (2026)

## Abstract (arXiv)

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map contains the estimates of relationships among objects in the map, and their uncertainties, given all the available information. The procedures provide a general solution to the problem of estimating uncertain relative spatial relationships. The estimates are probabilistic in nature, an advance over the previous, very conservative, worst-case approaches to the problem. Finally, the procedures are developed in the context of state-estimation and filtering theory, which provides a solid basis for numerous extensions.