# Probabilistic Parameter Estimators and Calibration Metrics for Pose Estimation from Image Features

arXiv: https://arxiv.org/abs/2407.16223 · HTML: https://mlsanity.com/paper/2407.16223/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 13 of 13)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [A Holistic Assessment of the Reliability of Machine Learning Systems](https://mlsanity.com/paper/2307.10586/) (2023)
- [Towards a Framework for Deep Learning Certification in Safety-Critical Applications Using Inherently Safe Design and Run-Time Error Detection](https://mlsanity.com/paper/2403.14678/) (2024)

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

- [LARD 2.0: Enhanced Datasets and Benchmarking for Autonomous Landing Systems](https://mlsanity.com/paper/2603.26748/) (2026)
- [Predictive Uncertainty for Runtime Assurance of a Real-Time Computer Vision-Based Landing System](https://mlsanity.com/paper/2508.09732/) (2025)
- [From Keypoints to Predictive Distributions: Post-Hoc Uncertainty for YOLO-Pose Models](https://mlsanity.com/paper/2607.26921/) (2026)
- [Protection Levels for Vision-Based Pose Estimation](https://mlsanity.com/paper/2608.10023/) (2026)
- [Robust Validation to Geometric Perturbations for Autonomous Pose Estimation](https://mlsanity.com/paper/2608.21066/) (2026)

## Abstract (arXiv)

This paper addresses the challenge of probabilistic parameter estimation given measurement uncertainty in real-time. We provide a general formulation and apply this to pose estimation for an autonomous visual landing system. We present three probabilistic parameter estimators: a least-squares sampling approach, a linear approximation method, and a probabilistic programming estimator. To evaluate these estimators, we introduce novel closed-form expressions for measuring calibration and sharpness specifically for multivariate normal distributions. Our experimental study compares the three estimators under various noise conditions. We demonstrate that the linear approximation estimator can produce sharp and well-calibrated pose predictions significantly faster than the other methods but may yield overconfident predictions in certain scenarios. Additionally, we demonstrate that these estimators can be integrated with a Kalman filter for continuous pose estimation during a runway approach where we observe a 50% improvement in sharpness while maintaining marginal calibration. This work contributes to the integration of data-driven computer vision models into complex safety-critical aircraft systems and provides a foundation for developing rigorous certification guidelines for such systems.