# Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion

arXiv: https://arxiv.org/abs/1809.03554 · HTML: https://mlsanity.com/paper/1809.03554/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2018.

## Built on by (most cited first, 6 of 6)

- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [Advances in Inference and Representation for Simultaneous Localization and Mapping](https://mlsanity.com/paper/2103.05041/) (2021)
- [On the Tightness of Semidefinite Relaxations for Rotation Estimation](https://mlsanity.com/paper/2101.02099/) (2021)
- [Fast and Robust Certifiable Estimation of the Relative Pose Between Two Calibrated Cameras](https://mlsanity.com/paper/2101.08524/) (2021)
- [Globally Optimal Multi-Scale Monocular Hand-Eye Calibration Using Dual Quaternions](https://mlsanity.com/paper/2201.04473/) (2022)
- [Towards Understanding The Semidefinite Relaxations of Truncated Least-Squares in Robust Rotation Search](https://mlsanity.com/paper/2207.08350/) (2022)

## Abstract (arXiv)

We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. This problem has been previously solved using a variety of techniques, including local optimization approaches that have no formal global optimality guarantees. We use a quadratic objective function to formulate calibration as a quadratically constrained quadratic program (QCQP). By leveraging recent advances in the optimization of QCQPs, we are able to use existing semidefinite program (SDP) solvers to obtain a certifiably global optimum via the Lagrangian dual problem. Our problem formulation can be globally optimized by existing general-purpose solvers in less than a second, regardless of the number of measurements available and the noise level. This enables a variety of robotic platforms to rapidly and robustly compute and certify a globally optimal set of calibration parameters without a prior estimate or operator intervention. We compare the performance of our approach with a local solver on extensive simulations and multiple real datasets. Finally, we present necessary observability conditions that connect our approach to recent theoretical results and analytically support the empirical performance of our system.