Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Spatiotemporal Calibration of Doppler Velocity Logs for Underwater Robots

Hongxu Zhao, Guangyang Zeng, Yunling Shao, Tengfei Zhang, Junfeng Wu

TL;DR

This work tackles joint spatiotemporal calibration for underwater sensing by formulating DVL extrinsics, clock offsets, and velocity scale as a MAP problem with a GP motion prior. The Unified Iterative Calibration (UIC) method alternates GP-based motion updates with gradient-based calibration refinements, supported by a sequential initialization that provides statistically consistent estimates. Theoretical and empirical analyses show consistency of clock and extrinsics estimators and reveal the importance of angular-velocity excitation for observability, with real-world pool experiments demonstrating competitive performance against baselines. The approach enables general multi-sensor fusion in underwater navigation and offers open-source tooling for broader adoption.

Abstract

The calibration of extrinsic parameters and clock offsets between sensors for high-accuracy performance in underwater SLAM systems remains insufficiently explored. Existing methods for Doppler Velocity Log (DVL) calibration are either constrained to specific sensor configurations or rely on oversimplified assumptions, and none jointly estimate translational extrinsics and time offsets. We propose a Unified Iterative Calibration (UIC) framework for general DVL sensor setups, formulated as a Maximum A Posteriori (MAP) estimation with a Gaussian Process (GP) motion prior for high-fidelity motion interpolation. UIC alternates between efficient GP-based motion state updates and gradient-based calibration variable updates, supported by a provably statistically consistent sequential initialization scheme. The proposed UIC can be applied to IMU, cameras and other modalities as co-sensors. We release an open-source DVL-camera calibration toolbox. Beyond underwater applications, several aspects of UIC-such as the integration of GP priors for MAP-based calibration and the design of provably reliable initialization procedures-are broadly applicable to other multi-sensor calibration problems. Finally, simulations and real-world tests validate our approach.

Spatiotemporal Calibration of Doppler Velocity Logs for Underwater Robots

TL;DR

This work tackles joint spatiotemporal calibration for underwater sensing by formulating DVL extrinsics, clock offsets, and velocity scale as a MAP problem with a GP motion prior. The Unified Iterative Calibration (UIC) method alternates GP-based motion updates with gradient-based calibration refinements, supported by a sequential initialization that provides statistically consistent estimates. Theoretical and empirical analyses show consistency of clock and extrinsics estimators and reveal the importance of angular-velocity excitation for observability, with real-world pool experiments demonstrating competitive performance against baselines. The approach enables general multi-sensor fusion in underwater navigation and offers open-source tooling for broader adoption.

Abstract

The calibration of extrinsic parameters and clock offsets between sensors for high-accuracy performance in underwater SLAM systems remains insufficiently explored. Existing methods for Doppler Velocity Log (DVL) calibration are either constrained to specific sensor configurations or rely on oversimplified assumptions, and none jointly estimate translational extrinsics and time offsets. We propose a Unified Iterative Calibration (UIC) framework for general DVL sensor setups, formulated as a Maximum A Posteriori (MAP) estimation with a Gaussian Process (GP) motion prior for high-fidelity motion interpolation. UIC alternates between efficient GP-based motion state updates and gradient-based calibration variable updates, supported by a provably statistically consistent sequential initialization scheme. The proposed UIC can be applied to IMU, cameras and other modalities as co-sensors. We release an open-source DVL-camera calibration toolbox. Beyond underwater applications, several aspects of UIC-such as the integration of GP priors for MAP-based calibration and the design of provably reliable initialization procedures-are broadly applicable to other multi-sensor calibration problems. Finally, simulations and real-world tests validate our approach.

Paper Structure

This paper contains 17 sections, 2 theorems, 26 equations, 6 figures, 1 table, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. Problem formulation
  4. DVL Measurement Model
  5. Unified Spatiotemporal Calibration Problem under GP Motion Prior
  6. METHODOLOGY
  7. Sequential Initialization Strategy
  8. Initialization of Motion State X
  9. Initialization of Calibration Variables
  10. Consistent clock offset estimator
  11. Consistent extrinsics estimator
  12. The Whole Algorithm
  13. NUMERICAL ANALYSIS
  14. Effect of bias elimination
  15. Performance under different excitation conditions
  16. ...and 2 more sections

Key Result

Theorem 1

${}^{b}\hat{\delta}_{T,d}$ and $\hat{\kappa}_d$ are $\sqrt{N}$-consistent estimates of ${}^{b}\delta_{T,d}^o$ and $\kappa_d^o$.

Figures (6)

  • Figure 1: DVL frame (blue) to base frame (stereo camera + IMU, orange) extrinsics.
  • Figure 2: Simulation results: (a) validates of the effect of bias elimination, (b) and (c) show the performances of two methods, BCD with a good initial value and the UIC initialization method, under large and small angular velocity excitations.
  • Figure 3: Water pool experiments. Left: Underwater robot; bottom right: AprilTag board; upper right: robot trajectory.
  • Figure 4: Trajectory A estimation using the parameters calibrated from trajectory B.
  • Figure 5: Performance of different methods with respect to the measurement number.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Remark 1