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An Efficient Closed-Form Solution to Full Visual-Inertial State Initialization

Samuel Cerezo, Seong Hun Lee, Javier Civera

TL;DR

This work addresses robust and fast initialization of the full visual–inertial state for SLAM without resorting to nonlinear optimization. It introduces a closed-form solution built on small-rotation and constant-velocity approximations, ensuring a compact, analytically tractable formulation that preserves motion–IMU coupling. A two-stage observability test guides when to finalize the initialization, balancing accuracy and latency. On EuRoC data, the method yields 10–20% lower initialization error than baselines while reducing initialization window by about 4× and computation time by around 5×, demonstrating practical impact for resource-constrained platforms.

Abstract

In this letter, we present a closed-form initialization method that recovers the full visual-inertial state without nonlinear optimization. Unlike previous approaches that rely on iterative solvers, our formulation yields analytical, easy-to-implement, and numerically stable solutions for reliable start-up. Our method builds on small-rotation and constant-velocity approximations, which keep the formulation compact while preserving the essential coupling between motion and inertial measurements. We further propose an observability-driven, two-stage initialization scheme that balances accuracy with initialization latency. Extensive experiments on the EuRoC dataset validate our assumptions: our method achieves 10-20% lower initialization error than optimization-based approaches, while using 4x shorter initialization windows and reducing computational cost by 5x.

An Efficient Closed-Form Solution to Full Visual-Inertial State Initialization

TL;DR

This work addresses robust and fast initialization of the full visual–inertial state for SLAM without resorting to nonlinear optimization. It introduces a closed-form solution built on small-rotation and constant-velocity approximations, ensuring a compact, analytically tractable formulation that preserves motion–IMU coupling. A two-stage observability test guides when to finalize the initialization, balancing accuracy and latency. On EuRoC data, the method yields 10–20% lower initialization error than baselines while reducing initialization window by about 4× and computation time by around 5×, demonstrating practical impact for resource-constrained platforms.

Abstract

In this letter, we present a closed-form initialization method that recovers the full visual-inertial state without nonlinear optimization. Unlike previous approaches that rely on iterative solvers, our formulation yields analytical, easy-to-implement, and numerically stable solutions for reliable start-up. Our method builds on small-rotation and constant-velocity approximations, which keep the formulation compact while preserving the essential coupling between motion and inertial measurements. We further propose an observability-driven, two-stage initialization scheme that balances accuracy with initialization latency. Extensive experiments on the EuRoC dataset validate our assumptions: our method achieves 10-20% lower initialization error than optimization-based approaches, while using 4x shorter initialization windows and reducing computational cost by 5x.

Paper Structure

This paper contains 12 sections, 24 equations, 2 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Notation and Preliminaries
  4. Rotation and Gyro Bias Initialization
  5. Initial Velocity, Translation, Gravity and Accelerometer Bias
  6. Closed-form initialization from linear point constraints
  7. Two–stages Observability Test
  8. Experiments
  9. Experimental Setup
  10. Closed-form gyroscope bias
  11. Full state Initialization
  12. Conclusions

Figures (2)

  • Figure 1: Relative computational costs of our observability tests. Note the significantly higher cost of the full observability test, which motivates our proposal of a first stage assessing translational observability.
  • Figure 2: Initialization accuracy vs. activation policy. We trigger closed-form initialization at three instants: (i) after a fixed 25-frame window ($\approx1.25\,\mathrm{s}$); (ii) when the first observability criteria (Translation Observability Test) is satisfied; and (iii) the second observability criteria (Full Observability Test) is satisfied. Panels report RMSE distributions in (a) gravity direction, (b) velocity, and (c) accelerometer bias. The Translation Observability Test already improves initialization accuracy, while the Full Observability Test yields the best overall performance.